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KANT'S THEORY OF KNOWLEDGE

by

H. A. PRICHARD

Fellow of Trinity College, Oxford







Oxford
At the Clarendon Press
1909

Henry Frowde, M.A.
Publisher to the University of Oxford
London, Edinburgh, New York
Toronto and Melbourne




PREFACE


This book is an attempt to think out the nature and tenability of
Kant's Transcendental Idealism, an attempt animated by the conviction
that even the elucidation of Kant's meaning, apart from any criticism,
is impossible without a discussion on their own merits of the main
issues which he raises.

My obligations are many and great: to Caird's _Critical Philosophy of
Kant_ and to the translations of Meiklejohn, Max Müller, and Professor
Mahaffy; to Mr. J. A. Smith, Fellow of Balliol College, and to Mr. H.
W. B. Joseph, Fellow of New College, for what I have learned from them
in discussion; to Mr. A. J. Jenkinson, Fellow of Brasenose College,
for reading and commenting on the first half of the MS.; to Mr. H. H.
Joachim, Fellow of Merton College, for making many important
suggestions, especially with regard to matters of translation; to Mr.
Joseph, for reading the whole of the proofs and for making many
valuable corrections; and, above all, to my wife for constant and
unfailing help throughout, and to Professor Cook Wilson, to have been
whose pupil I count the greatest of philosophical good fortunes. Some
years ago it was my privilege to be a member of a class with which
Professor Cook Wilson read a portion of Kant's _Critique of Pure
Reason_, and subsequently I have had the advantage of discussing with
him several of the more important passages. I am especially indebted
to him in my discussion of the following topics: the distinction
between the Sensibility and the Understanding (pp. 27-31, 146-9,
162-6), the term 'form of perception' (pp. 37, 40, 133 fin.-135), the
_Metaphysical Exposition of Space_ (pp. 41-8), Inner Sense (Ch. V,
and pp. 138-9), the _Metaphysical Deduction of the Categories_ (pp.
149-53), Kant's account of 'the reference of representations to an
object' (pp. 178-86), an implication of perspective (p. 90), the
impossibility of a 'theory' of knowledge (p. 245), and the points
considered, pp. 200 med.-202 med., 214 med.-215 med., and 218. The
views expressed in the pages referred to originated from Professor
Cook Wilson, though it must not be assumed that he would accept them
in the form in which they are there stated.




CONTENTS


  CHAPTER I                                                     PAGE
  THE PROBLEM OF THE _Critique_                                    1

  CHAPTER II
  THE SENSIBILITY AND THE UNDERSTANDING                           27

  CHAPTER III
  SPACE                                                           36

  CHAPTER IV
  PHENOMENA AND THINGS IN THEMSELVES                              71

  NOTE
  THE FIRST ANTINOMY                                             101

  CHAPTER V
  TIME AND INNER SENSE                                           103

  CHAPTER VI
  KNOWLEDGE AND REALITY                                          115

  CHAPTER VII
  THE METAPHYSICAL DEDUCTION OF THE CATEGORIES                   140

  CHAPTER VIII
  THE TRANSCENDENTAL DEDUCTION OF THE CATEGORIES                 161

  CHAPTER IX
  GENERAL CRITICISM OF THE TRANSCENDENTAL DEDUCTION OF THE
  CATEGORIES                                                     214

  CHAPTER X
  THE SCHEMATISM OF THE CATEGORIES                               246

  CHAPTER XI
  THE MATHEMATICAL PRINCIPLES                                    260

  CHAPTER XII
  THE ANALOGIES OF EXPERIENCE                                    268

  CHAPTER XIII
  THE POSTULATES OF EMPIRICAL THOUGHT                            308

  NOTE
  THE REFUTATION OF IDEALISM                                     319




REFERENCES


  A     = First edition of the _Critique of Pure Reason_.
  B     = Second edition of the _Critique of Pure Reason_.
  Prol. = Kant's _Prolegomena to any future Metaphysic_.
  M     = Meiklejohn's Translation of the _Critique of Pure Reason_.
  Mah.  = Mahaffy. Translation of Kant's _Prolegomena to any future
          Metaphysic_. (The pages referred to are those of the first
          edition; these are also to be found in the text of the
          second edition.)
  Caird = Caird's _Critical Philosophy of Kant_.




CHAPTER I

THE PROBLEM OF THE _CRITIQUE_


The problem of the _Critique_ may be stated in outline and
approximately in Kant's own words as follows.

Human reason is called upon to consider certain questions, which it
cannot decline, as they are presented by its own nature, but which it
cannot answer. These questions relate to God, freedom of the will, and
immortality. And the name for the subject which has to deal with these
questions is metaphysics. At one time metaphysics was regarded as the
queen of all the sciences, and the importance of its aim justified the
title. At first the subject, propounding as it did a dogmatic system,
exercised a despotic sway. But its subsequent failure brought it into
disrepute. It has constantly been compelled to retrace its steps;
there has been fundamental disagreement among philosophers, and no
philosopher has successfully refuted his critics. Consequently the
current attitude to the subject is one of weariness and indifference.
Yet humanity cannot really be indifferent to such problems; even those
who profess indifference inevitably make metaphysical assertions; and
the current attitude is a sign not of levity but of a refusal to put
up with the illusory knowledge offered by contemporary philosophy. Now
the objects of metaphysics, God, freedom, and immortality, are not
objects of experience in the sense in which a tree or a stone is an
object of experience. Hence our views about them cannot be due to
experience; they must somehow be apprehended by pure reason, i. e. by
thinking and without appeal to experience. Moreover, it is in fact by
thinking that men have always tried to solve the problems concerning
God, freedom, and immortality. What, then, is the cause of the
unsatisfactory treatment of these problems and men's consequent
indifference? It must, in some way, lie in a failure to attain the
sure scientific method, and really consists in the neglect of an
inquiry which should be a preliminary to all others in metaphysics.
Men ought to have begun with a critical investigation of pure reason
itself. Reason should have examined its own nature, to ascertain in
general the extent to which it is capable of attaining knowledge
without the aid of experience. This examination will decide whether
reason is able to deal with the problems of God, freedom, and
immortality at all; and without it no discussion of these problems
will have a solid foundation. It is this preliminary investigation
which the _Critique of Pure Reason_ proposes to undertake. Its aim is
to answer the question, 'How far can reason go, without the material
presented and the aid furnished by experience?' and the result
furnishes the solution, or at least the key to the solution, of all
metaphysical problems.

Kant's problem, then, is similar to Locke's. Locke states[1] that his
purpose is to inquire into the original, certainty, and extent of
human knowledge; and he says, "If, by this inquiry into the nature of
the understanding I can discover the powers thereof; how far they
reach, to what things they are in any degree proportionate, and where
they fail us; I suppose it may be of use to prevail with the busy mind
of man, to be more cautious in meddling with things exceeding its
comprehension; to stop when it is at the utmost extent of its tether;
and to sit down in a quiet ignorance of those things, which, upon
examination, are found to be beyond the reach of our capacities."
Thus, to use Dr. Caird's analogy,[2] the task which both Locke and
Kant set themselves resembled that of investigating a telescope,
before turning it upon the stars, to determine its competence for the
work.

    [1] Locke's _Essay_, i, 1, §§ 2, 4.

    [2] Caird, i, 10.

The above outline of Kant's problem is of course only an outline. Its
definite formulation is expressed in the well-known question, 'How are
_a priori_ synthetic judgements possible?'[3] To determine the meaning
of this question it is necessary to begin with some consideration of
the terms '_a priori_' and 'synthetic'.

    [3] B. 19, M. 12.

While there is no difficulty in determining what Kant would have
recognized as an _a priori_ judgement, there is difficulty in
determining what he meant by calling such a judgement _a priori_. The
general account is given in the first two sections of the
Introduction. An _a priori_ judgement is introduced as something
opposed to an _a posteriori_ judgement, or a judgement which has its
source in experience. Instances of the latter would be 'This body is
heavy', and 'This body is hot'. The point of the word 'experience' is
that there is direct apprehension of some individual, e. g. an
individual body. To say that a judgement has its source in experience
is of course to imply a distinction between the judgement and
experience, and the word 'source' may be taken to mean that the
judgement depends for its validity upon the experience of the
individual thing to which the judgement relates. An _a priori_
judgement, then, as first described, is simply a judgement which is
not _a posteriori_. It is independent of all experience; in other
words, its validity does not depend on the experience of individual
things. It might be illustrated by the judgement that all three-sided
figures must have three angles. So far, then, no positive meaning has
been given to _a priori_.[4]

    [4] Kant is careful to exclude from the class of _a priori_
    judgements proper what may be called relatively _a priori_
    judgements, viz. judgements which, though not independent of
    all experience, are independent of experience of the facts to
    which they relate. "Thus one would say of a man who
    undermined the foundations of his house that he might have
    known _a priori_ that it would fall down, i. e. that he did
    not need to wait for the experience of its actual falling
    down. But still he could not know this wholly _a priori_, for
    he had first to learn through experience that bodies are
    heavy and consequently fall, if their supports are taken
    away." (B. 2, M. 2.)

Kant then proceeds, not as we should expect, to state the positive
meaning of _a priori_; but to give tests for what is _a priori_. Since
a test implies a distinction between itself and what is tested, it is
implied that the meaning of _a priori_ is already known.[5]

    [5] It may be noted that in this passage (Introduction, §§ 1
    and 2) Kant is inconsistent in his use of the term 'pure'.
    Pure knowledge is introduced as a species of _a priori_
    knowledge: "_A priori_ knowledge, if nothing empirical is
    mixed with it, is called pure". (B. 3, M. 2, 17.) And in
    accordance with this, the proposition 'every change has a
    cause' is said to be _a priori_ but impure, because the
    conception of change can only be derived from experience. Yet
    immediately afterwards, pure, being opposed in general to
    empirical, can only mean _a priori_. Again, in the phrase
    'pure _a priori_' (B. 4 fin., M. 3 med.), the context shows
    that 'pure' adds nothing to '_a priori_', and the proposition
    'every change must have a cause' is expressly given as an
    instance of pure _a priori_ knowledge. The inconsistency of
    this treatment of the causal rule is explained by the fact
    that in the former passage he is thinking of the conception
    of change as empirical, while in the latter he is thinking of
    the judgement as not empirical. At bottom in this passage
    'pure' simply means _a priori_.

The tests given are necessity and strict universality.[6] Since
judgements which are necessary and strictly universal cannot be based
on experience, their existence is said to indicate another source of
knowledge. And Kant gives as illustrations, (1) any proposition in
mathematics, and (2) the proposition 'Every change must have a cause'.

    [6] In reality, these tests come to the same thing, for
    necessity means the necessity of connexion between the
    subject and predicate of a judgement, and since empirical
    universality, to which strict universality is opposed, means
    numerical universality, as illustrated by the proposition
    'All bodies are heavy', the only meaning left for strict
    universality is that of a universality reached not through an
    enumeration of instances, but through the apprehension of a
    necessity of connexion.

So far Kant has said nothing which determines the positive meaning of
_a priori_. A clue is, however, to be found in two subsequent phrases.
He says that we may content ourselves with having established as a
fact the pure use of our faculty of knowledge.[7] And he adds that not
only in judgements, but even in conceptions, is an _a priori_ origin
manifest.[8] The second statement seems to make the _a priori_
character of a judgement consist in its origin. As this origin cannot
be experience, it must, as the first statement implies, lie in our
faculty of knowledge. Kant's point is that the existence of universal
and necessary judgements shows that we must possess a faculty of
knowledge capable of yielding knowledge without appeal to experience.
The term _a priori_, then, has some reference to the existence of this
faculty; in other words, it gives expression to a doctrine of 'innate
ideas'. Perhaps, however, it is hardly fair to press the phrase
'_test_ of _a priori_ judgements'. If so, it may be said that on the
whole, by _a priori_ judgements Kant really means judgements which are
universal and necessary, and that he regards them as implying a
faculty which gives us knowledge without appeal to experience.

    [7] B. 5, M. 4.

    [8] Ibid.

We may now turn to the term 'synthetic judgement'. Kant distinguishes
analytic and synthetic judgements thus. In any judgement the predicate
B either belongs to the subject A, as something contained (though
covertly) in the conception A, or lies completely outside the
conception A, although it stands in relation to it. In the former case
the judgement is called analytic, in the latter synthetic.[9] 'All
bodies are extended' is an analytic judgement; 'All bodies are heavy'
is synthetic. It immediately follows that only synthetic judgements
extend our knowledge; for in making an analytic judgement we are only
clearing up our conception of the subject. This process yields no new
knowledge, for it only gives us a clearer view of what we know
already. Further, all judgements based on experience are synthetic,
for it would be absurd to base an analytical judgement on experience,
when to make the judgement we need not go beyond our own conceptions.
On the other hand, _a priori_ judgements are sometimes analytic and
sometimes synthetic. For, besides analytical judgements, all
judgements in mathematics and certain judgements which underlie
physics are asserted independently of experience, and they are
synthetic.

    [9] B. 10, M. 7.

Here Kant is obviously right in vindicating the synthetic character of
mathematical judgements. In the arithmetical judgement 7 + 5 = 12, the
thought of certain units as a group of twelve is no mere repetition of
the thought of them as a group of five added to a group of seven.
Though the same units are referred to, they are regarded differently.
Thus the thought of them as twelve means either that we think of them
as formed by adding one unit to a group of eleven, or that we think of
them as formed by adding two units to a group of ten, and so on. And
the assertion is that the same units, which can be grouped in one way,
can also be grouped in another. Similarly, Kant is right in pointing
out that the geometrical judgement, 'A straight line between two
points is the shortest,' is synthetic, on the ground that the
conception of straightness is purely qualitative,[10] while the
conception of shortest distance implies the thought of quantity.

    [10] Straightness means identity of direction.

It should now be an easy matter to understand the problem expressed
by the question, 'How are _a priori_ synthetic judgements possible?'
Its substance may be stated thus. The existence of _a posteriori_
synthetic judgements presents no difficulty. For experience is
equivalent to perception, and, as we suppose, in perception we are
confronted with reality, and apprehend it as it is. If I am asked,
'How do I know that my pen is black or my chair hard?' I answer that
it is because I see or feel it to be so. In such cases, then, when my
assertion is challenged, I appeal to my experience or perception of
the reality to which the assertion relates. My appeal raises no
difficulty because it conforms to the universal belief that if
judgements are to rank as knowledge, they must be made to conform to
the nature of things, and that the conformity is established by appeal
to actual experience of the things. But do _a priori_ synthetic
judgements satisfy this condition? Apparently not. For when I assert
that every straight line is the shortest way between its extremities,
I have not had, and never can have, experience of all possible
straight lines. How then can I be sure that all cases will conform to
my judgement? In fact, how can I anticipate my experience at all? How
can I make an assertion about any individual until I have had actual
experience of it? In an _a priori_ synthetic judgement the mind in
some way, in virtue of its own powers and independently of experience,
makes an assertion to which it claims that reality must conform. Yet
why should reality conform? _A priori_ judgements of the other
kind, viz. analytic judgements, offer no difficulty, since they
are at bottom tautologies, and consequently denial of them is
self-contradictory and meaningless. But there is difficulty where a
judgement asserts that a term B is connected with another term A, B
being neither identical with nor a part of A. In this case there is no
contradiction in asserting that A is not B, and it would seem that
only experience can determine whether all A is or is not B. Otherwise
we are presupposing that things must conform to our ideas about them.
Now metaphysics claims to make _a priori_ synthetic judgements, for it
does not base its results on any appeal to experience. Hence, before
we enter upon metaphysics, we really ought to investigate our right to
make _a priori_ synthetic judgements at all. Therein, in fact, lies
the importance to metaphysics of the existence of such judgements in
mathematics and physics. For it shows that the difficulty is not
peculiar to metaphysics, but is a general one shared by other
subjects; and the existence of such judgements in mathematics is
specially important because there their validity or certainty has
never been questioned.[11] The success of mathematics shows that at any
rate under certain conditions _a priori_ synthetic judgements are
valid, and if we can determine these conditions, we shall be able to
decide whether such judgements are possible in metaphysics. In this
way we shall be able to settle a disputed case of their validity by
examination of an undisputed case. The general problem, however, is
simply to show what it is which makes _a priori_ synthetic judgements
as such possible; and there will be three cases, those of mathematics,
of physics, and of metaphysics.

    [11] Kant points out that this certainty has usually been
    attributed to the analytic character of mathematical
    judgements, and it is of course vital to his argument that
    he should be successful in showing that they are really
    synthetic.

The outline of the solution of this problem is contained in the
Preface to the Second Edition. There Kant urges that the key is to be
found by consideration of mathematics and physics. If the question be
raised as to what it is that has enabled these subjects to advance, in
both cases the answer will be found to lie in a change of method.
"Since the earliest times to which the history of human reason
reaches, mathematics has, among that wonderful nation the Greeks,
followed the safe road of a science. Still it is not to be supposed
that it was as easy for this science to strike into, or rather to
construct for itself, that royal road, as it was for logic, in which
reason has only to do with itself. On the contrary, I believe that it
must have remained long in the stage of groping (chiefly among the
Egyptians), and that this change is to be ascribed to a _revolution_,
due to the happy thought of one man, through whose experiment the path
to be followed was rendered unmistakable for future generations, and
the certain way of a science was entered upon and sketched out once
for all.... A new light shone upon the first man (Thales, or whatever
may have been his name) who demonstrated the properties of the
isosceles triangle; for he found that he ought not to investigate
that which he saw in the figure or even the mere conception of the
same, and learn its properties from this, but that he ought to produce
the figure by virtue of that which he himself had thought into it _a
priori_ in accordance with conceptions and had represented (by means
of a construction), and that in order to know something with certainty
_a priori_ he must not attribute to the figure any property other than
that which necessarily follows from that which he has himself
introduced into the figure, in accordance with his conception."[12]

    [12] B. x-xii, M. xxvi.

Here Kant's point is as follows. Geometry remained barren so long as
men confined themselves either to the empirical study of individual
figures, of which the properties were to be discovered by observation,
or to the consideration of the mere conception of various kinds of
figure, e. g. of an isosceles triangle. In order to advance, men had
in some sense to produce the figure through their own activity, and in
the act of constructing it to recognize that certain features were
necessitated by those features which they had given to the figure in
constructing it. Thus men had to make a triangle by drawing three
straight lines so as to enclose a space, and then to recognize that
three angles must have been made by the same process. In this way the
mind discovered a general rule, which must apply to all cases, because
the mind itself had determined the nature of the cases. A property B
follows from a nature A; all instances of A must possess the property
B, because they have solely that nature A which the mind has given
them and whatever is involved in A. The mind's own rule holds good in
all cases, because the mind has itself determined the nature of the
cases.

Kant's statements about physics, though not the same, are analogous.
Experiment, he holds, is only fruitful when reason does not follow
nature in a passive spirit, but compels nature to answer its own
questions. Thus, when Torricelli made an experiment to ascertain
whether a certain column of air would sustain a given weight, he had
previously calculated that the quantity of air was just sufficient to
balance the weight, and the significance of the experiment lay in his
expectation that nature would conform to his calculations and in the
vindication of this expectation. Reason, Kant says, must approach
nature not as a pupil but as a judge, and this attitude forms the
condition of progress in physics.

The examples of mathematics and physics suggest, according to Kant,
that metaphysics may require a similar revolution of standpoint, the
lack of which will account for its past failure. An attempt should
therefore be made to introduce such a change into metaphysics. The
change is this. Hitherto it has been assumed that our knowledge must
conform to objects. This assumption is the real cause of the failure
to extend our knowledge _a priori_, for it limits thought to the
analysis of conceptions, which can only yield tautological judgements.
Let us therefore try the effect of assuming that objects must conform
to our knowledge. Herein lies the Copernican revolution. We find that
this reversal of the ordinary view of the relation of objects to the
mind enables us for the first time to understand the possibility of _a
priori_ synthetic judgements, and even to demonstrate certain laws
which lie at the basis of nature, e. g. the law of causality. It is
true that the reversal also involves the surprising consequence that
our faculty of knowledge is incapable of dealing with the objects of
metaphysics proper, viz. God, freedom, and immortality, for the
assumption limits our knowledge to objects of possible experience. But
this very consequence, viz. the impossibility of metaphysics, serves
to test and vindicate the assumption. For the view that our knowledge
conforms to objects as things in themselves leads us into an insoluble
contradiction when we go on, as we must, to seek for the
unconditioned; while the assumption that objects must, as phenomena,
conform to our way of representing them, removes the contradiction[13].
Further, though the assumption leads to the denial of speculative
knowledge in the sphere of metaphysics, it is still possible that
reason in its practical aspect may step in to fill the gap. And the
negative result of the assumption may even have a positive value. For
if, as is the case, the moral reason, or reason in its practical
aspect, involves certain postulates concerning God, freedom, and
immortality, which are rejected by the speculative reason, it is
important to be able to show that these objects fall beyond the scope
of the speculative reason. And if we call reliance on these
postulates, as being presuppositions of morality, faith, we may say
that knowledge must be abolished to make room for faith.

    [13] Cf. pp. 101-2.

This answer to the main problem, given in outline in the Preface, is
undeniably plausible. Yet examination of it suggests two criticisms
which affect Kant's general position.

In the first place, the parallel of mathematics which suggests the
'Copernican' revolution does not really lead to the results which Kant
supposes. Advance in mathematics is due to the adoption not of any
conscious assumption but of a certain procedure, viz. that by which we
draw a figure and thereby see the necessity of certain relations
within it. To preserve the parallel, the revolution in metaphysics
should have consisted in the adoption of a similar procedure, and
advance should have been made dependent on the application of an at
least quasi-mathematical method to the objects of metaphysics.
Moreover, since these objects are God, freedom, and immortality, the
conclusion should have been that we ought to study God, freedom, and
immortality by somehow constructing them in perception and thereby
gaining insight into the necessity of certain relations. Success or
failure in metaphysics would therefore consist simply in success or
failure to see the necessity of the relations involved. Kant, however,
makes the condition of advance in metaphysics consist in the adoption
not of a method of procedure but of an assumption, viz. that objects
conform to the mind. And it is impossible to see how this assumption
can assist what, on Kant's theory, it ought to have assisted, viz. the
study of God, freedom, and immortality, or indeed the study of
anything. In geometry we presuppose that individual objects conform to
the universal rules of relation which we discover. Now suppose we
describe a geometrical judgement, e. g. that two straight lines cannot
enclose a space, as a mental law, because we are bound to think it
true. Then we may state the presupposition by saying that objects,
e. g. individual pairs of straight lines, must conform to such a mental
law. But the explicit recognition of this presupposition and the
conscious assertion of it in no way assist the solution of particular
geometrical problems. The presupposition is really a condition of
geometrical thinking at all. Without it there is no geometrical
thinking, and the recognition of it places us in no better position
for the study of geometrical problems. Similarly, if we wish to think
out the nature of God, freedom, and immortality, we are not assisted
by assuming that these objects must conform to the laws of our
thinking. We must presuppose this conformity if we are to think at
all, and consciousness of the presupposition puts us in no better
position. What is needed is an insight similar to that which we have
in geometry, i. e. an insight into the necessity of the relations
under consideration such as would enable us to see, for example, that
being a man, as such, involves living for ever.

Kant has been led into the mistake by a momentary change in the
meaning given to 'metaphysics'. For the moment he is thinking of
metaphysics, not as the inquiry concerned with God, freedom, and
immortality, but as the inquiry which has to deal with the problem as
to how we can know _a priori_. This problem is assisted, at any rate
prima facie, by the assumption that things must conform to the mind.
And this assumption can be said to be suggested by mathematics,
inasmuch as the mathematician presupposes that particular objects must
correspond to the general rules discovered by the mind. From this
point of view Kant's only mistake, if the parallelism is to be
maintained, is that he takes for an assumption which enables the
mathematician to advance a metaphysical presupposition of the advance,
on which the mathematician never reflects, and awareness of which
would in no way assist his mathematics.

In the second place the 'Copernican' revolution is not strictly the
revolution which Kant supposes it to be. He speaks as though his aim
is precisely to reverse the ordinary view of the relation of the mind
to objects. Instead of the mind being conceived as having to conform
to objects, objects are to be conceived as having to conform to the
mind. But if we consider Kant's real position, we see that these views
are only verbally contrary, since the word object refers to something
different in each case. On the ordinary view objects are something
outside the mind, in the sense of independent of it, and the ideas,
which must conform to objects, are something within the mind, in the
sense of dependent upon it. The conformity then is of something within
the mind to something outside it. Again, the conformity means that one
of the terms, viz. the object, exists first and that then the other
term, the idea, is fitted to or made to correspond to it. Hence the
real contrary of this view is that ideas, within the mind, exist first
and that objects outside the mind, coming into existence afterwards,
must adapt themselves to the ideas. This of course strikes us as
absurd, because we always think of the existence of the object as the
presupposition of the existence of the knowledge of it; we do not
think the existence of the knowledge as the presupposition of the
existence of the object. Hence Kant only succeeds in stating the
contrary of the ordinary view with any plausibility, because in doing
so he makes the term object refer to something which like 'knowledge'
is within the mind. His position is that objects within the mind must
conform to our general ways of knowing. For Kant, therefore, the
conformity is not between something within and something without the
mind, but between two realities within the mind, viz. the individual
object, as object of perception, i. e. a phenomenon, and our general
ways of perceiving and thinking. But this view is only verbally the
contrary of the ordinary view, and consequently Kant does not succeed
in reversing the ordinary view that we know objects independent of or
outside the mind, by bringing our ideas into conformity with them. In
fact, his conclusion is that we do not know this object, i. e. the
thing in itself, at all. Hence his real position should be stated by
saying not that the ordinary view puts the conformity between mind and
things in the wrong way, but that we ought not to speak of conformity
at all. For the thing in itself being unknowable, our ideas can never
be made to conform to it. Kant then only reaches a conclusion which is
apparently the reverse of the ordinary view by substituting another
object for the thing in itself, viz. the phenomenon or appearance of
the thing in itself to us.

Further, this second line of criticism, if followed out, will be found
to affect his statement of the problem as well as that of its
solution. It will be seen that the problem is mis-stated, and that the
solution offered presupposes it to be mis-stated. His statement of the
problem takes the form of raising a difficulty which the existence of
_a priori_ knowledge presents to the ordinary view, according to which
objects are independent of the mind, and ideas must be brought into
conformity with them. In a synthetic _a priori_ judgement we claim to
discover the nature of certain objects by an act of our thinking, and
independently of actual experience of them. Hence if a supporter of
the ordinary view is asked to justify the conformity of this judgement
or idea with the objects to which it relates, he can give no answer.
The judgement having _ex hypothesi_ been made without reference to the
objects, the belief that the objects must conform to it is the merely
arbitrary supposition that a reality independent of the mind must
conform to the mind's ideas. But Kant, in thus confining the
difficulty to _a priori_ judgements, implies that empirical judgements
present no difficulty to the ordinary view; since they rest upon
actual experience of the objects concerned, they are conformed to the
objects by the very process through which they arise. He thereby fails
to notice that empirical judgements present a precisely parallel
difficulty. It can only be supposed that the conformity of empirical
judgements to their objects is guaranteed by the experience upon which
they rest, if it be assumed that in experience we apprehend objects as
they are. But our experience or perception of individual objects is
just as much mental as the thinking which originates _a priori_
judgements. If we can question the truth of our thinking, we can
likewise question the truth of our perception. If we can ask whether
our ideas must correspond to their objects, we can likewise ask
whether our perceptions must correspond to them. The problem relates
solely to the correspondence between something within the mind and
something outside it; it applies equally to perceiving and thinking,
and concerns all judgements alike, empirical as well as _a priori_.
Kant, therefore, has no right to imply that empirical judgements raise
no problem, if he finds difficulty in _a priori_ judgements. He is
only able to draw a distinction between them, because, without being
aware that he is doing so, he takes account of the relation of the
object to the subject in the case of an _a priori_ judgement, while in
the case of an empirical judgement he ignores it. In other words, in
dealing with the general connexion between the qualities of an
object, he takes into account the fact that we are thinking it, but,
in dealing with the perception of the coexistence of particular
qualities of an object, he ignores the fact that we are perceiving it.
Further, that the real problem concerns all synthetic judgements alike
is shown by the solution which he eventually reaches. His conclusion
turns out to be that while both empirical and _a priori_ judgements
are valid of phenomena, they are not valid of things in themselves;
i. e. that of things in themselves we know nothing at all, not even
their particular qualities. Since, then, his conclusion is that even
empirical judgements are not valid of things in themselves, it shows
that the problem cannot be confined to _a priori_ judgements, and
therefore constitutes an implicit criticism of his statement of the
problem.

Must there not, however, be some problem peculiar to _a priori_
judgements? Otherwise why should Kant have been led to suppose that
his problem concerned them only? Further consideration will show that
there is such a problem, and that it was only owing to the mistake
indicated that Kant treated this problem as identical with that of
which he actually offered a solution. In the universal judgements of
mathematics we apprehend, as we think, general rules of connexion
which must apply to all possible cases. Such judgements, then,
presuppose a conformity between the connexions which we discover and
all possible instances. Now Kant's treatment of this conformity as a
conformity between our ideas and things has two implications. In the
first place, it implies, as has been pointed out, that relation to the
subject, as thinking, is taken into account in the case of the
universal connexion, and that relation to the subject, as perceiving,
is ignored in the case of the individual thing. In the second place,
it implies that what is related to the subject as the object of its
thought must be subjective or mental; that because we have to think
the general connexion, the connexion is only our own idea, the
conformity of things to which may be questioned. But the treatment, to
be consistent, should take account of relation to the subject in both
cases or in neither. If the former alternative be accepted, then the
subjective character attributed by Kant in virtue of this relation to
what is object of thought, and equally attributable to what is object
of perception, reduces the problem to that of the conformity in
general of all ideas, including perceptions, within the mind to things
outside it; and this problem does not relate specially to _a priori_
judgements. To discover the problem which relates specially to them,
the other alternative must be accepted, that of ignoring relation to
the subject in both cases. The problem then becomes 'What renders
possible or is presupposed by the conformity of individual things to
certain laws of connexion?' And, inasmuch as to deny the conformity is
really to deny that there are laws of connexion,[14] the problem
reduces itself to the question, 'What is the presupposition of the
existence of definite laws of connexion in the world?' And the only
answer possible is that reality is a system or a whole of connected
parts, in other words, that nature is uniform. Thus it turns out that
the problem relates to the uniformity of nature, and that the
question 'How are _a priori_ synthetic judgements possible?' has in
reality nothing to do with the problem of the relation of reality to
the knowing subject, but is concerned solely with the nature of
reality.

    [14] To object that the laws in question, being laws which we
    have thought, may not be the true laws, and that therefore
    there may still be other laws to which reality conforms, is
    of course to reintroduce relation to the thinking subject.

Further, it is important to see that the alternative of ignoring
relation to the subject is the right one, not only from the point of
view of the problem peculiar to _a priori_ judgements, but also from
the point of view of the nature of knowledge in general. Perceiving
and thinking alike presuppose that reality is immediately object of
the mind, and that the act of apprehension in no way affects or enters
into the nature of what we apprehend about reality. If, for instance,
I assert on the strength of perception that this table is round, I
imply that I see the table, and that the shape which I judge it to
have is not affected by the fact that I am perceiving it; for I mean
that the table really is round. If some one then convinces me that I
have made a mistake owing to an effect of foreshortening, and that the
table is really oval, I amend my assertion, not by saying that the
table is round but only to my apprehension, but by saying that it
looks round. Thereby I cease to predicate roundness of the table
altogether; for I mean that while it still looks round, it is not
really so. The case of universal judgements is similar. The statement
that a straight line is the shortest distance between its extremities
means that it really is so. The fact is presupposed to be in no way
altered by our having apprehended it. Moreover, reality is here just
as much implied to be directly object of the mind as it is in the case
of the singular judgement. Making the judgement consists, as we say,
in _seeing_ the connexion between the direction between two points
and the shortest distance between them. The connexion of real
characteristics is implied to be directly object of thought.[16] Thus
both perceiving and thinking presuppose that the reality to which they
relate is directly object of the mind, and that the character of it
which we apprehend in the resulting judgement is not affected or
altered by the fact that we have had to perceive or conceive the
reality.[17]

    [15] Cf. Bosanquet, _Logic_, vol. ii, p. 2.

    [16] In saying that a universal judgement is an immediate
    apprehension of fact, it is of course not meant that it can
    be actualized by itself or, so to say, _in vacuo_. Its
    actualization obviously presupposes the presentation of
    individuals in perception or imagination. Perception or
    imagination thus forms the necessary occasion of a universal
    judgement, and in that sense mediates it. Moreover, the
    universal judgement implies an act of abstraction by which
    we specially attend to those universal characters of the
    individuals perceived or imagined, which enter into the
    judgement. But, though our apprehension of a universal
    connexion thus implies a process, and is therefore mediated,
    yet the connexion, when we apprehend it, is immediately our
    object. There is nothing between it and us.

    [17] For a fuller discussion of the subject see Chh. IV and
    VI.

Kant in the formulation of his problem implicitly admits this
presupposition in the case of perception. He implies that empirical
judgements involve no difficulty, because they rest upon the
perception or experience of the objects to which they relate. On the
other hand, he does not admit the presupposition in the case of
conception, for he implies that in _a priori_ judgements we are not
confronted with reality but are confined to our own ideas. Hence we
ought to ask why Kant is led to adopt an attitude in the latter case
which he does not adopt in the former. The answer appears to be
twofold. In the first place, there is an inveterate tendency to think
of universals, and therefore of the connexions between them, as being
not objective realities[18] but mere ideas. In other words, we tend to
adopt the conceptualist attitude, which regards individuals as the
only reality, and universals as mental fictions. In consequence, we
are apt to think that while in perception, which is of the individual,
we are confronted by reality, in universal judgements, in which we
apprehend connexions between universals, we have before us mere ideas.
Kant may fairly be supposed to have been unconsciously under the
influence of this tendency. In the second place, we apprehend a
universal connexion by the operation of thinking. Thinking is
essentially an activity; and since activity in the ordinary sense in
which we oppose action to knowledge originates something, we tend to
think of the activity of thinking as also originating something, viz.
that which is our object when we think. Hence, since we think of what
is real as independent of us and therefore as something which we may
discover but can in no sense make, we tend to think of the object of
thought as only an idea. On the other hand, what is ordinarily called
perception, though it involves the activity of thinking, also involves
an element in respect of which we are passive. This is the fact
pointed to by Kant's phrase 'objects are _given_ in perception'. In
virtue of this passive element we are inclined to think that in
perception we simply stand before the reality in a passive attitude.
The reality perceived is thought to be, so to say, there, existing
independently of us; relation to the subject is unnoticed because of
our apparently wholly passive attitude. At times, and especially when
he is thinking of the understanding as a faculty of spontaneity, Kant
seems to have been under the influence of this second tendency.

    [18] i. e. as not having a place in the reality which, as we
    think, exists independently of the mind.

The preceding summary of the problem of the _Critique_ represents the
account given in the two Prefaces and the Introduction. According to
this account, the problem arises from the unquestioned existence of _a
priori_ knowledge in mathematics and physics and the problematic
existence of such knowledge in metaphysics, and Kant's aim is to
determine the range within which _a priori_ knowledge is possible.
Thus the problem is introduced as relating to _a priori_ knowledge as
such, no distinction being drawn between its character in different
cases. Nevertheless the actual discussion of the problem in the body
of the _Critique_ implies a fundamental distinction between the nature
of _a priori_ knowledge in mathematics and its nature in physics, and
in order that a complete view of the problem may be given, this
distinction must be stated.

The 'Copernican' revolution was brought about by consideration of the
facts of mathematics. Kant accepted as an absolute starting-point the
existence in mathematics of true universal and necessary judgements.
He then asked, 'What follows as to the nature of the objects known in
mathematics from the fact that we really know them?' Further, in his
answer he accepted a distinction which he never examined or even
questioned, viz. the distinction between things in themselves and
phenomena.[19] This distinction assumed, Kant inferred from the truth
of mathematics that things in space and time are only phenomena.
According to him mathematicians are able to make the true judgements
that they do make only because they deal with phenomena. Thus Kant in
no way sought to _prove_ the truth of mathematics. On the contrary, he
argued from the truth of mathematics to the nature of the world which
we thereby know. The phenomenal character of the world being thus
established, he was able to reverse the argument and to regard the
phenomenal character of the world as _explaining_ the validity of
mathematical judgements. They are valid, because they relate to
phenomena. And the consideration which led Kant to take mathematics
as his starting-point seems to have been the self-evidence of
mathematical judgements. As we directly apprehend their necessity,
they admit of no reasonable doubt.

    [19] Cf. Ch. IV. This distinction should of course have been
    examined by one whose aim it was to determine how far our
    knowledge can reach.

    [20] For the self-evidence of mathematics to Kant compare B.
    120, M. 73 and B. 200, M. 121.

On the other hand, the general principles underlying physics, e. g.
that every change must have a cause, or that in all change the quantum
of matter is constant, appeared to Kant in a different light. Though
certainly not based on experience, they did not seem to him
self-evident.[21] Hence,[22] in the case of these principles, he
sought to give what he did not seek to give in the case of
mathematical judgements, viz. a proof of their truth.[23] The nerve of
the proof lies in the contention that these principles are involved
not merely in any general judgement in physics, e. g. 'All bodies are
heavy,' but even in any singular judgement, e. g. 'This body is
heavy,' and that the validity of singular judgements is universally
conceded. Thus here the fact upon which he takes his stand is not the
admitted truth of the universal judgements under consideration, but
the admitted truth of any singular judgement in physics. His
treatment, then, of the universal judgements of mathematics and that
of the principles underlying physics are distinguished by the fact
that, while he accepts the former as needing no proof, he seeks to
prove the latter from the admitted validity of singular judgements in
physics. At the same time the acceptance of mathematical judgements
and the proof of the _a priori_ principles of physics have for Kant a
common presupposition which distinguishes mathematics and physics from
metaphysics. Like universal judgements in mathematics, singular
judgements in physics, and therefore the principles which they
presuppose, are true only if the objects to which they relate are
phenomena. Both in mathematics and physics, therefore, it is a
condition of _a priori_ knowledge that it relates to phenomena and not
to things in themselves. But, just for this reason, metaphysics is in
a different position; since God, freedom, and immortality can never be
objects of experience, _a priori_ knowledge in metaphysics, and
therefore metaphysics itself, is impossible. Thus for Kant the very
condition, the realization of which justifies the acceptance of
mathematical judgements and enables us to prove the principles of
physics, involves the impossibility of metaphysics.

    [21] This is stated B. 200, M. 121. It is also implied B.
    122, M. 75, B. 263-4, M. 160, and by the argument of the
    _Analytic_ generally.

    [22] This appears to be the real cause of the difference of
    treatment, though it is not the reason assigned by Kant
    himself, cf. B. 120, M. 73-4.

    [23] His remarks about pure natural science in B. 20, M. 13
    and Prol. § 4 sub fin., do not represent the normal attitude
    of the _Critique_.

Further, the distinction drawn between _a priori_ judgements in
mathematics and in physics is largely responsible for the difficulty
of understanding what Kant means by _a priori_. His unfortunate
tendency to explain the term negatively could be remedied if it could
be held either that the term refers solely to mathematical judgements
or that he considers the truth of the law of causality to be
apprehended in the same way that we see that two and two are four. For
an _a priori_ judgement could then be defined as one in which the
mind, on the presentation of an individual in perception or
imagination, and in virtue of its capacity of thinking, apprehends the
necessity of a specific relation. But this definition is precluded by
Kant's view that the law of causality and similar principles, though
_a priori_, are not self-evident.




CHAPTER II

THE SENSIBILITY AND THE UNDERSTANDING


The distinction between the sensibility and the understanding[1] is
to Kant fundamental both in itself and in relation to the conclusions
which he reaches. An outline, therefore, of this distinction must
precede any statement or examination of the details of his position.
Unfortunately, in spite of its fundamental character, Kant never
thinks of questioning or criticizing the distinction in the form in
which he draws it, and the presence of certain confusions often
renders it difficult to be sure of his meaning.

    [1] Cf. B. 1, 29, 33, 74-5, 75, 92-4; M. 1, 18, 21, 45-46,
    57.

The distinction may be stated in his own words thus: "There are two
stems of human knowledge, which perhaps spring from a common but to us
unknown root, namely sensibility and understanding."[2] "Our knowledge
springs from two fundamental sources of the mind; the first receives
representations[3] (receptivity for impressions); the second is the
power of knowing an object by means of these representations
(spontaneity of conceptions). Through the first an object is _given_
to us; through the second the object is _thought_ in relation to the
representation (which is a mere determination of the mind). Perception
and conceptions constitute, therefore, the elements of all our
knowledge, so that neither conceptions without a perception in some
way corresponding to them, nor perception without conceptions can
yield any knowledge.... Neither of these qualities has a preference
over the other. Without sensibility no object would be given to us,
and without understanding no object would be thought. Thoughts without
content are empty, perceptions without conceptions are blind. Hence it
is as necessary for the mind to make its conceptions sensuous (i. e.
to add to them the object in perception) as to make its perceptions
intelligible (i. e. to bring them under conceptions). Neither of these
powers or faculties can exchange its function. The understanding
cannot perceive, and the senses cannot think. Only by their union can
knowledge arise."[4]

    [2] B. 29, M. 18

    [3] For the sake of uniformity _Vorstellung_ has throughout
    been translated by 'representation', though sometimes, as in
    the present passage, it would be better rendered by
    'presentation'.

    [4] B. 74-5, M. 45-6.

The distinction so stated appears straightforward and, on the
whole,[5] sound. And it is fairly referred to by Kant as the
distinction between the faculties of perceiving and conceiving or
thinking, provided that the terms perceiving and conceiving or
thinking be taken to indicate a distinction within perception in the
ordinary sense of the word. His meaning can be stated thus: 'All
knowledge requires the realization of two conditions; an individual
must be presented to us in perception, and we as thinking beings must
bring this individual under or recognize it as an instance of some
universal. Thus, in order to judge 'This is a house' or 'That is red'
we need the presence of the house or of the red colour in perception,
and we must 'recognize' the house or the colour, i. e. apprehend the
individual as a member of a certain kind. Suppose either condition
unrealized. Then if we suppose a failure to conceive, i. e. to
apprehend the individual as a member of some kind, we see that our
perception--if it could be allowed to be anything at all--would be
blind i. e. indeterminate, or a mere 'blur'. What we perceived would
be for us as good as nothing. In fact, we could not even say that we
were perceiving. Again, if we suppose that we had merely the
conception of a house, and neither perceived nor had perceived an
individual to which it applied, we see that the conception, being
without application, would be neither knowledge nor an element in
knowledge. Moreover, the content of a conception is derived from
perception; it is only through its relation to perceived individuals
that we become aware of a universal. To know the meaning of 'redness'
we must have experienced individual red things; to know the meaning of
'house' we must at least have had experience of individual men and of
their physical needs. Hence 'conceptions' without 'perceptions' are
void or empty. The existence of conceptions presupposes experience of
corresponding individuals, even though it also implies the activity of
thinking in relation to these individuals.'[6]

    [5] Cf. p. 29, note 1.

    [6] Kant's account implies that he has in view only empirical
    knowledge; in any case it only applies to empirical
    conceptions.

Further, it is true to say that as perceiving we are passive; we do
not do anything. This, as has been pointed out, is the element of
truth contained in the statement that objects are _given_ to us. On
the other hand, it may be truly said that as conceiving, in the sense
of bringing an individual under a universal, we are essentially
active. This is presupposed by the notice or attention involved in
perception ordinarily so called, i. e. perception in the full sense
in which it includes conceiving as well as perceiving.[7] Kant,
therefore, is justified in referring to the sensibility as a
'receptivity' and to the understanding as a 'spontaneity'.

    [7] This distinction within perception is of course
    compatible with the view that the elements so distinguished
    are inseparable.

The distinction, so stated, appears, as has been already said,
intelligible and, in the main[8], valid. Kant, however, renders the
elucidation of his meaning difficult by combining with this view of
the distinction an incompatible and unwarranted theory of perception.
He supposes,[9] without ever questioning the supposition, that
perception is due to the operation of things outside the mind, which
act upon our sensibility and thereby produce sensations. On this
supposition, what we perceive is not, as the distinction just stated
implies, the thing itself, but a sensation produced by it.
Consequently a problem arises as to the meaning on this supposition of
the statements 'by the sensibility objects are given to us' and 'by
the understanding they are thought'. The former statement must mean
that when a thing affects us there is a sensation. It cannot mean that
by the sensibility we know that there exists a thing which causes the
sensation, for this knowledge would imply the activity of thinking;
nor can it mean that in virtue of the sensibility the thing itself is
presented to us. The latter statement must mean that when sensation
arises, the understanding judges that there is something causing it;
and this assertion must really be _a priori_, because not dependent
upon experience. Unfortunately the two statements so interpreted are
wholly inconsistent with the account of the functions of the
sensibility and the understanding which has just been quoted.

    [8] See p. 29, note 1.

    [9] Cf. B. 1, M. 1.

Further, this theory of perception has two forms. In its first form
the theory is physical rather than metaphysical, and is based upon
our possession of physical organs. It assumes that the reality to be
apprehended is the world of space and time, and it asserts that by the
action of bodies upon our physical organs our sensibility is affected,
and that thereby sensations are originated in us. Thereupon a problem
arises. For if the contribution of the sensibility to our knowledge
of the physical world is limited to a succession of sensations,
explanation must be given of the fact that we have succeeded with
an experience confined to these sensations in acquiring knowledge
of a world which does not consist of sensations.[10] Kant, in fact,
in the _Aesthetic_ has this problem continually before him, and
tries to solve it. He holds that the mind, by means of its forms of
perception and its conceptions of the understanding, superinduces upon
sensations, as data, spatial and other relations, in such a way that
it acquires knowledge of the spatial world.

    [10] Cf. B. 1 init., M. 1 init.; B. 34, M. 21 sub fin.

An inherent difficulty, however, of this 'physical' theory of
perception leads to a transformation of it. If, as the theory
supposes, the cause of sensation is outside or beyond the mind, it
cannot be known. Hence the initial assumption that this cause is the
physical world has to be withdrawn, and the cause of sensation comes
to be thought of as the thing in itself of which we can know nothing.
This is undoubtedly the normal form of the theory in Kant's mind.

It may be objected that to attribute to Kant at any time the physical
form of the theory is to accuse him of an impossibly crude confusion
between things in themselves and the spatial world, and that he can
never have thought that the cause of sensation, being as it is outside
the mind, is spatial. But the answer is to be found in the fact that
the problem just referred to as occupying Kant's attention in the
_Aesthetic_ is only a problem at all so long as the cause of sensation
is thought of as a physical body. For the problem 'How do we,
beginning with mere sensation, come to know a spatial and temporal
world?' is only a problem so long as it is supposed that the cause of
sensation is a spatial and temporal world or a part of it, and that
this world is what we come to know. If the cause of sensation, as
being beyond the mind, is held to be unknowable and so not known to be
spatial or temporal, the problem has disappeared. Corroboration is
given by certain passages[11] in the _Critique_ which definitely
mention 'the senses', a term which refers to bodily organs, and by
others[12] to which meaning can be given only if they are taken to
imply that the objects which affect our sensibility are not unknown
things in themselves, but things known to be spatial. Even the use of
the plural in the term 'things in themselves' implies a tendency to
identify the unknowable reality beyond the mind with bodies in space.
For the implication that different sensations are due to different
things in themselves originates in the view that different sensations
are due to the operation of different spatial bodies.

    [11] E. g. B. 1 init., M. 1 init., and B. 75 fin., M. 46,
    lines 12, 13 [for 'the sensuous faculty' should be
    substituted 'the senses'].

    [12] E. g. B. 42, lines 11, 12; M. 26, line 13; A. 100, Mah.
    195 ('even in the absence of the object'). Cf. B. 182-3, M.
    110-1 (see pp. 257-8, and note p. 257), and B. 207-10, M.
    126-8 (see pp. 263-5).

It is now necessary to consider how the distinction between the
sensibility and the understanding contributes to articulate the
problem 'How are _a priori_ synthetic judgements possible?' As has
been pointed out, Kant means by this question, 'How is it possible
that the mind is able, in virtue of its own powers, to make universal
and necessary judgements which anticipate its experience of objects?'
To this question his general answer is that it is possible and only
possible because, so far from ideas, as is generally supposed, having
to conform to things, the things to which our ideas or judgements
relate, viz. phenomena, must conform to the nature of the mind. Now,
if the mind's knowing nature can be divided into the sensibility and
the understanding, the problem becomes 'How is it possible for the
mind to make such judgements in virtue of its sensibility and its
understanding?' And the answer will be that it is possible because the
things concerned, i. e. phenomena, must conform to the sensibility and
the understanding, i. e. to the mind's perceiving and thinking nature.
But both the problem and the answer, so stated, give no clue to the
particular _a priori_ judgements thus rendered possible nor to the
nature of the sensibility and the understanding in virtue of which we
make them. It has been seen, however, that the judgements in question
fall into two classes, those of mathematics and those which form the
presuppositions of physics. And it is Kant's aim to relate these
classes to the sensibility and the understanding respectively. His
view is that mathematical judgements, which, as such, deal with
spatial and temporal relations, are essentially bound up with our
perceptive nature, i. e. with our sensibility, and that the principles
underlying physics are the expression of our thinking nature, i. e. of
our understanding. Hence if the vindication of this relation between
our knowing faculties and the judgements to which they are held to
give rise is approached from the side of our faculties, it must be
shown that our sensitive nature is such as to give rise to
mathematical judgements, and that our understanding or thinking nature
is such as to originate the principles underlying physics. Again, if
the account of this relation is to be adequate, it must be shown to be
exhaustive, i. e. it must be shown that the sensibility and the
understanding give rise to no other judgements. Otherwise there may be
other _a priori_ judgements bound up with the sensibility and the
understanding which the inquiry will have ignored. Kant, therefore, by
his distinction between the sensibility and the understanding, sets
himself another problem, which does not come into sight in the first
formulation of the general question 'How are _a priori_ synthetic
judgements possible?' He has to determine what _a priori_ judgements
are related to the sensibility and to the understanding respectively.
At the same time the distinction gives rise to a division within the
main problem. His chief aim is to discover how it is that _a priori_
judgements are universally applicable. But, as Kant conceives
the issue, the problem requires different treatment according
as the judgements in question are related to the sensibility or
to the understanding. Hence arises the distinction between the
_Transcendental Aesthetic_ and the _Transcendental Analytic_, the
former dealing with the _a priori_ judgements of mathematics, which
relate to the sensibility, and the latter dealing with the _a priori_
principles of physics, which originate in the understanding. Again,
within each of these two divisions we have to distinguish two
problems, viz. 'What _a priori_ judgements are essentially related to
the faculty in question?' and 'How is it that they are applicable to
objects?'

It is important, however, to notice that the distinction between the
sensibility and the understanding, in the form in which it serves as a
basis for distinguishing the _Aesthetic_ and the _Analytic_, is not
identical with or even compatible with the distinction, as Kant states
it when he is considering the distinction in itself and is not
thinking of any theory which is to be based upon it. In the latter
case the sensibility and the understanding are represented as
inseparable faculties involved in _all_ knowledge.[13] Only from the
union of both can knowledge arise. But, regarded as a basis for the
distinction between the _Aesthetic_ and the _Analytic_, they are
implied to be the source of different kinds of knowledge, viz.
mathematics and the principles of physics. It is no answer to this to
urge that Kant afterwards points out that space as an object
presupposes a synthesis which does not belong to sense. No doubt this
admission implies that even the apprehension of spatial relations
involves the activity of the understanding. But the implication is
really inconsistent with the existence of the _Aesthetic_ as a
distinct part of the subject dealing with a special class of _a
priori_ judgements.

    [13] B. 74-5, M. 45-6; cf. pp. 27-9.

    [14] B. 160 note, M. 98 note.




CHAPTER III

SPACE


It is the aim of the _Aesthetic_ to deal with the _a priori_ knowledge
which relates to the sensibility. This knowledge, according to Kant,
is concerned with space and time. Hence he has to show _firstly_ that
our apprehension of space and time is _a priori_, i. e. that it is not
derived from experience but originates in our apprehending nature; and
_secondly_ that within our apprehending nature this apprehension
belongs to the sensibility and not to the understanding, or, in his
language, that space and time are forms of perception or sensibility.
Further, if his treatment is to be exhaustive, he should also show
_thirdly_ that space and time are the only forms of perception. This,
however, he makes no attempt to do except in one passage,[1] where the
argument fails. The first two points established, Kant is able to
develop his main thesis, viz. that it is a condition of the validity
of the _a priori_ judgements which relate to space and time that these
are characteristics of phenomena, and not of things in themselves.

    [1] B. 58, M. 35.

It will be convenient to consider his treatment of space and time
separately, and to begin with his treatment of space. It is necessary,
however, first of all to refer to the term 'form of perception'. As
Kant conceives a form of perception, it involves three antitheses.

(1) As a _form_ of perception it is opposed, as a way or mode of
perceiving, to particular perceptions.

(2) As a form or mode of _perception_ it is opposed to a form or mode
of _conception_.

(3) As a form of _perception_ it is also opposed, as a way in which we
apprehend things, to a way in which things are.

While we may defer consideration of the second and third antitheses,
we should at once give attention to the nature of the first, because
Kant confuses it with two other antitheses. There is no doubt that in
general a _form_ of perception means for Kant a general capacity of
perceiving which, as such, is opposed to the actual perceptions in
which it is manifested. For according to him our spatial perceptions
are not foreign to us, but manifestations of our general perceiving
nature; and this view finds expression in the assertion that space is
a form of perception or of sensibility.[2]

    [2] Cf. B. 43 init., M. 26 med.

Unfortunately, however, Kant frequently speaks of this form of
perception as if it were the same thing as the actual perception of
empty space.[3] In other words, he implies that such a perception is
possible, and confuses it with a potentiality, i. e. the power of
perceiving that which is spatial. The confusion is possible because it
can be said with some plausibility that a perception of empty
space--if its possibility be allowed--does not inform us about actual
things, but only informs us what must be true of things, if there
prove to be any; such a perception, therefore, can be thought of as a
possibility of knowledge rather than as actual knowledge.

    [3] e. g. B. 34, 35, M. 22; B. 41, M. 25; _Prol._ §§ 9-11.
    The commonest expression of the confusion is to be found in
    the repeated assertion that space is a pure perception.

The second confusion is closely related to the first, and arises from
the fact that Kant speaks of space not only as a form of _perception_,
but also as the form of _phenomena_ in opposition to sensation as
their matter. "That which in the phenomenon corresponds to[4] the
sensation I term its matter; but that which effects that the manifold
of the phenomenon can be arranged under certain relations I call the
form of the phenomenon. Now that in which alone our sensations can be
arranged and placed in a certain form cannot itself be sensation.
Hence while the matter of all phenomena is only given to us _a
posteriori_, their form [i. e. space] must lie ready for them all
together _a priori_ in the mind."[5] Here Kant is clearly under the
influence of his theory of perception.[6] He is thinking that, given
the origination of sensations in us by the thing in itself, it is the
business of the mind to arrange these sensations spatially in order to
attain knowledge of the spatial world.[7] Space being, as it were,
a kind of empty vessel in which sensations are arranged, is said
to be the form of phenomena.[8] Moreover, if we bear in mind that
ultimately bodies in space are for Kant only spatial arrangements
of sensations,[9] we see that the assertion that space is the form
of phenomena is only Kant's way of saying that all bodies are
spatial.[10] Now Kant, in thus asserting that space is the form of
phenomena, is clearly confusing this assertion with the assertion that
space is a form of perception, and he does so in consequence of the
first confusion, viz. that between a capacity of perceiving and an
actual perception of empty space. For in the passage last quoted he
continues thus: "I call all representations[11] _pure_ (in the
transcendental sense) in which nothing is found which belongs to
sensation. Accordingly there will be found _a priori_ in the mind the
pure form of sensuous perceptions in general, wherein all the manifold
of phenomena is perceived in certain relations. This pure form of
sensibility will also itself be called _pure perception_. Thus,
if I abstract from the representation of a body that which the
understanding thinks respecting it, such as substance, force,
divisibility, &c., and also that which belongs to sensation, such as
impenetrability, hardness, colour, &c., something is still left over
for me from this empirical perception, viz. extension and shape. These
belong to pure perception, which exists in the mind _a priori_, even
without an actual object of the senses or a sensation, as a mere form
of sensibility." Here Kant has passed, without any consciousness of a
transition, from treating space as that in which the manifold of
sensation is arranged to treating it as a capacity of perceiving.
Moreover, since Kant in this passage speaks of space as a perception,
and thereby identifies space with the perception of it,[12] the
confusion may be explained thus. The form of phenomena is said to be
the space in which all sensations are arranged, or in which all bodies
are; space, apart from all sensations or bodies, i. e. empty, being
the object of a pure perception, is treated as identical with a pure
perception, viz. the perception of empty space; and the perception of
empty space is treated as identical with a capacity of perceiving that
which is spatial.[13]

    [4] 'Corresponds to' must mean 'is'.

    [5] B. 34, M. 21.

    [6] Cf. pp. 30-2.

    [7] It is impossible, of course, to see how such a process
    can give us knowledge of the spatial world, for, whatever
    bodies in space are, they are not arrangements of sensations.
    Nevertheless, Kant's theory of perception really precludes
    him from holding that bodies are anything else than
    arrangements of sensations, and he seems at times to accept
    this view explicitly, e. g. B. 38, M. 23 (quoted p. 41),
    where he speaks of our representing sensations as external
    to and next to each other, and, therefore, as in different
    places.

    [8] It may be noted that it would have been more natural to
    describe the particular shape of the phenomenon (i. e. the
    particular spatial arrangement of the sensations) rather than
    space as the form of the phenomenon; for the matter to which
    the form is opposed is said to be sensation, and that of
    which it is the matter is said to be the phenomenon, i. e.
    a body in space.

    [9] Cf. note 4, p. 38.

    [10] Cf. _Prol._ § 11 and p. 137.

    [11] Cf. p. 41, note 1.

    [12] Cf. p. 51, note 1.

    [13] The same confusion (and due to the same cause) is
    implied _Prol_. § 11, and B. 42 (b), M. 26 (b) first
    paragraph. Cf. B. 49 (b), M. 30 (b).

The existence of the confusion, however, is most easily realized by
asking, 'How did Kant come to think of space and time as the _only_
forms of perception?' It would seem obvious that the perception of
_anything_ implies a form of perception in the sense of a mode or
capacity of perceiving. To perceive colours implies a capacity for
seeing; to hear noises implies a capacity for hearing. And these
capacities may fairly be called forms of perception. As soon as this
is realized, the conclusion is inevitable that Kant was led to think
of space and time as the only forms of perception, because in this
connexion he was thinking of each as a form of phenomena, i. e. as
something in which all bodies or their states are, or, from the point
of view of our knowledge, as that in which sensuous material is to be
arranged; for there is nothing except space and time in which such
arrangement could plausibly be said to be carried out.

As has been pointed out, Kant's argument falls into two main parts,
one of which prepares the way for the other. The aim of the former is
to show _firstly_ that our apprehension of space is _a priori_, and
_secondly_ that it belongs to perception and not to conception. The
aim of the latter is to conclude from these characteristics of our
apprehension of space that space is a property not of things in
themselves but only of phenomena. These arguments may be considered in
turn.

The really valid argument adduced by Kant for the _a priori_ character
of our apprehension of space is based on the nature of geometrical
judgements. The universality of our judgements in geometry is not
based upon experience, i. e. upon the observation of individual things
in space. The necessity of geometrical relations is apprehended
directly in virtue of the mind's own apprehending nature.
Unfortunately in the present context Kant ignores this argument and
substitutes two others, both of which are invalid.

1. "Space is no empirical conception[14] which has been derived from
external[15] experiences. For in order that certain sensations may be
related to something external to me (that is, to something in a
different part of space from that in which I am), in like manner, in
order that I may represent them as external to and next to each other,
and consequently as not merely different but as in different places,
the representation of space must already exist as a foundation.
Consequently, the representation of space cannot be borrowed from the
relations of external phenomena through experience; but, on the
contrary, this external experience is itself first possible only
through the said representation."[16] Here Kant is thinking that in
order to apprehend, for example, that A is to the right of B we must
first apprehend empty space. He concludes that our apprehension of
space is _a priori_, because we apprehend empty space _before_ we
become aware of the spatial relations of individual objects in it.

    [14] _Begriff_ (conception) here is to be understood loosely
    not as something opposed to _Anschauung_ (perception), but as
    equivalent to the genus of which _Anschauung_ and _Begriff_
    are species, i. e. _Vorstellung_, which maybe rendered by
    'representation' or 'idea', in the general sense in which
    these words are sometimes used to include 'thought' and
    'perception'.

    [15] The next sentence shows that 'external' means, not
    'produced by something external to the mind', but simply
    'spatial'.

    [16] B. 38, M. 23-4.

To this the following reply may be made. (_a_) The term _a priori_
applied to an apprehension should mean, not that it arises prior to
experience, but that its validity is independent of experience. (_b_)
That to which the term _a priori_ should be applied is not the
apprehension of empty space, which is individual, but the apprehension
of the nature of space in general, which is universal. (_c_) We do not
apprehend empty space before we apprehend individual spatial relations
of individual bodies or, indeed, at any time. (_d_) Though we come to
apprehend _a priori_ the nature of space in general, the apprehension
is not prior but posterior in time to the apprehension of individual
spatial relations. (_e_) It does not follow from the temporal priority
of our apprehension of individual spatial relations that our
apprehension of the nature of space in general is 'borrowed from
experience', and is therefore not _a priori_.

2. "We can never represent to ourselves that there is no space, though
we can quite well think that no objects are found in it. It must,
therefore, be considered as the condition of the possibility of
phenomena, and not as a determination dependent upon them, and it is
an _a priori_ representation, which necessarily underlies external
phenomena."[17]

    [17] B. 38, M. 24.

Here the premise is simply false. If 'represent' or 'think' means
'believe', we can no more represent or think that there are no
objects in space than that there is no space. If, on the other hand,
'represent' or 'think' means 'make a mental picture of', the assertion
is equally false. Kant is thinking of empty space as a kind of
receptacle for objects, and the _a priori_ character of our
apprehension of space lies, as before, in the supposed fact that
in order to apprehend objects in space we must begin with the
apprehension of empty space.

The examination of Kant's arguments for the _perceptive_ character
of our apprehension of space is a more complicated matter. By way of
preliminary it should be noticed that they presuppose the possibility
in general of distinguishing features of objects which belong to the
perception of them from others which belong to the conception of them.
In particular, Kant holds that our apprehension of a body as a
substance, as exercising force and as divisible, is due to our
understanding as conceiving it, while our apprehension of it as
extended and as having a shape is due to our sensibility as perceiving
it.[18] The distinction, however, will be found untenable in
principle; and if this be granted, Kant's attempt to distinguish in
this way the extension and shape of an object from its other features
can be ruled out on general grounds. In any case, it must be conceded
that the arguments fail by which he seeks to show that space in
particular belongs to perception.

    [18] B. 35, M. 22 (quoted p. 39). It is noteworthy (1) that
    the passage contains no _argument_ to show that extension and
    shape are not, equally with divisibility, _thought_ to belong
    to an object, (2) that impenetrability, which is here said
    to belong to sensation, obviously cannot do so, and (3) that
    (as has been pointed out, p. 39) the last sentence of the
    paragraph in question presupposes that we have a perception
    of empty space, and that this is a _form_ of perception.

There appears to be no way of distinguishing perception and conception
as the apprehension of different realities[19] except as the
apprehension of the individual and of the universal respectively.
Distinguished in this way, the faculty of perception is that in virtue
of which we apprehend the individual, and the faculty of conception is
that power of reflection in virtue of which a universal is made the
explicit object of thought.[20] If this be granted, the only test for
what is perceived is that it is individual, and the only test for what
is conceived is that it is universal. These are in fact the tests
which Kant uses. But if this be so, it follows that the various
characteristics of objects cannot be divided into those which are
perceived and those which are conceived. For the distinction between
universal and individual is quite general, and applies to all
characteristics of objects alike. Thus, in the case of colour, we can
distinguish colour in general and the individual colours of individual
objects; or, to take a less ambiguous instance, we can distinguish a
particular shade of redness and its individual instances. Further, it
may be said that perception is of the individual shade of red of the
individual object, and that the faculty by which we become explicitly
aware of the particular shade of red in general is that of conception.
The same distinction can be drawn with respect to hardness, or shape,
or any other characteristic of objects. The distinction, then,
between perception and conception can be drawn with respect to any
characteristic of objects, and does not serve to distinguish one from
another.

    [19] And _not_ as mutually involved in the apprehension
    of any individual reality.

    [20] This distinction is of course different to that
    previously drawn _within_ perception in the full sense
    between perception in a narrow sense and conception
    (pp. 28-9).

Kant's arguments to show that our apprehension of space belongs to
perception are two in number, and both are directed to show not, as
they should, that space is a _form_ of perception, but that it is a
_perception_.[21] The first runs thus: "Space is no discursive, or, as
we say, general conception of relations of things in general, but a
pure perception. For, in the first place, we can represent to
ourselves only one space, and if we speak of many spaces we mean
thereby only parts of one and the same unique space. Again, these
parts cannot precede the one all-embracing space as the component
parts, as it were, out of which it can be composed, but can be thought
only in it. Space is essentially one; the manifold in it, and
consequently the general conception of spaces in general, rests solely
upon limitations."[22]

    [21] Kant uses the phrase 'pure perception'; but 'pure' can
    only mean 'not containing sensation', and consequently adds
    nothing relevant.

    [22] B. 39, M. 24. The concluding sentences of the paragraph
    need not be considered.

Here Kant is clearly taking the proper test of perception. Its object,
as being an individual, is unique; there is only one of it, whereas
any conception has a plurality of instances. But he reaches his
conclusion by supposing that we first perceive empty space and then
become aware of its parts by dividing it. Parts of space are
essentially limitations of the one space; therefore to apprehend them
we must first apprehend space. And since space is _one_, it must be
object of perception; in other words, space, in the sense of the one
all-embracing space, i. e. the totality of individual spaces, is
something perceived.

The argument appears open to two objections. In the _first_ place, we
do _not_ perceive space as a whole, and then, by dividing it, come to
apprehend individual spaces. We perceive individual spaces, or,
rather, individual bodies occupying individual spaces.[23] We then
apprehend that these spaces, as spaces, involve an infinity of other
spaces. In other words, it is reflection on the general nature of
space, the apprehension of which is involved in our apprehension of
individual spaces or rather of bodies in space, which gives rise to
the apprehension of the totality[24] of spaces, the apprehension being
an act, not of perception, but of thought or conception. It is
necessary, then, to distinguish (_a_) individual spaces, which we
perceive; (_b_) the nature of space in general, of which we become
aware by reflecting upon the character of perceived individual spaces,
and which we conceive; (_c_) the totality of individual spaces, the
thought of which we reach by considering the nature of space in
general.

    [23] This contention is not refuted by the objection that our
    distinct apprehension of an individual space is always bound
    up with an indistinct apprehension of the spaces immediately
    surrounding it. For our indistinct apprehension cannot be
    supposed to be of the whole of the surrounding space.

    [24] It is here assumed that a whole or a totality can be
    infinite. Cf. p. 102.

In the _second_ place, the distinctions just drawn afford no ground
for distinguishing space as something perceived from any other
characteristic of objects as something conceived; for any other
characteristic admits of corresponding distinctions. Thus, with
respect to colour it is possible to distinguish (_a_) individual
colours which we perceive; (_b_) colouredness in general, which we
conceive by reflecting on the common character exhibited by individual
colours and which involves various kinds or species of colouredness;
(_c_) the totality of individual colours, the thought of which is
reached by considering the nature of colouredness in general.[25]

    [25] For a possible objection and the answer thereto, see
    note, p. 70.

Both in the case of colour and in that of space there is to be found
the distinction between universal and individual, and therefore also
that between conception and perception. It may be objected that after
all, as Kant points out, there is only one space, whereas there are
many individual colours. But the assertion that there is only one
space simply means that all individual bodies in space are related
spatially. This will be admitted, if the attempt be made to think of
two bodies as in different spaces and therefore as not related
spatially. Moreover, there is a parallel in the case of colour, since
individual coloured bodies are related by way of colour, e. g. as
brighter and duller; and though such a relation is different from a
relation of bodies in respect of space, the difference is due to the
special nature of the universals conceived, and does not imply a
difference between space and colour in respect of perception and
conception. In any case, space as a whole is not object of perception,
which it must be if Kant is to show that space, as being one, is
perceived; for space in this context must mean the totality of
individual spaces.

Kant's second argument is stated as follows: "Space is represented as
an infinite _given_ magnitude. Now every conception must indeed be
considered as a representation which is contained in an infinite
number of different possible representations (as their common mark),
and which therefore contains these _under itself_, but no conception
can, as such, be thought of as though it contained _in itself_ an
infinite number of representations. Nevertheless, space is so
conceived, for all parts of space _ad infinitum_ exist simultaneously.
Consequently the original representation of space is an _a priori
perception_ and not a _conception_." In other words, while a
conception implies an infinity of individuals which come under it, the
elements which constitute the conception itself (e. g. that of
triangularity or redness) are not infinite; but the elements which go
to constitute space are infinite, and therefore space is not a
conception but a perception.

Though, however, space in the sense of the infinity of spaces may be
said to contain an infinite number of spaces if it be meant that it
_is_ these infinite spaces, it does not follow, nor is it true, that
space in this sense is object of perception.

The aim of the arguments just considered, and stated in § 2 of
the _Aesthetic_, is to establish the two characteristics of our
apprehension of space,[26] from which it is to follow that space is a
property of things only as they appear to us and not as they are in
themselves. This conclusion is drawn in § 4. §§ 2 and 4 therefore
complete the argument. § 3, a passage added in the second edition
of the _Critique_, interrupts the thought, for ignoring § 2, it once
more establishes the _a priori_ and perceptive character of our
apprehension of space, and independently draws the conclusion drawn in
§ 4. Since, however, Kant draws the final conclusion in the same way
in § 3 and in § 4, and since a passage in the _Prolegomena_,[27] of
which § 3 is only a summary, gives a more detailed account of Kant's
thought, attention should be concentrated on § 3, together with the
passage in the _Prolegomena_.

    [26] viz. that it is _a priori_ and a pure perception.

    [27] §§ 6-11.

It might seem at the outset that since the arguments upon which Kant
bases the premises for his final argument have turned out invalid, the
final argument itself need not be considered. The argument, however,
of § 3 ignores the preceding arguments for the _a priori_ and
perceptive character of our apprehension of space. It returns to the
_a priori_ synthetic character of geometrical judgements, upon which
stress is laid in the Introduction, and appeals to this as the
justification of the _a priori_ and perceptive character of our
apprehension of space.

The argument of § 3 runs as follows: "Geometry is a science which
determines the properties of space synthetically and yet _a priori_.
What, then, must be the representation of space, in order that such a
knowledge of it may be possible? It must be originally perception, for
from a mere conception no propositions can be deduced which go beyond
the conception, and yet this happens in geometry. But this perception
must be _a priori_, i. e. it must occur in us before all
sense-perception of an object, and therefore must be pure, not
empirical perception. For geometrical propositions are always
apodeictic, i. e. bound up with the consciousness of their necessity
(e. g. space has only three dimensions), and such propositions cannot
be empirical judgements nor conclusions from them."

"Now how can there exist in the mind an external perception[28] which
precedes[29] the objects themselves, and in which the conception of
them can be determined _a priori_? Obviously not otherwise than in so
far as it has its seat in the subject only, as the formal nature of
the subject to be affected by objects and thereby to obtain _immediate
representation_, i. e. _perception_ of them, and consequently only as
the form of the external sense in general."[30]

    [28] 'External perception' can only mean perception of what
    is spatial.

    [29] _Vorhergeht._

    [30] 'Formal nature _to be affected by objects_' is not
    relevant to the context.

Here three steps are taken. From the _synthetic_ character of
geometrical judgements it is concluded that space is not something
which we _conceive_, but something which we _perceive_. From their _a
priori_ character, i. e. from the consciousness of necessity involved,
it is concluded that the perception of space must be _a priori_ in a
new sense, that of taking place _before_ the perception of objects in
it.[31] From the fact that we perceive space before we perceive
objects in it, and thereby are able to anticipate the spatial
relations which condition these objects, it is concluded that space is
only a characteristic of our perceiving nature, and consequently that
space is a property not of things in themselves, but only of things as
perceived by us.[32]

    [31] Cf. B. 42, M. 26 (a) fin., (b) second sentence.

    [32] Cf. B. 43, M. 26-7.

Two points in this argument are, even on the face of it, paradoxical.
Firstly, the term _a priori_, as applied not to geometrical judgements
but to the perception of space, is given a temporal sense; it means
not something whose validity is independent of experience and which is
the manifestation of the nature of the mind, but something which takes
place before experience. Secondly, the conclusion is not that the
perception of space _is the manifestation of_ the mind's perceiving
nature, but that it _is_ the mind's perceiving nature. For the
conclusion is that space[33] is the formal nature of the subject to be
affected by objects, and therefore the form of the external sense in
general. Plainly, then, Kant here confuses an actual perception and a
form or way of perceiving. These points, however, are more explicit in
the corresponding passage in the _Prolegomena_.[34]

    [33] Kant draws no distinction between space and the
    perception of space, or, rather, habitually speaks of space
    as a perception. No doubt he considers that his view that
    space is only a characteristic of phenomena justifies
    the identification of space and the perception of it.
    Occasionally, however, he distinguishes them. Thus he
    sometimes speaks of the representation of space (e. g.
    B. 38-40, M. 23-4); in _Prol._, § 11, he speaks of a pure
    perception of space and time; and in B. 40, M. 25, he says
    that our representation of space must be perception. But this
    language is due to the pressure of the facts, and not to his
    general theory; cf. pp. 135-6.

    [34] §§ 6-11.

It begins thus: "Mathematics carries with it thoroughly apodeictic
certainty, that is, absolute necessity, and, therefore, rests on no
empirical grounds, and consequently is a pure product of reason, and,
besides, is thoroughly synthetical. How, then, is it possible for
human reason to accomplish such knowledge entirely _a priori_?... But
we find that all mathematical knowledge has this peculiarity, that it
must represent its conception previously in _perception_, and indeed
_a priori_, consequently in a perception which is not empirical but
pure, and that otherwise it cannot take a single step. Hence its
judgements are always _intuitive_.... This observation on the nature
of mathematics at once gives us a clue to the first and highest
condition of its possibility, viz. that there must underlie it _a pure
perception_ in which it can exhibit or, as we say, _construct_ all its
conceptions in the concrete and yet _a priori_. If we can discover
this pure perception and its possibility, we may thence easily explain
how _a priori_ synthetical propositions in pure mathematics are
possible, and consequently also how the science itself is possible.
For just as empirical perception enables us without difficulty to
enlarge synthetically in experience the conception which we frame of
an object of perception through new predicates which perception itself
offers us, so pure perception also will do the same, only with the
difference that in this case the synthetical judgement will be _a
priori_ certain and apodeictic, while in the former case it will be
only _a posteriori_ and empirically certain; for the latter [i. e. the
empirical perception on which the _a posteriori_ synthetic judgement
is based] contains only that which is to be found in contingent
empirical perception, while the former [i. e. the pure perception on
which the _a priori_ synthetic judgement is based] contains that which
is bound to be found in pure perception, since, as _a priori_
perception, it is inseparably connected with the conception _before
all experience_ or individual sense-perception."

This passage is evidently based upon the account which Kant gives in
the _Doctrine of Method_ of the method of geometry.[35] According to
this account, in order to apprehend, for instance, that a three-sided
figure must have three angles, we must draw in imagination or on paper
an individual figure corresponding to the conception of a three-sided
figure. We then see that the very nature of the act of construction
involves that the figure constructed must possess three angles as well
as three sides. Hence, perception being that by which we apprehend the
individual, a perception is involved in the act by which we form a
geometrical judgement, and the perception can be called _a priori_, in
that it is guided by our _a priori_ apprehension of the necessary
nature of the act of construction, and therefore of the figure
constructed.

    [35] B. 740 ff., M. 434 ff. Compare especially the following:
    "_Philosophical_ knowledge is _knowledge of reason_ by means
    of _conceptions_; mathematical knowledge is knowledge by
    means of the _construction_ of conceptions. But the
    _construction_ of a conception means the _a priori_
    presentation of a perception corresponding to it. The
    construction of a conception therefore demands a
    _non-empirical_ perception, which, therefore, as a
    perception, is an _individual_ object, but which none the
    less, as the construction of a conception (a universal
    representation), must express in the representation universal
    validity for all possible perceptions which come under that
    conception. Thus I construct a triangle by presenting the
    object corresponding to the conception, either by mere
    imagination in pure perception, or also, in accordance with
    pure perception, on paper in empirical perception, but in
    both cases completely _a priori_, without having borrowed
    the pattern of it from any experience. The individual drawn
    figure is empirical, but nevertheless serves to indicate the
    conception without prejudice to its universality, because in
    this empirical perception we always attend only to the act of
    construction of the conception, to which many determinations,
    e. g. the magnitude of the sides and of the angles, are
    wholly indifferent, and accordingly abstract from these
    differences, which do not change the conception of the
    triangle."

The account in the _Prolegomena_, however, differs from that of the
_Doctrine of Method_ in one important respect. It asserts that the
perception involved in a mathematical judgement not only may, but
must, be pure, i. e. must be a perception in which no spatial object
is present, and it implies that the perception must take place
_before_ all experience of actual objects.[36] Hence _a priori_,
applied to perception, has here primarily, if not exclusively, the
temporal meaning that the perception takes place _antecedently to all
experience_.[37]

    [36] This becomes more explicit in § 8 and ff.

    [37] This is also, and more obviously, implied in §§ 8-11.

The thought of the passage quoted from the _Prolegomena_ can be stated
thus: 'A mathematical judgement implies the perception of an
individual figure antecedently to all experience. This may be said to
be the first condition of the possibility of mathematical judgements
which is revealed by reflection. There is, however, a prior or higher
condition. The perception of an individual figure involves as its
basis another pure perception. For we can only construct and therefore
perceive an individual figure in empty space. Space is that _in which_
it must be constructed and perceived. A perception[38] of empty space
is, therefore, necessary. If, then, we can discover how this
perception is possible, we shall be able to explain the possibility of
_a priori_ synthetical judgements of mathematics.'

    [38] _Pure_ perception only means that the space perceived is
    empty.

Kant continues as follows: "But with this step the difficulty seems to
increase rather than to lessen. For henceforward the question is '_How
is it possible to perceive anything a priori?_' A perception is such a
representation as would immediately depend upon the presence of the
object. Hence it seems impossible _originally_ to perceive _a priori_,
because perception would in that case have to take place without an
object to which it might refer, present either formerly or at the
moment, and accordingly could not be perception.... How can
_perception_ of the object precede the object itself?"[39] Kant here
finds himself face to face with the difficulty created by the
preceding section. Perception, as such, involves the actual presence
of an object; yet the pure perception of space involved by
geometry--which, as pure, is the perception of empty space, and which,
as the perception of empty space, is _a priori_ in the sense of
temporally prior to the perception of actual objects--presupposes that
an object is not actually present.

    [39] _Prol._ § 8.

The solution is given in the next section. "Were our perception
necessarily of such a kind as to represent things _as they are in
themselves_, no perception would take place _a priori_, but would
always be empirical. For I can only know what is contained in the
object in itself, if it is present and given to me. No doubt it is
even then unintelligible how the perception of a present thing should
make me know it as it is in itself, since its qualities cannot migrate
over into my faculty of representation; but, even granting this
possibility, such a perception would not occur _a priori_, i. e.
before the object was presented to me; for without this presentation,
no basis of the relation between my representation and the object can
be imagined; the relation would then have to rest upon inspiration. It
is therefore possible only in one way for my perception to precede the
actuality of the object and to take place as _a priori_ knowledge,
viz. _if it contains nothing but the form of the sensibility, which
precedes in me, the subject, all actual impressions through which I am
affected by objects_. For I can know _a priori_ that objects of the
senses can only be perceived in accordance with this form of the
sensibility. Hence it follows that propositions which concern merely
this form of sensuous perception will be possible and valid for
objects of the senses, and in the same way, conversely, that
perceptions which are possible _a priori_ can never concern any things
other than objects of our senses."

This section clearly constitutes the turning-point in Kant's argument,
and primarily expresses, in an expanded form, the central doctrine of
§ 3 of the _Aesthetic_, that an external perception anterior to
objects themselves, and in which our conceptions of objects can be
determined _a priori_, is possible, if, and only if, it has its seat
in the subject as its formal nature of being affected by objects, and
consequently as the form of the external sense in general. It argues
that, since this is true, and since geometrical judgements involve
such a perception anterior to objects, space must be only the[40] form
of sensibility.

    [40] _The_ and not _a_, because, for the moment, time is
    ignored.

Now why does Kant think that this conclusion follows? Before we can
answer this question we must remove an initial difficulty. In this
passage Kant unquestionably identifies a form of perception with an
actual perception. It is at once an actual perception and a capacity
of perceiving. This is evident from the words, "It is possible only in
one way for my perception to precede the actuality of the object ...
viz. _if it contains nothing but the form of the sensibility_."[41]
The identification becomes more explicit a little later. "A pure
perception (of space and time) can underlie the empirical perception
of objects, because it is nothing but the mere form of the
sensibility, which precedes the actual appearance of the objects, in
that it in fact first makes them possible. Yet this faculty of
perceiving _a priori_ affects not the matter of the phenomenon, i. e.
that in it which is sensation, for this constitutes that which is
empirical, but only its form, viz. space and time."[42] His argument,
however, can be successfully stated without this identification. It is
only necessary to re-write his cardinal assertion in the form 'the
perception of space must be nothing but the _manifestation_ of the
form of the sensibility'. Given this modification, the question
becomes, 'Why does Kant think that the perception of empty space,
involved by geometrical judgements, can be only a manifestation of our
perceiving nature, and not in any way the apprehension of a real
quality of objects?' The answer must be that it is because he thinks
that, while in empirical perception a real object is present, in the
perception of empty space a real object is not present. He regards
this as proving that the latter perception is only of something
subjective or mental. "Space and time, by being pure _a priori_
perceptions, prove that they are mere forms of our sensibility which
must precede all empirical perception, i. e. sense-perception of
actual objects."[43] His main conclusion now follows easily enough. If
in perceiving empty space we are only apprehending a manifestation of
our perceiving nature, what we apprehend in a geometrical judgement is
really a law of our perceiving nature, and therefore, while it _must_
apply to our perceptions of objects or to objects as perceived, it
_cannot_ apply to objects apart from our perception, or, at least,
there is no ground for holding that it does so.

    [41] _Prol._, § 9.

    [42] _Prol._, § 11.

    [43] _Prol._, § 10.

If, however, this fairly represents Kant's thought, it must be allowed
that the conclusion which he should have drawn is different, and even
that the conclusion which he does draw is in reality incompatible with
his starting-point.

His starting-point is the view that the truth of geometrical
judgements presupposes a perception of empty space, in virtue of which
we can discover rules of spatial relation which must apply to all
spatial objects subsequently perceived. His problem is to discover the
presupposition of this presupposition. The proper answer must be, not
that space is a form of sensibility or a way in which objects appear
to us, but that space is the form of all objects, i. e. that all
objects are spatial.[44] For in that case they must be subject to the
laws of space, and therefore if we can discover these laws by a study
of empty space, the only condition to be satisfied, if the objects of
subsequent perception are to conform to the laws which we discover, is
that all objects should be spatial. Nothing is implied which enables
us to decide whether the objects are objects as they are in themselves
or objects as perceived; for in either case the required result
follows. If in empirical perception we apprehend things only as they
appear to us, and if space is the form of them as they appear to us,
it will no doubt be true that the laws of spatial relation which we
discover must apply to things as they appear to us. But on the other
hand, if in empirical perception we apprehend things as they are, and
if space is their form, i. e. if things are spatial, it will be
equally true that the laws discovered by geometry must apply to things
as they are.

    [44] Kant expresses the assertion that space is the form of
    all objects by saying that space is the form of _phenomena_.
    This of course renders easy an unconscious transition from
    the thesis that space is the form of objects to the quite
    different thesis that space is the form of sensibility; cf.
    p. 39.

Again, Kant's starting-point really commits him to the view that space
is a characteristic of things as they are. For--paradoxical though it
may be--his problem is to explain the possibility of _perceiving a
priori_, i. e. of _perceiving_ the characteristics of an object
anterior to the actual presence of the object in perception.[45] This
implies that _empirical_ perception, which involves the actual
presence of the object, involves no difficulty; in other words, it is
implied that empirical perception is of objects as they are. And we
find Kant admitting this to the extent of allowing _for the sake of
argument_ that the perception of a present thing can make us know the
thing as it is in itself.[46] But if empirical perception gives us
things as they are, and if, as is the case, and as Kant really
presupposes, the objects of empirical perception are spatial, then,
since space is their form, the judgements of geometry must relate to
things as they are. It is true that on this view Kant's first
presupposition of geometrical judgements has to be stated by saying
that we are able to perceive a real characteristic of things in space,
before we perceive the things; and, no doubt, Kant thinks this
impossible. According to him, when we perceive empty space no object
is present, and therefore what is before the mind must be merely
mental. But no greater difficulty is involved than that involved in
the corresponding supposition required by Kant's own view. It is
really just as difficult to hold that we can perceive a characteristic
of things as they appear to us _before_ they appear, as to hold that
we can perceive a characteristic of them as they are in themselves
_before_ we perceive them.

    [45] Cf. _Prol._, Section 8.

    [46] _Prol._, § 9 (cf. p. 55).

The fact is that the real difficulty with which Kant is grappling in
the _Prolegomena_ arises, not from the supposition that spatial bodies
are things in themselves, but from the supposed presupposition of
geometry that we must be able to perceive empty space before we
perceive bodies in it. It is, of course, impossible to defend the
perception of empty space, but _if_ it be maintained, the space
perceived must be conceded to be not, as Kant thinks, something mental
or subjective, but a real characteristic of things. For, as has been
pointed out, the paradox of pure perception is reached solely through
the consideration that, while in empirical perception we perceive
objects, in pure perception we do not, and since the objects of
empirical perception are spatial, space must be a real characteristic
of them.

The general result of the preceding criticism is that Kant's
conclusion does not follow from the premises by which he supports it.
It should therefore be asked whether it is not possible to take
advantage of this hiatus by presenting the argument for the merely
phenomenal character of space without any appeal to the possibility of
perceiving empty space. For it is clear that what was primarily before
Kant, in writing the _Critique_, was the _a priori_ character of
geometrical judgements themselves, and not the existence of a
perception of empty space which they were held to presuppose.[47]

    [47] The difficulty with which Kant is struggling in the
    _Prolegomena_, §§ 6-11, can be stated from a rather different
    point of view by saying that the thought that geometrical
    judgements imply a perception of empty space led him to apply
    the term '_a priori_' to perception as well as to judgement.
    The term, _a priori_, applied to judgements has a valid
    meaning; it means, not that the judgement is made prior to
    all experience, but that it is not based upon experience,
    being originated by the mind in virtue of its own powers of
    thinking. Applied to perception, however, '_a priori_' must
    mean prior to all experience, and, since the object of
    perception is essentially individual (cf. B. 741, M. 435),
    this use of the term gives rise to the impossible task of
    explaining how a perception can take place prior to the
    actual experience of an individual in perception (cf.
    _Prol._, § 8).

If, then, the conclusion that space is only the form of sensibility
can be connected with the _a priori_ character of geometrical
judgements without presupposing the existence of a perception of empty
space, his position will be rendered more plausible.

This can be done as follows. The essential characteristic of a
geometrical judgement is not that it takes place prior to experience,
but that it is not based upon experience. Thus a judgement, arrived at
by an activity of the mind in which it remains within itself and does
not appeal to actual experience of the objects to which the judgement
relates, is implied to hold good of those objects. If the objects were
things as they are in themselves, the validity of the judgement could
not be justified, for it would involve the gratuitous assumption that
a necessity of thought is binding on things which _ex hypothesi_ are
independent of the nature of the mind. If, however, the objects in
question are things as perceived, they will be through and through
conditioned by the mind's perceiving nature; and, consequently, if a
geometrical rule, e. g. that a three-sided figure must have three
angles, is really a law of the mind's perceiving nature, all
individual perceptions, i. e. all objects as perceived by us, will
necessarily conform to the law. Therefore, in the latter case, and in
that only, will the universal validity of geometrical judgements be
justified. Since, then, geometrical judgements are universally valid,
space, which is that of which geometrical laws are the laws, must be
merely a form of perception or a characteristic of objects as
perceived by us.

This appears to be the best form in which the substance of Kant's
argument, stripped of unessentials, can be stated. It will be
necessary to consider both the argument and its conclusion.

The argument, so stated, is undeniably plausible. Nevertheless,
examination of it reveals two fatal defects. In the first place, its
starting-point is false. To Kant the paradox of geometrical judgements
lies in the fact that they are not based upon an appeal to experience
of the things to which they relate. It is implied, therefore, that
judgements which are based on experience involve no paradox, and for
the reason that in experience we apprehend things as they are.[48] In
contrast with this, it is implied that in geometrical judgements the
connexion which we apprehend is not real, i. e. does not relate to
things as they are. Otherwise, there would be no difficulty; if in
geometry we apprehended rules of connexion relating to things as they
are, we could allow without difficulty that the things must conform to
them. No such distinction, however, can be drawn between _a priori_
and empirical judgements. For the necessity of connexion, e. g.
between being a three-sided figure and being a three-angled figure, is
as much a characteristic of things as the empirically-observed shape
of an individual body, e. g. a table. Geometrical judgements,
therefore, cannot be distinguished from empirical judgements on the
ground that in the former the mind remains within itself, and does not
immediately apprehend fact or a real characteristic of reality.[49]
Moreover, since in a geometrical judgement we do in fact think that we
are apprehending a real connexion, i. e. a connexion which applies to
things and to things as they are in themselves, to question the
reality of the connexion is to question the validity of thinking
altogether, and to do this is implicitly to question the validity of
our thought about the nature of our own mind, as well as the validity
of our thought about things independent of the mind. Yet Kant's
argument, in the form in which it has just been stated, presupposes
that our thought is valid at any rate when it is concerned with our
perceptions of things, even if it is not valid when concerned with the
things as they are in themselves.

    [48] Cf. p. 17.

    [49] For the reasons which led Kant to draw this distinction
    between empirical and _a priori_ judgements, cf. pp. 21-2.

This consideration leads to the second criticism. The supposition that
space is only a form of perception, even if it be true, _in no way
assists_ the explanation of the universal validity of geometrical
judgements. Kant's argument really confuses a _necessity_ of relation
with the _consciousness of a necessity_ of relation. No doubt, if it
be a law of our perceiving nature that, whenever we perceive an object
as a three-sided figure, the object as perceived contains three
angles, it follows that any object as perceived will conform to this
law; just as if it be a law of things as they are in themselves that
three-sided figures contain three angles, all three-sided figures will
in themselves have three angles. But what has to be explained is the
universal applicability, not of a law, but of a judgement about a law.
For Kant's real problem is to explain why _our judgement_ that a
three-sided figure must contain three angles must apply to all
three-sided figures. Of course, if it be granted that in the judgement
we apprehend the true law, the problem may be regarded as solved. But
how are we to know that what we judge _is_ the true law? The answer is
in no way facilitated by the supposition that the judgement relates to
our perceiving nature. It can just as well be urged that what we think
to be a necessity of our perceiving nature is not a necessity of it,
as that what we think to be a necessity of things as they are in
themselves is not a necessity of them. The best, or rather the only
possible, answer is simply that that of which we apprehend the
necessity must be true, or, in other words, that we _must_ accept the
validity of thought. Hence nothing is gained by the supposition that
space is a form of sensibility. If what we judge to be necessary is,
as such, valid, a judgement relating to things in themselves will be
as valid as a judgement relating to our perceiving nature.[50]

    [50] The same criticism can be urged against Kant's appeal to
    the necessity of _constructing_ geometrical figures. The
    conclusion drawn from the necessity of construction is stated
    thus: "If the object (the triangle) were something in itself
    without relation to you the subject, how could you say that
    that which lies necessarily in your subjective conditions of
    constructing a triangle must also necessarily belong to the
    triangle in itself?" (B. 65, M. 39). Kant's thought is that
    the laws of the mind's constructing nature must apply to
    objects, if, and only if, the objects are the mind's own
    construction. Hence it is open to the above criticism if, in
    the criticism, 'construct' be substituted for 'perceive'.

This difficulty is concealed from Kant by his insistence on the
_perception_ of space involved in geometrical judgements. This leads
him at times to identify the judgement and the perception, and,
therefore, to speak of the judgement as a perception. Thus we find him
saying that mathematical judgements are always _perceptive_,[51] and
that "It is only possible for my perception to precede the actuality
of the object and take place as _a priori_ knowledge, if &c."[52]
Hence, if, in addition, a geometrical judgement, as being a judgement
about a necessity, be identified with a necessity of judging, the
conformity of things to these universal judgements will become the
conformity of things to rules or necessities of our judging, i. e. of
our perceiving nature, and Kant's conclusion will at once follow.[53]
Unfortunately for Kant, a geometrical judgement, however closely
related to a perception, must itself, as the apprehension of what is
necessary and universal, be an act of thought rather than of
perception, and therefore the original problem of the conformity of
things to our mind can be forced upon him again, even after he thinks
that he has solved it, in the new form of that of the conformity
within the mind of perceiving to thinking.

    [51] _Prol._, § 7.

    [52] _Prol._, § 9.

    [53] Cf. (_Introduction_, B. xvii, M. xxix): "But if the
    object (as object of the senses) conforms to the nature of
    our faculty of perception, I can quite well represent to
    myself the possibility of _a priori_ knowledge of it [i. e.
    mathematical knowledge]."

The fact is simply that the universal validity of geometrical
judgements can in no way be 'explained'. It is not in the least
explained or made easier to accept by the supposition that objects
are 'phenomena'. These judgements must be accepted as being what we
presuppose them to be in making them, viz. the direct apprehension of
necessities of relation between real characteristics of real things.
To explain them by reference to the phenomenal character of what is
known is really--though contrary to Kant's intention--to throw doubt
upon their validity; otherwise, they would not need explanation. As a
matter of fact, it is _impossible_ to question their validity. In the
act of judging, doubt is impossible. Doubt can arise only when
we subsequently reflect and temporarily lose our hold upon the
consciousness of necessity in judging.[54] The doubt, however, since
it is non-existent in our geometrical consciousness, is really
groundless,[55] and, therefore, the problem to which it gives rise is
unreal. Moreover if, _per impossibile_, doubt could be raised, it
could not be set at rest. No vindication of a judgement in which we
are conscious of a necessity could do more than take the problem a
stage further back, by basing it upon some other consciousness of a
necessity; and since this latter judgement could be questioned for
precisely the same reason, we should only be embarking upon an
infinite process.

    [54] Cf. Descartes, _Princ. Phil._ i. § 13, and _Medit._ v
    sub fin.

    [55] The view that kinds of space other than that with which
    we are acquainted are possible, though usually held and
    discussed by mathematicians, belongs to them _qua_
    metaphysicians, and not _qua_ mathematicians.

We may now consider Kant's conclusion in abstraction from the
arguments by which he reaches it. It raises three main difficulties.

In the first place, it is not the conclusion to be expected from
Kant's own standpoint. The phenomenal character of space is inferred,
not from the fact that we make judgements at all, but from the fact
that we make judgements of a particular kind, viz. _a priori_
judgements. From this point of view empirical judgements present no
difficulty. It should, therefore, be expected that the qualities which
we attribute to things in empirical judgements are not phenomenal, but
belong to things as they are. Kant himself implies this in drawing his
conclusion concerning the nature of space. "Space does not represent
any quality of things in themselves or things in relation to one
another; that is, it does not represent any determination of things
which would attach to the objects themselves and would remain, even
though we abstracted from all subjective conditions of perception. For
neither absolute nor relative[56] determinations of objects can be
perceived prior to the existence of the things to which they belong,
and therefore not _a priori_."[57] It is, of course, implied that in
experience, where we do not discover determinations of objects prior
to the existence of the objects, we do apprehend determinations of
things as they are in themselves, and not as they are in relation to
us. Thus we should expect the conclusion to be, not that all that we
know is phenomenal--which is Kant's real position--but that spatial
(and temporal) relations alone are phenomenal, i. e. that they alone
are the result of a transmutation due to the nature of our perceiving
faculties.[58] This conclusion would, of course, be absurd, for what
Kant considers to be the empirically known qualities of objects
disappear, if the spatial character of objects is removed. Moreover,
Kant is prevented by his theory of perception from seeing that this is
the real solution of his problem, absurd though it may be. Since
perception is held to arise through the origination of sensations by
things in themselves, empirical knowledge is naturally thought of as
knowledge about sensations, and since sensations are palpably within
the mind, and are held to be due to things in themselves, knowledge
about sensations can be regarded as phenomenal.

    [56] The first sentence shows that 'relative determinations'
    means, not 'determinations of objects in relation to us', but
    'determinations of objects in relation to one another.' Cf.
    B. 37, M. 23; and B. 66 fin., 67 init., M. 40 (where these
    meanings are confused).

    [57] B. 42, M. 26.

    [58] This conclusion is also to be expected because,
    inconsistently with his real view, Kant is here (B. 41-2, M.
    25-6) under the influence of the presupposition of our
    ordinary consciousness that in perception we are confronted
    by things in themselves, known to be spatial, and not by
    appearances produced by unknown things in themselves. Cf. (B.
    41, M. 25) "and thereby of obtaining immediate representation
    of them [i. e. objects];" and (B. 42, M. 26) "the receptivity
    of the subject to be affected by objects necessarily precedes
    all perceptions of these objects." These sentences identify
    things in themselves and bodies in space, and thereby imply
    that in empirical perception we perceive things in themselves
    and as they _are_.

On the other hand, if we consider Kant's conclusion from the point of
view, not of the problem which originates it, but of the distinction
in terms of which he states it, viz. that between things as they are
in themselves and things as perceived by us, we are led to expect the
contrary result. Since perception is the being affected by things, and
since the nature of the affection depends upon the nature of our
capacity of being affected, in _all_ perception the object will become
distorted or transformed, as it were, by our capacity of being
affected. The conclusion, therefore, should be that in all judgements,
empirical as well as _a priori_, we apprehend things only as
perceived. The reason why Kant does not draw this conclusion is
probably that given above, viz. that by the time Kant reaches the
solution of his problem empirical knowledge has come to relate to
sensation only; consequently, it has ceased to occur to him that
empirical judgements could possibly give us knowledge of things as
they are. Nevertheless, Kant should not have retained in his
formulation of the problem a distinction irreconcilable with his
solution of it; and if he had realized that he was doing so he might
have been compelled to modify his whole view.

The second difficulty is more serious. If the truth of geometrical
judgements presupposes that space is only a property of objects as
perceived by us, it is a paradox that geometricians should be
convinced, as they are, of the truth of their judgements. They
undoubtedly think that their judgements apply to things as they are in
themselves, and not merely as they appear to us. They certainly do not
think that the relations which they discover apply to objects only as
perceived. Not only, therefore, do they not think that bodies in space
are phenomena, but they do not even leave it an open question whether
bodies are phenomena or not. Hence, if Kant be right, they are really
in a state of illusion, for on his view the true geometrical judgement
should include in itself the phenomenal character of spatial
relations; it should be illustrated by expressing Euclid I. 5 in
the form that the equality of the angles at the base of an isosceles
triangle belongs to objects as perceived. Kant himself lays this down.
"The proposition 'all objects are beside one another in space'
is valid under[59] the limitation that these things are taken as
objects of our sensuous perception. If I join the condition to the
perception, and say 'all things, as external phenomena, are beside
one another in space', the rule is valid universally, and without
limitation."[60] Kant, then, is in effect allowing that it is possible
for geometricians to make judgements, of the necessity of which
they are convinced, and yet to be wrong; and that, therefore, the
apprehension of the necessity of a judgement is no ground of its
truth. It follows that the truth of geometrical judgements can no
longer be accepted as a starting-point of discussion, and, therefore,
as a ground for inferring the phenomenal character of space.

    [59] A. reads 'only under'

    [60] B. 43, M. 27.

There seems, indeed, one way of avoiding this consequence, viz. to
suppose that for Kant it was an absolute starting-point, which nothing
would have caused him to abandon, that only those judgements of which
we apprehend the necessity are true. It would, of course, follow that
geometricians would be unable to apprehend the necessity of
geometrical judgements, and therefore to make such judgements, until
they had discovered that things as spatial were only phenomena. It
would not be enough that they should think that the phenomenal or
non-phenomenal character of things as spatial must be left an open
question for the theory of knowledge to decide. In this way the
necessity of admitting the illusory character of geometry would be
avoided. The remedy, however, is at least as bad as the disease.
For it would imply that geometry must be preceded by a theory of
knowledge, which is palpably contrary to fact. Nor could Kant accept
it; for he avowedly bases his theory of knowledge, i. e. his view
that objects as spatial are phenomena, upon the truth of geometry;
this procedure would be circular if the making of true geometrical
judgements was allowed to require the prior adoption of his theory of
knowledge.

The third difficulty is the most fundamental. Kant's conclusion (and
also, of course, his argument) presupposes the validity of the
distinction between phenomena and things in themselves. If, then, this
distinction should prove untenable in principle, Kant's conclusion
with regard to space must fail on general grounds, and it will even
have been unnecessary to consider his arguments for it. The importance
of the issue, however, requires that it should be considered in a
separate chapter.

    NOTE to page 47.

    The argument is not affected by the contention that, while
    the totality of spaces is infinite, the totality of colours
    or, at any rate, the totality of instances of some other
    characteristic of objects is finite; for this difference
    will involve no difference in respect of perception and
    conception. In both cases the apprehension that there is a
    totality will be reached in the same way, i. e. through the
    _conception_ of the characteristic in general, and the
    apprehension in the one case that the totality is infinite
    and in the other that it is finite will depend on the
    apprehension of the special nature of the characteristic in
    question.




CHAPTER IV

PHENOMENA AND THINGS IN THEMSELVES


The distinction between phenomena and things in themselves can be best
approached by considering Kant's formulation of the alternative views
of the nature of space and time. "What are space and time? Are they
real existences? Or are they merely determinations or relations of
things, such, however, as would also belong to them in themselves,
even if they were not perceived, or are they attached to the form of
perception only, and consequently to the subjective nature of our
mind, without which these predicates can never be attributed to any
thing?"[1]

    [1] B. 37, M. 23.

Of these three alternatives, the first can be ignored. It is opposed
to the second, and is the view that space and time are things rather
than relations between things. This opposition falls within the first
member of the wider opposition between things as they are in
themselves and things as they are as perceived, and Kant, and indeed
any one, would allow that if space and time belong to things as they
are in themselves and not to things only as perceived, they are
relations between things rather than things. The real issue,
therefore, lies between the second and third alternatives. Are space
and time relations between things which belong to them both in
themselves and also as perceived by us, or are they relations which
belong to things only as perceived?

To this question we may at once reply that, inasmuch as it involves an
impossible antithesis, it is wholly unreal. The thought of a property
or a relation which belongs to things as perceived involves a
contradiction. To take Plato's example, suppose that we are looking at
a straight stick, partially immersed in water. If we have not
previously seen the stick, and are ignorant of the laws of refraction,
we say that the stick is bent. If, however, we learn the effect of
refraction, and observe the stick from several positions, we alter our
assertion. We say that the stick is not really bent, but only looks or
appears bent to us. But, if we reflect at all, we do not express our
meaning by saying that the stick _is_ bent to us as perceiving, though
not in reality.[2] The word 'is' essentially relates to what really
is. If, therefore, the phrase 'to us as perceiving' involves an
opposition to the phrase 'in reality', as it must if it is to be a
real qualification of 'is', it cannot rightly be added to the word
'is'. To put the matter more explicitly, the assertion that something
_is_ so and so implies that it is so and so in itself, whether it be
perceived or not, and therefore the assertion that something is so and
so to us as perceiving, though not in itself, is a contradiction in
terms. The phrase 'to us as perceiving', as a restriction upon the
word 'is', merely takes back the precise meaning of the word 'is'.
That to which the phrase can be added is not the word 'is', but the
word 'looks' or 'appears'. We can rightly say that the stick looks or
appears bent to us as perceiving. But even then the addition only
helps to make explicit the essential meaning of 'appears', for
'appears' really means 'appears to us', and 'as perceiving' only
repeats the meaning of 'appears' from the side of the perceiving
subject as opposed to that of the object perceived. The essential
point, however, is thereby brought out that the phrase 'to us as
perceiving' essentially relates not to what a thing is, but to what it
looks or appears to us.

    [2] Similarly, we do not say--if we mean what we say--of a
    man who is colour blind that an object which others call blue
    _is_ pink to him or to his perception, but that it _looks_
    pink to him.

What, then, is the proper statement of Kant's view that space is a
determination of things only as they appear to us, and not as they are
in themselves? It should be said that things are not in reality
spatial, but only look or appear spatial to us. It should not be said
that they _are_ spatial for our perception, though not in themselves.
Thus the view properly stated implies that space is an illusion,
inasmuch as it is not a real property of things at all. This
implication, however, is precisely the conclusion which Kant wishes to
avoid. He takes infinite trouble to explain that he does not hold
space and time to be illusions.[3] Though _transcendentally ideal_
(i. e. though they do not belong to things in themselves), they are
_empirically real_. In other words, space and time are real relations
of _something_, though not of things in themselves.

    [3] B. 44, 52, 53-4, 62-3, 69-70; M. 27, 31-2, 37-8, 41-2;
    _Prol._, § 13, Remark iii.

How, then, does Kant obtain something of which space and time can be
regarded as really relations? He reaches it by a transition which at
first sight seems harmless. In stating the fact of perception he
substitutes for the assertion that things appear so and so to us the
assertion that things produce appearances in us. In this way, instead
of an assertion which relates to the thing and states what it is not
but only appears, he obtains an assertion which introduces a second
reality distinct from the thing, viz. an appearance or phenomenon, and
thereby he gains something other than the thing to which space can be
attached as a real predicate. He thus gains something in respect of
which, with regard to spatial relations we can be said to have
_knowledge_ and not illusion. For the position now is that space,
though not a property of things in themselves, _is_ a property of
phenomena or appearances; in other words, that while things in
themselves are not spatial, phenomena and appearances _are_ spatial.
As evidence of this transition, it is enough to point out that, while
he states the _problem_ in the form 'Are things in themselves spatial
or are they only spatial as appearing to us?'[4] he usually states the
_conclusion_ in the form 'Space is the form of phenomena', i. e.
phenomena are spatial. A transition is thereby implied from 'things as
appearing' to 'appearances'. At the same time, it is clear that Kant
is not aware of the transition, but considers the expressions
equivalent, or, in other words, fails to distinguish them. For both
modes of stating the conclusion are to be found even in the same
sentence. "This predicate [space] is applied to things only in so far
as they appear to us, i. e. are objects of sensibility [i. e.
phenomena]."[5] Again, the common phrase 'things as phenomena' implies
the same confusion. Moreover, if Kant had realized that the transition
was more than one of phraseology he must have seen that it was
necessary to recast his argument.

    [4] This is Kant's way of putting the question which should
    be expressed by asking, 'Are things spatial, or do they only
    look spatial?'

    [5] B. 43, M. 26. Cf. _Prol._, § 9 fin. with § 10 init.

It may be said, then, that Kant is compelled to end with a different
distinction from that with which he begins. He begins with the
distinction between things as they are in themselves and things as
they appear to us, the distinction relating to one and the same
reality regarded from two different points of view. He ends with the
distinction between two different realities, things-in-themselves,[6]
external to, in the sense of independent of, the mind, and phenomena
or appearances within it. Yet if his _argument_ is to be valid, the
two distinctions should be identical, for it is the first distinction
to which the argument appeals.[7] In fact, we find him expressing what
is to him the same distinction now in the one way and now in the other
as the context requires.

    [6] It should be noticed that 'things-in-themselves' and
    'things as they are in themselves' have a different meaning.

    [7] Cf. p. 55 and ff.

The final form of Kant's conclusion, then, is that while things in
themselves are not, or, at least, cannot be known to be spatial,
'phenomena,' or the appearances produced in us by things in
themselves, are spatial. Unfortunately, the conclusion in this form is
no more successful than it is in the former form, that things are
spatial only as perceived. Expressed by the formula 'phenomena are
spatial', it has, no doubt, a certain plausibility; for the word
'phenomena' to some extent conceals the essentially mental character
of what is asserted to be spatial. But the plausibility disappears on
the substitution of 'appearances'--the true equivalent of Kant's
_Erscheinungen_--for 'phenomena'. Just as it is absurd to describe the
fact that the stick only looks bent by saying that, while the stick is
not bent, the appearance which it produces is bent, so it is, even on
the face of it, nonsense to say that while things are not spatial, the
appearances which they produce in us are spatial. For an 'appearance',
being necessarily something mental, cannot possibly be said to be
extended. Moreover, it is really an abuse of the term 'appearance' to
speak of appearances _produced by_ things, for this phrase implies a
false severance of the appearance from the things which appear. If
there are 'appearances' at all, they are appearances _of_ things and
not appearances _produced by_ them. The importance of the distinction
lies in the difference of implication. To speak of appearances
produced by things is to imply that the object of perception is merely
something mental, viz. an appearance. Consequently, access to a
non-mental reality is excluded; for a perception of which the object
is something belonging to the mind's own being cannot justify an
inference to something beyond the mind, and the result is inevitably
solipsism. On the other hand, the phrase 'appearances of things',
whatever defects it may have, at least implies that it is a non-mental
reality which appears, and therefore that in perception we are in
direct relation to it; the phrase, therefore, does not imply from the
very beginning that the apprehension of a non-mental reality is
impossible.

The objection will probably be raised that this criticism is much too
summary. We do, it will be said, distinguish in ordinary consciousness
between appearance and reality. Consequently there must be some form
in which Kant's distinction between things in themselves and phenomena
and the conclusion based upon it are justified. Moreover, Kant's
reiterated assertion that his view does not imply that space is an
illusion, and that the distinction between the real and the illusory
is possible _within_ phenomena, requires us to consider more closely
whether Kant may not after all be entitled to hold that space is not
an illusion.[8]

    [8] Cf. p. 93 and ff.

This objection is, of course, reasonable. No one can satisfy himself
of the justice of the above criticisms until he has considered the
real nature of the distinction between appearance and reality. This
distinction must, therefore, be analysed. But before this is done it
is necessary, in order to discover the real issue, to formulate the
lines on which Kant may be defended. 'The reality,' it may be urged,
'which ideally we wish to know must be admitted to exist _in itself_,
in the sense of independently of the perception, and consequently its
nature must be admitted to be independent of perception. Ideally,
then, our desire is to know things[9] as they are in themselves, a
desire sufficiently expressed by the assertion that we desire to know
things, for to know them is to know them as they are, i. e. as they
are independently of perception. Again, since the reality which we
desire to know consists of individuals, and since the apprehension of
an individual implies perception, knowledge of reality requires
perception. If in perception we apprehended reality as it is, no
difficulty would arise. But we do not, for we are compelled to
distinguish what things are, and what they look or appear; and what
they appear essentially relates to perception. We perceive them as
they look or appear and, therefore, not as they are, for what they
look and what they are are _ex hypothesi_ distinguished. And this fact
constitutes a fatal obstacle to knowledge in general. We cannot know
anything as it _is_. At least the negative side of Kant's position
must be justified. We never can know things as they are in themselves.
What then do we know? Two alternative answers may be given. It may be
held that the positive side of Kant's position, though indefensible in
the form that we know things as they appear to us, is valid in the
form that we know what things look or appear. This, no doubt, implies
that our ordinary beliefs about reality are illusory, for what things
look is _ex hypothesi_ different from what they are. But the
implication does not constitute an important departure from Kant's
view. For in any case only that is knowledge proper which relates to
things as they are, and therefore the supposed knowledge of things as
they appear may be discarded without serious loss. On the other hand,
it may be held that the positive side of Kant's position can be
vindicated in the form that, while we do not know things in
themselves,[10] we do know the appearances which they produce in us.
It is true that this view involves the difficulty of maintaining that
appearances are spatial, but the difficulty is not insuperable.
Moreover, in this form the doctrine has the advantage that, unlike the
former, it does not imply that the knowledge which we have is only of
illusions, for instead of implying that our knowledge is merely
knowledge of what things look but really are not, it implies that we
know the real nature of realities of another kind, viz. of
appearances. Again, in this form of the view, it may be possible to
vindicate Kant's doctrine that the distinction between the real and
the illusory is tenable within what we know, for it may be possible to
distinguish within appearances between a 'real' appearance[11] and an
'illusory' appearance.[12]'

    [9] 'Things' is substituted for 'the reality which we believe
    to exist independently of perception' in order to conform
    to Kant's language. The substitution, of course, has the
    implication--which Kant took for granted--that the reality
    consists of a plurality of individuals.

    [10] 'Things in themselves' has here to be substituted for
    'things as they are in themselves' in the statement of the
    negative side of the position, in order to express the proper
    antithesis, which is now that between two things, the one
    known and the other unknown, and not that between two points
    of view from which one and the same thing is known and not
    known respectively.

    [11] _Erscheinung._

    [12] _Schein._

An implication of this defence should be noticed. The issue relates
to the nature of space[13], and may be stated in terms of it. For,
since space is a presupposition of all other properties which the
non-philosophical consciousness attributes to physical things, it
makes no difference whether we say that things _only appear_ heavy,
hard, in motion, &c., or whether we say that things _only appear_
spatial. In the same way it is a matter of indifference whether we say
that, though things are not heavy, hard, &c., their appearances are
so, or whether we say that, though things are not spatial, their
appearances are so. The issue, then, concerns the possibility of
maintaining either that things only appear spatial, or that the
appearances which they produce are spatial, while the things
themselves are not, or, at least cannot be known to be, spatial.

    [13] We might add time also; but, for a reason which will
    appear later (p. 139), it can be neglected.

The tenability of these alternative positions has to be considered
apart from the argument of the _Aesthetic_, for this, as we have seen,
breaks down. At the outset it is important to realize that these
positions are the product of philosophical reflection, and constitute
general theories of knowledge. As has been pointed out, the
distinction between appearance and reality first arises in our
ordinary or scientific consciousness.[14] In this consciousness we are
compelled to distinguish between appearance and reality with respect
to the details of a reality which, as a whole, or, in principle, we
suppose ourselves to know. Afterwards in our philosophical
consciousness we come to reflect upon this distinction and to raise
the question whether it is not applicable to reality as a whole. We
ask with respect to knowledge in general, and not merely with respect
to certain particular items of knowledge, whether we know or can know
reality, and not merely appearance. The two positions just stated are
alternative ways of answering the question in the negative. They are,
then, philosophical views based upon a distinction found in our
ordinary consciousness. Consequently, in order to decide whether the
distinction will bear the superstructure placed upon it by the
philosophical consciousness, it is necessary to examine the
distinction as it exists in our ordinary consciousness.

    [14] I. e. the consciousness for which the problems are those
    of science as opposed to philosophy.

The distinction is applied in our ordinary consciousness both to the
primary and to the secondary qualities of matter, i. e. to the size,
shape, position and motion of physical bodies, and to their colour,
warmth, &c. We say, for instance, that the moon looks[15] or appears
as large as the sun, though really it is much smaller. We say that
railway lines, though parallel, look convergent, just as we say that
the straight stick in water looks bent. We say that at sunset the sun,
though really below the horizon, looks above it. Again, we say that to
a person who is colour blind the colour of an object looks different
to what it really is, and that the water into which we put our hand
may be warmer than it appears to our touch.

    [15] 'Looks' means 'appears to sight', and 'looks' is
    throughout used as synonymous with 'appear', where the
    instance under discussion relates to visual perception.

The case of the primary qualities may be considered first. Since the
instances are identical in principle, and only differ in complexity,
it will be sufficient to analyse the simplest, that of the apparent
convergence of the railway lines.

Two points at once force themselves upon our notice. In the first
place, we certainly suppose that we perceive the reality which we wish
to know, i. e. the reality which, as we suppose, exists independently
of our perception, and not an 'appearance' of it. It is, as we say,
the real lines which we see. Even the term 'convergent', in the
assertion that the lines look convergent, conveys this implication.
For 'convergent' is essentially a characteristic not of an appearance
but of a reality, in the sense in which something independent of
perception may be opposed as a reality to an 'appearance', which, as
such, presupposes perception. We can say neither that an appearance is
convergent, nor that the appearance of the lines is convergent. Only a
reality similar to the lines, e. g. two roads, can be said to be
convergent. Our ordinary thought, therefore, furnishes no ground for
the view that the object of perception is not the thing, but merely an
appearance of or produced by it. In the second place, the assertion
that the lines _look_ convergent implies considerable knowledge of the
real nature of the reality to which the assertion relates. Both the
terms 'lines' and 'convergent' imply that the reality _is_ spatial.
Further, if the context is such that we mean that, while the lines
look convergent, we do not know their real relation, we imply that
the lines really possess some characteristic which falls within the
genus to which convergence belongs, i. e. we imply that they are
convergent, divergent, or parallel. If, on the other hand, the context
is such that we mean that the lines only look convergent, we imply
that the lines are parallel, and therefore presuppose complete
knowledge in respect of the very characteristic in regard to which we
state what is only appearance. The assertion, then, in respect of a
primary quality, that a thing looks so and so implies knowledge of its
general character as spatial, and ignorance only of a detail; and the
assertion that a thing only looks or appears so and so implies
knowledge of the detail in question.

Attention may now be drawn to a general difficulty which may be raised
with respect to the use of the terms 'looks' and 'appears'. It may be
stated thus: 'If the lines are not convergent, how is it possible even
to say that they _look_ convergent? Must it not be implied that at
least under _certain_ circumstances we should perceive the lines as
they are? Otherwise, why should we use the words 'look' or 'appear' at
all? Moreover, this implication can be pushed further; for if we
maintain that we perceive the real lines, we may reasonably be asked
whether we must not under _all_ circumstances perceive them as they
are. It seems as though a reality cannot be perceived except as it
is.' It is the view to which this difficulty gives rise which is
mainly responsible for the doctrine that the object of perception is
not the reality, but an appearance. Since we do distinguish between
what things look and what they are, it would seem that the object of
perception cannot be the thing, but only an appearance produced by
it. Moreover, the doctrine gains in plausibility from the existence of
certain illusions in the case of which the reality to which the
illusion relates seems non-existent. For instance, if we look steadily
at the flame of a candle, and then press one eyeball with a finger, we
see, as we say, two candles;[16] but since _ex hypothesi_ there is
only one candle, it seems that what we see must be, not the candle,
but two images or appearances produced by it.

    [16] Cf. Dr. Stout, on 'Things and Sensations' (_Proceedings
    of the British Academy_, vol. ii).

This difficulty is raised in order to draw attention to the fact that,
in the case of the railway lines, where it can be met on its own
ground[17], this is because, and only because, we believe space to be
'real', i. e. to be a characteristic of reality, and because we
understand its nature. The distinction between the actual and the
apparent angle made by two straight lines presupposes a limiting case
in which they coincide. If the line of sight along which we observe
the point of intersection of two lines is known to be at right angles
to both lines, we expect, and rightly expect, to see the angle of
intersection as it is. Again, if we look at a short portion of two
railway lines from a point known to be directly above them, and so
distant that the effects of perspective are imperceptible, we can say
that the lines look what they are, viz. parallel. Thus, from the point
of view of the difficulty which has been raised, there is this
justification in general for saying that two lines _look_ parallel or
_look_ at right angles, that we know that in certain cases what they
look is identical with what they are. In the same way, assertions of
the type that the moon _looks_ as large as the sun receive
justification from our knowledge that two bodies of equal size and
equally distant from the observer _are_ what they look, viz. of the
same size. And in both cases the justification presupposes knowledge
of the reality of space and also such insight into its nature as
enables us to see that in certain cases there must be an identity
between what things look and what they are in respect of certain
spatial relations. Again, in such cases we see that so far is it from
being necessary to think that a thing must be perceived as it is, that
it is not only possible but necessary to distinguish what a thing
looks from what it is, and precisely in consequence of the nature of
space. The visual perception of spatial relations from its very nature
presupposes a particular point of view. Though the perception itself
cannot be spatial, it presupposes a particular point in space as a
standpoint or point of view,[18] and is therefore subject to
conditions of perspective. This is best realized by considering the
supposition that perfect visual powers would enable us to see the
whole of a body at once, and that this perception would be possible if
we had eyes situated all round the body. The supposition obviously
breaks down through the impossibility of combining two or more points
of view in one perception. But if visual perception is necessarily
subject to conditions of perspective, the spatial relations of bodies
can never look what they are except in the limiting case referred to.
Moreover, this distinction is perfectly intelligible, as we should
expect from the necessity which we are under of drawing it. We
understand perfectly why it is that bodies must, in respect of their
spatial relations, look different to what they are, and we do so
solely because we understand the nature of space, and therefore also
the conditions of perspective involved in the perception of what is
spatial. It is, therefore, needless to make the assertion 'Two lines
appear convergent' intelligible by converting the verb 'appears' into
a substantive, viz. an 'appearance', and then making the assertion
relate to an 'appearance'. For--apart from the fact that this would
not achieve the desired end, since no suitable predicate could be
found for the appearance--the assertion that the lines _look_ or
_appear_ convergent is perfectly intelligible in itself, though not
capable of being stated in terms of anything else.[19] If we
generalize this result, we may say that the distinction between
appearance and reality, drawn with regard to the primary qualities of
bodies, throughout presupposes the reality of space, and is made
possible, and indeed necessary, by the nature of space itself.

    [17] Cf., however, p. 87 and pp. 89-91.

    [18] This is, of course, not refuted by the reminder that we
    see with two eyes, and that these are in different places.

    [19] It is important to notice that the proper formula to
    express what is loosely called 'an appearance' is 'A looks or
    appears B', and that this cannot be analysed into anything
    more simple and, in particular, into a statement about
    'appearances'. Even in the case of looking at the candle,
    there is no need to speak of two 'appearances' or 'images'.
    Before we discover the truth, the proper assertion is 'The
    body which we perceive looks as if it were two candles', and,
    after we discover the truth, the proper assertion is 'The
    candle looks as if it were in two places'.

We may now turn to the way in which we draw the distinction with
respect to the secondary qualities of physical things. It must, it
seems, be admitted that in our ordinary consciousness we treat these
qualities as real qualities of bodies. We say that a bell is noisy;
that sugar is sweet; that roses smell; that a mustard plaster is hot;
that the sky is blue. It must also be admitted that in our ordinary
consciousness we draw a distinction between appearance and reality
_within_ these qualities, just as we do _within_ the primary
qualities. Just as we speak of the right or real shape of a body, so
we speak of its right or real colour, taste, &c., and distinguish
these from its apparent colours, taste, &c., to some individual. We
thereby imply that these qualities are real qualities of bodies, and
that the only difficulty is to determine the particular character of
the quality in a given case. Yet, as the history of philosophy shows,
it takes but little reflection to throw doubt on the reality of these
qualities. The doubt arises not merely from the apparent impossibility
of finding a principle by which to determine the right or real quality
in a given case, but also and mainly from misgivings as to the
possible reality of heat, smell, taste, noise, and colour apart from a
percipient. It must also be admitted that this misgiving is well
founded; in other words, that these supposed real qualities do
presuppose a percipient, and therefore cannot be qualities of things,
since the qualities of a thing must exist independently of the
perception of the thing.[20] This will readily be allowed in the case
of all the secondary qualities except colour. No one, it may
reasonably be said, who is familiar with and really faces the issue,
will maintain that sounds, smells, tastes, and sensations of touch
exist apart from a sensitive subject. So much is this the case, that
when once the issue is raised, it is difficult and, in the end,
impossible to use the word 'appear' in connexion with these qualities.
Thus it is difficult and, in the end, impossible to say that a bell
_appears_ noisy, or that sugar _appears_ sweet. We say, rather, that
the bell and the sugar produce certain sensations[21] in us.

    [20] Cf. pp. 72-3, and 91.

    [21] _Not_ 'appearances'.

The case of colour, however, is more difficult. From the closeness of
its relation to the shape of bodies, it seems to be a real quality of
bodies, and not something relative to a sensitive subject like the
other secondary qualities. In fact, so intimate seems the relation of
colour to the shape of bodies, that it would seem--as has, of course,
often been argued--that if colour be relative to a sensitive subject,
the primary qualities of bodies must also be relative to a sensitive
subject, on the ground that shape is inseparable from colour.[22] Yet
whether this be so or not, it must, in the end, be allowed that colour
does presuppose a sensitive subject in virtue of its own nature, and
quite apart from the difficulty--which is in itself insuperable--of
determining the right colour of individual bodies. It must, therefore,
be conceded that colour is not a quality of bodies. But if this be
true, the use of the term 'look' or 'appear' in connexion with colour
involves a difficulty which does not arise when it is used in
connexion with the primary qualities. Bodies undoubtedly look or
appear coloured. Now, as has already been suggested,[23] the term
'look' seems to presuppose some identity between what a thing is and
what it looks, and at least the possibility of cases in which they are
what they look--a possibility which, as we have seen, is realized in
the case of the primary qualities. Yet, if colour is not a quality of
bodies, then, with respect to colour, things look what they never are,
or, in other words, are wholly different from what they look;[24] and
since it seems impossible to hold that colour is really a property of
bodies, this conclusion must, in spite of its difficulty, be admitted
to be true.

    [22] Cf. p. 91 note.

    [23] Cf. p. 82.

    [24] It is assumed that there is not even plausibility in the
    supposition of continuity or identity between colour proper
    and its physical conditions in the way of light vibrations.

There remain, however, to be noticed two respects in which assertions
concerning what things look in respect of colour agree with
corresponding assertions in respect of the primary qualities. They
imply that what we perceive is a reality, in the sense already
explained.[25] Thus the assertion that the grass looks green implies
that it is a reality which looks green, or, in other words, that the
object of perception is a reality, and not an 'appearance'. Again,
such assertions imply that the reality about which the assertion is
made is spatial. The term 'grass' implies extension, and only what is
extended can be said to look coloured. If it be urged that what looks
coloured need only _look_ extended, it may be replied that the two
considerations which lead us to think that things only _look_ coloured
presuppose that they _are_ spatial. For the two questions, the
consideration of which leads to this conclusion, are, 'What is the
right or real colour of an individual thing?' and 'Has it really any
colour at all, or does it only look coloured?' and neither question is
significant unless the thing to which it refers is understood to be
spatial.

    [25] I. e. in the sense of something which exists
    independently of perception.

We may now return to the main issue. Is it possible to maintain either
(1) the position that only appearances are spatial and possess all the
qualities which imply space, or (2) the position that things only
appear spatial and only appear or look as if they possessed the
qualities which imply space? It may be urged that these questions have
already been implicitly answered in the negative. For the division of
the qualities of things into primary and secondary is exhaustive, and,
as has been shown, the distinction between 'appearance' and 'reality',
when drawn with respect to the primary qualities and to colour--the
only secondary quality with respect to which the term 'appears' can
properly be used[26]--presupposes the reality of space. Consequently,
since we do draw the distinction, we must accept the reality of that
which is the condition of drawing it at all. But even though this be
conceded--and the concession is inevitable--the problem cannot be
regarded as solved until we have discovered what it is in the nature
of space which makes both positions untenable. Moreover, the admission
that in the case of colour there is no identity between what things
look and what they are removes at a stroke much of the difficulty of
one position, viz. that we only know what things look or appear, and
not what they are. For the admission makes it impossible to maintain
as a general principle that there must be some identity between what
they look and what they are. Consequently, it seems _possible_ that
things should be wholly different from what they appear, and, if so,
the issue cannot be decided on general grounds. What is in substance
the same point may be expressed differently by saying that just as
things only _look_ coloured, so things may only _look_ spatial. We are
thus again[27] led to see that the issue really turns on the nature of
space and of spatial characteristics in particular.

    [26] Cf. pp. 86-7.

    [27] Cf. p. 79.

In discussing the distinction between the real and the apparent shape
of bodies, it was argued that while the nature of space makes it
necessary to distinguish in general between what a body looks and what
it is, yet the use of the term _look_ receives justification from the
existence of limiting cases in which what a thing looks and what it is
are identical. The instances considered, however, related to qualities
involving only two dimensions, e. g. convergence and bentness, and it
will be found that the existence of these limiting cases is due solely
to this restriction. If the assertion under consideration involves a
term implying three dimensions, e. g. 'cubical' or 'cylindrical',
there are no such limiting cases. Since our visual perception is
necessarily subject to conditions of perspective, it follows that
although we can and do see a cube, we can never see it as it _is_.
It _is_, so to say, in the way in which a child draws the side of a
house, i. e. with the effect of perspective eliminated; but it never
can be seen in this way. No doubt, our unreflective knowledge of the
nature of perspective enables us to allow for the effect of
perspective, and to ascertain the real shape of a solid object from
what it looks when seen from different points. In fact, the habit of
allowing for the effect of perspective is so thoroughly ingrained in
human beings that the child is not aware that he is making this
allowance, but thinks that he draws the side of the house as he sees
it. Nevertheless, it is true that we never see a cube as it is, and if
we say that a thing looks cubical, we ought only to mean that it looks
precisely what a thing looks which is a cube.

It is obvious, however, that two dimensions are only an abstraction
from three, and that the spatial relations of bodies, considered
fully, involve three dimensions; in other words, spatial
characteristics are, properly speaking, three-dimensional. It follows
that terms which fully state spatial characteristics can never
express what things look, but only what they are. A body may be
cylindrical, and we may see a cylindrical body; but such a body can
never, strictly speaking, _look_ cylindrical. The opposition, however,
between what a thing _is_ and what it _looks_ implies that what it
_is_ is independent of a percipient, for it is precisely correlation
to a percipient which is implied by 'looking' or 'appearing'. In fact,
it is the view that what a thing really is it is, independently of
a percipient, that forms the real starting-point of Kant's thought.
It follows, then, that the spatial characteristics of things, and
therefore space itself, must belong to what they are in themselves
apart from a percipient, and not to what they look.[28] Consequently,
it is so far from being true that we only know what things look and
not what they are, that in the case of spatial relations we actually
know what things are, even though they never look what they are.

    [28] This consideration disposes of the view that, if colour
    is relative to perception, the primary qualities, as being
    inseparable from colour, must also be relative to perception;
    for it implies that the primary qualities cannot from their
    very nature be relative to perception. Moreover, if the
    possibility of the separation of the primary qualities from
    colour is still doubted, it is only necessary to appeal to
    the blind man's ability to apprehend the primary qualities,
    though he may not even know what the word 'colour' means. Of
    course, it must be admitted that some sensuous elements are
    involved in the apprehension of the primary qualities, but
    the case of the blind man shows that these may relate to
    sight instead of to touch. Moreover, it, of course, does not
    follow from the fact that sensuous elements are inseparable
    from our perception of bodies that they belong to, and are
    therefore inseparable from, the bodies perceived.

This conclusion, however, seems to present a double difficulty. It is
admitted that we perceive things as they look, and not as they are.
How, then, is it possible for the belief that things _are_ spatial to
arise? For how can we advance from knowledge of what they look to
knowledge of what they are but do not look? Again, given that the
belief has arisen, may it not after all be illusion? No vindication
seems possible. For how can it be possible to base the knowledge of
what things are, independently of perception, upon the knowledge of
what they look? Nevertheless, the answer is simple. In the case of the
perception of what is spatial there is no transition _in principle_
from knowledge of what things look to knowledge of what things are,
though there is continually such a transition _in respect of details_.
It is, of course, often necessary, and often difficult, to determine
the precise position, shape, &c., of a thing, and if we are to come to
a decision, we must appeal to what the thing looks or appears under
various conditions. But, from the very beginning, our consciousness of
what a thing appears in respect of spatial characteristics implies the
consciousness of it as spatial and therefore also as, in particular,
three-dimensional. If we suppose the latter consciousness absent, any
assertion as to what a thing appears in respect of spatial
characteristics loses significance. Thus, although there is a process
by which we come to learn that railway lines are really parallel,
there is no process by which we come to learn that they are really
spatial. Similarly, although there is a process by which we become
aware that a body is a cube, there is no process by which we become
aware that it has a solid shape of some kind; the process is only
concerned with the determination of the precise shape of the body.
The second difficulty is, therefore, also removed. For if assertions
concerning the apparent shape, &c. of things presuppose the
consciousness that the things _are_ spatial, to say that this
consciousness may be illusory is to say that all statements concerning
what things _appear_, in respect of spatial relations, are equally
illusory. But, since it is wholly impossible to deny that we can and
do state what things appear in this respect, the difficulty must fall
to the ground.

There remains to be answered the question whether Kant's position is
tenable in its other form, viz. that while we cannot say that reality
is spatial, we can and must say that the appearances which it produces
are spatial. This question, in view of the foregoing, can be answered
as soon as it is stated. We must allow that reality is spatial, since,
as has been pointed out, assertions concerning the apparent shape of
things presuppose that they are spatial. We must equally allow that an
appearance cannot be spatial. For on the one hand, as has just been
shown, space and spatial relations can only qualify something the
existence of which is not relative to perception, since it is
impossible to perceive what is spatial as it is; and on the other hand
an appearance, as being _ex hypothesi_ an appearance to some one,
i. e. to a percipient, must be relative to perception.

We may say, then, generally, that analysis of the distinction between
appearance and reality, as it is actually drawn in our ordinary
consciousness, shows the falsity of both forms of the philosophical
agnosticism which appeals to the distinction. We know things; not
appearances. We know what things are; and not merely what they appear
but are not. We may also say that Kant cannot possibly be successful
in meeting, at least in respect of space, what he calls 'the easily
foreseen but worthless objection that the ideality of space and of
time would turn the whole sensible world into pure illusion'.[29] For
space, according to him, is not a property of things in themselves; it
cannot, as has been shown, be a property of appearances; to say that
it is a property of things as they appear to us is self-contradictory;
and there is nothing else of which it can be said to be a property.

    [29] _Prol_., § 13, Remark iii. (Cf. p. 100 note.) Cf. the
    confused note B. 70, M. 42. (See Dr. Vaihinger's Commentary
    on the _Critique_, ii, 488 ff.)

In conclusion, it may be pointed out that the impossibility that
space[30] and spatial characteristics should qualify appearances
renders untenable Kant's attempt to draw a distinction between reality
and appearance _within_ 'phenomena' or 'appearances'. The passage in
which he tries to do so runs as follows:

    [30] The case of time can be ignored, since, as will be seen
    later (pp. 112-14), the contention that space is 'ideal'
    really involves the admission that time is real.

"We generally indeed distinguish in appearances that which essentially
belongs to the perception of them, and is valid for every human
sense in general, from that which belongs to the same perception
accidentally, as valid not for the sensibility in general, but for a
particular state or organization of this or that sense. Accordingly,
we are accustomed to say that the former is knowledge which represents
the object itself, whilst the latter represents only the appearance
of the same. This distinction, however, is only empirical. If we stop
here (as is usual) and do not again regard that empirical perception
as itself a mere phenomenon (as we ought to do), in which nothing
which concerns a thing in itself is to be found, our transcendental
distinction is lost; and in that case we are after all believing that
we know things in themselves, although in the world of sense,
investigate its objects as profoundly as we may, we have to do with
nothing but appearances. Thus we call the rainbow a mere appearance
during a sunny shower, but the rain the thing in itself; and this is
right, if we understand the latter conception only physically as that
which in universal experience and under all different positions with
regard to the senses is in perception so and so determined and not
otherwise. But if we consider this empirical element[31] in general,
and inquire, without considering its agreement with every human sense,
whether it represents an object in itself (not the raindrops, for
their being phenomena by itself makes them empirical objects), the
question of the relation of the representation to the object is
transcendental; and not only are the raindrops mere appearances, but
even their circular form, nay, even the space in which they fall,
are nothing in themselves but mere modifications or fundamental
dispositions of our sensuous perception; the transcendental object,
however, remains unknown to us."[32]

    [31] _Dieses Empirische._

    [32] B. 62-3, M. 37-8. _Erscheinung_ is here translated
    'appearance'.

Kant's meaning is plain. He is anxious to justify the physical
distinction made in our ordinary or non-philosophical consciousness
between a thing in itself and a mere appearance,[33] but at the same
time to show that it falls within appearances, in respect of the
philosophical distinction between things in themselves and appearances
or phenomena. The physical distinction is the first of which we become
aware, and it arises through problems connected with our senses.
Owing, presumably, to the contradictions which would otherwise ensue,
the mind is forced to distinguish between things and the 'appearances'
which they produce, and to recognize that they do not correspond. The
discrepancy is due to the fact that our perceptions are conditioned by
the special positions of our physical organs with regard to the object
of perception, and we discover its real nature by making allowance for
these special positions. We thereby advance in knowledge to the extent
of overcoming an obstacle due to the nature of our senses. But, this
obstacle overcome, philosophical reflection forces upon us another.
The thing which we distinguish in our ordinary consciousness from its
appearances is, after all, only another appearance; and although the
physical problem is solved concerning its accordance with our special
senses, there remains the philosophical problem as to whether this
appearance need correspond to what in the end is the real thing, viz.
that which exists in itself and apart from all perception. The only
possible answer is that it need not. We therefore can only know
appearances and not reality; in other words, we cannot have knowledge
proper. At the same time, our knowledge of appearances is objective to
the extent that the appearances in question are the same for every
one, and for us on various occasions; for the effects due to special
positions of our senses have been removed. If, therefore, we return to
the physical distinction, we see that the 'things' to which it refers
are only a special kind of appearance, viz. that which is the same for
every one, and for us at all times. The physical distinction, then,
being a distinction between one kind of appearance and another, falls
within 'phenomena' or 'appearances'.

    [33] It should be noticed that the passage is, in the main,
    expressed in terms of the distinction between 'things' and
    'appearances', and not, as it should be, in terms of the
    distinction between what things are and what things appear
    or look.

Now the obvious objection to this line of thought is that the result
of the second or metaphysical application of the distinction between
reality and appearance is to destroy or annul the first or physical
application of it. To oppose the rain, i. e. the raindrops as the
thing in itself to the rainbow as a mere appearance is to imply that
the rain is not an appearance. For though what is opposed to a _mere_
appearance may still be an appearance, it cannot be called an
appearance at all if it be described as the thing in itself. If it be
only another appearance, it is the same in principle as that to which
it is opposed, and consequently cannot be opposed to it. Thus, if Kant
means by the rain, in distinction from the rainbow, the appearance
when, as we say, we see the circular raindrops, the title of this
appearance to the term thing in itself is no better than that of the
rainbow; it is, in fact, if anything, worse, for the appearance is
actual only under exceptional circumstances. We may never see the
raindrops thus, or in Kant's language, have this 'appearance'; and
therefore, in general, an appearance of this kind is not actual but
only possible. The truth is that we can only distinguish something as
the thing in itself from an appearance, so long as we mean by the
thing in itself what Kant normally means by it, viz. something which
exists independently of perception and is not an appearance at
all.[34] That of which Kant is really thinking, and which he _calls_
the appearance which is the thing, in distinction from a mere
appearance, is not an appearance; on the contrary, it is the raindrops
themselves, which he describes as circular and as falling through
space, and which, as circular and falling, must exist and have these
characteristics in themselves apart from a percipient. Kant's formula
for an empirical thing, i. e. a thing which is an appearance, viz.
'that which in universal experience and under all different positions
with regard to the senses is in perception so and so determined', is
merely an attempt to achieve the impossible, viz. to combine in one
the characteristics of a thing and an appearance. While the reference
to _perception_ and to _position with regard to the senses_ implies
that what is being defined is an appearance, the reference to
_universal_ experience, to _all_ positions with regard to the senses,
and to that which _is so and so determined_ implies that it is a
thing. But, plainly, mention of position with regard to the senses, if
introduced at all, should refer to the _differences_ in perception due
to the different position of the object in particular cases. There is
nothing of which it can be said that we perceive it in the same way or
that it looks the same from _all_ positions. When Kant speaks of that
which under _all_ different positions with regard to the senses is so
and so determined, he is really referring to something in the
consideration of which all reference to the senses has been discarded;
it is what should be described as that which _in reality and apart
from_ all positions with regard to the senses is so and so determined;
and this, as such, cannot be an appearance. Again, the qualification
of 'is so and so determined' by 'in perception' is merely an attempt
to treat as relative to perception, and so as an appearance, what is
essentially independent of perception.[35] Kant, no doubt, is thinking
of a real presupposition of the process by which we distinguish
between the real and the apparent qualities of bodies, i. e. between
what they are and what they appear. We presuppose that that quality is
really, and not only apparently, a quality of a body, which we and
every one, judging from what it looks under various conditions (i. e.
'in universal experience'), must believe it to possess in itself and
independently of all perception. His mistake is that in formulating
this presupposition he treats as an appearance, and so as relative to
perception, just that which is being distinguished from what, as an
appearance, is relative to perception.

    [34] Hence Kant's protest (B. 45, M. 27), against
    illustrating the ideality of space by the 'inadequate'
    examples of colour, taste, &c., must be unavailing. For his
    contention is that, while the assertion that space is not a
    property of things means that it is not a property of things
    in themselves, the assertion that colour, for example, is not
    a property of a rose only means that it is not a property of
    a thing in itself in an empirical sense, i. e. of an
    appearance of a special kind.

    [35] Cf. pp. 72-3.

Underlying the mistake is the identification of perception with
judgement. Our apprehension of what things _are_ is essentially a
matter of thought or judgement, and not of perception. We do not
_perceive_[36] but _think_ a thing as it is. It is true that we can
follow Kant's language so far as to say that our judgement that the
portion of the great circle joining two points on the surface of a
sphere is the shortest way between them _via_ the surface belongs
essentially to the thinking faculty of every intelligent being, and
also that it is valid for all intelligences, in the sense that they
must all hold it to be true; and we can contrast this judgement with a
perception of the portion of the great circle as something which,
though it cannot be said to be invalid, still differs for different
beings according to the position from which they perceive it. Kant,
however, treats the judgement as a _perception_; for if we apply his
general assertion to this instance, we find him saying that what we
judge the portion of the great circle to be essentially belongs to the
_perception_ of it, and is valid for the _sensuous_ faculty of every
human being, and that thereby it can be distinguished from what
belongs to the same perception of a great circle accidentally, e. g.
its apparent colour, which is valid only for a particular organization
of this or that sense.[37] In this way he correlates what the great
circle really is, as well as what it looks, with perception, and so is
able to speak of what it is for perception. But, in fact, what the
great circle is, is correlated with thought, and not with perception;
and if we raise Kant's transcendental problem in reference not to
perception but to thought, it cannot be solved in Kant's agnostic
manner. For it is a presupposition of thinking that things are in
themselves what we think them to be; and from the nature of the case a
presupposition of thinking not only cannot be rightly questioned, but
cannot be questioned at all.

    [36] Cf. pp. 72-3.

    [37] In the _Prol._, § 13, Remark iii, Kant carefully
    distinguishes judgement from perception, but destroys the
    effect of the distinction by regarding judgement as referring
    to what is relative to perception, viz. appearances.




NOTE ON THE FIRST ANTINOMY


Kant holds that the antinomy or contradiction which arises when we
consider the character of the world as spatial and temporal, viz. that
we are equally bound to hold that the world is infinite in space and
time, and that it is finite in space and time, is due to regarding the
world as a thing in itself. He holds that the contradiction
disappears, as soon as it is recognized that the world is only a
phenomenon, for then we find that we need only say that the world is
_capable_ of being extended infinitely in respect of time and
space.[1] Objects in space and time are only phenomena, and, as such,
are actual only in perception. When we say that a past event, or that
a body which we do not perceive, is real, we merely assert the
possibility of a 'perception'. "All events from time immemorial prior
to my existence mean nothing else than the possibility of prolonging
the chain of experience from the present perception upwards to the
conditions which determine this perception according to time."[2]
"That there may be inhabitants of the moon, although no one has ever
seen them, must certainly be admitted, but this assertion only means
that we could come upon them in the possible progress of
experience."[3] The contradictions, therefore, can be avoided by
substituting for the actual infinity of space and time, as relating to
things in themselves, the possible infinity of a series of
'perceptions'.

    [1] B. 532-3, M. 315.

    [2] B. 523, M. 309.

    [3] B. 521, M. 308.

This contention, if successful, is clearly important. If it could be
shown that the treatment of the world as a thing in itself is the
source of a contradiction, we should have what at least would seem a
strong, if not conclusive, ground for holding that the world is a
phenomenon, and, consequently, that the distinction between phenomena
and things in themselves is valid.

Professor Cook Wilson has, however, pointed out that Kant's own
doctrine does not avoid the difficulty. For, though, according to
Kant, the infinity of actual representations of spaces and times is
only possible, yet the possibilities of these representations will be
themselves infinite, and, as such, will give rise to contradictions
similar to those involved in the infinity of space and time. Moreover,
as Professor Cook Wilson has also pointed out, there is no
contradiction involved in the thought of the world as spatial and
temporal; for, as we see when we reflect, we always presuppose that
space and time are infinite, and we are only tempted to think that
they must be finite, because, when maintaining that the world must be
a whole, we are apt to make the false assumption, without in any way
questioning it, that any whole must be finite.




CHAPTER V

TIME AND INNER SENSE


The arguments by which Kant seeks to show that time is not a
determination of things in themselves but only a form of perception
are, _mutatis mutandis_, identical with those used in his treatment of
space.[1] They are, therefore, open to the same criticisms, and need
no separate consideration.

    [1] Cf. B. 46-9, §§ 4, 5 and 6 (a), M. 28-30, §§ 5, 6 and 7
    (a) with B. 38-42, § 2 (1-4), and § (3) to (a) inclusive, M.
    23-6, §§ 2, 3, and 4 (a). The only qualification needed is
    that, since the parts of time cannot, like those of space,
    be said to exist simultaneously, B. § 4 (5), M. § 5, 5 is
    compelled to appeal to a different consideration from that
    adduced in the parallel passage on space (B. § 2 (4), M. § 2,
    4). Since, however, B. § 4 (5), M. § 5, 5 introduces no new
    matter, but only appeals to the consideration already urged
    (B. § 4, 4, M. § 5, 4), this difference can be neglected. B.
    § 5, M. § 6 adds a remark about change which does not affect
    the main argument.

Time, however, according to Kant, differs from space in one important
respect. It is the form not of outer but of inner sense; in other
words, while space is the form under which we perceive things, time is
the form under which we perceive ourselves. It is upon this difference
that attention must be concentrated. The existence of the difference
at all is upon general grounds surprising. For since the arguments by
which Kant establishes the character of time as a form of perception
run _pari passu_ with those used in the case of space, we should
expect time, like space, to be a form under which we perceive things;
and, as a matter of fact, it will be found that the only _argument_
used to show that time is the form of inner, as opposed to outer,
sense is not only independent of Kant's general theory of forms of
sense, but is actually inconsistent with it.[2] Before, however, we
attempt to decide Kant's right to distinguish between inner and outer
sense, we must consider the facts which were before Kant's mind in
making the distinction.

    [2] B. 49 (b), M. 30 (b). See pp. 109-12.

These facts and, to a large extent, the frame of mind in which Kant
approached them, find expression in the passage in Locke's _Essay_,
which explains the distinction between 'ideas of sensation' and 'ideas
of reflection'.

"Whence has it [i. e. the mind] all the materials of reason and
knowledge? To this I answer, in one word, from experience.... Our
observation, employed either about external, sensible objects, or
about the internal operations of our minds, perceived and reflected
on, by ourselves, is that which supplies our understandings with all
the materials of thinking. These two are the fountains of
knowledge...."

"First, Our senses, conversant about particular sensible objects, do
convey into the mind several distinct perceptions of things, according
to those various ways, wherein those objects do affect them: and thus
we come by those ideas we have of Yellow, White, Heat, Cold, Soft,
Hard, Bitter, Sweet, and all those, which we call sensible qualities;
which, when I say the senses convey into the mind, I mean, they, from
external objects, convey into the mind what produces there those
perceptions. This great source of most of the ideas we have, depending
wholly upon our senses, and derived by them to the understanding, I
call _sensation_."

"Secondly, The other fountain, from which experience furnisheth the
understanding with ideas, is the perception of the operations of our
own mind within us, as it is employed about the ideas it has got;
which operations, when the soul comes to reflect on, and consider, do
furnish the understanding with another set of ideas, which could not
be had from things without; and such are Perception, Thinking,
Doubting, Believing, Reasoning, Knowing, Willing, and all the
different actings of our own minds; which we being conscious of, and
observing in ourselves, do, from these, receive into our
understandings as distinct ideas, as we do from bodies affecting our
senses. This source of ideas every man has wholly in himself; and
though it be not sense as having nothing to do with external objects,
yet it is very like it, and might properly enough be called internal
sense. But, as I call the other sensation, so I call this
_reflection_; the ideas it affords being such only as the mind gets,
by reflecting on its own operations within itself."[3]

    [3] Locke, _Essay_, ii, 1, §§ 2-4.

Here Locke is thinking of the distinction between two attitudes of
mind, which, however difficult it may be to state satisfactorily, must
in some sense be recognized. The mind, undoubtedly, in virtue of its
powers of perceiving and thinking--or whatever they may be--becomes
through a temporal process aware of a spatial world in its varied
detail. In the first instance, its attention is absorbed in the world
of which it thus becomes aware; subsequently, however, it is in some
way able to direct its attention away from this world to the
activities in virtue of which it has become aware of this world, and
in some sense to make itself its own object. From being conscious it
becomes self-conscious. This process by which the mind turns its
attention back upon itself is said to be a process of 'reflection'.
While we should say that it is by perception that we become aware of
things in the physical world, we should say that it is by reflection
that we become aware of our activities of perceiving, thinking,
willing, &c. Whatever difficulties the thought of self-consciousness
may involve, and however inseparable, and perhaps even temporally
inseparable, the attitudes of consciousness and self-consciousness may
turn out to be, the distinction between these attitudes must be
recognized. The object of the former is the world, and the object of
the latter is in some sense the mind itself; and the attitudes may be
described as that of our ordinary, scientific, or unreflecting
consciousness and that of reflection.

The significance of Locke's account of this distinction lies for our
purposes in its anticipation of Kant. He states the second attitude,
as well as the first, in terms of sense. Just as in our apprehension
of the world things external to, in the sense of existing
independently of, the mind are said to act on our physical organs or
'senses', and thereby to produce 'perceptions' in the mind, so the
mind is said to become conscious of its own operations by 'sense'. We
should notice, however, that Locke hesitates to use the word 'sense'
in the latter case, on the ground that it involves no operation of
external things (presumably upon our physical organs), though he
thinks that the difficulty is removed by calling the sense in question
'internal'.

Kant is thinking of the same facts, and also states them in terms of
sense, though allowance must be made for the difference of standpoint,
since for him 'sense', in the case of the external sense, refers not
to the affection of our physical organs by physical bodies, but to the
affection of the mind by things in themselves. Things in themselves
act on our minds and produce in them appearances, or rather
sensations, and outer sense is the mind's capacity for being so
affected by outer things, i. e. things independent of the mind. This
is, in essentials, Kant's statement of the attitude of consciousness,
i. e. of our apprehension of the world which exists independently of
the mind, and which, for him, is the world of things in themselves. He
also follows Locke in giving a parallel account of the attitude of
self-consciousness. He asks, 'How can the subject perceive itself?'
Perception _in man_ is essentially passive; the mind must be
_affected_ by that which it perceives. Consequently, if the mind is to
perceive itself, it must be affected by its own activity; in other
words, there must be an inner sense, i. e. a capacity in virtue of
which the mind is affected by itself.[4] Hence Kant is compelled to
extend his agnosticism to the knowledge of ourselves. Just as we do
not know things, but only the appearances which they produce in
us,[5] so we do not know ourselves, but only the appearances which we
produce in ourselves; and since time is a mode of relation of these
appearances, it is a determination not of ourselves, but only of the
appearances due to ourselves.

    [4] Cf. B. 67 fin., M. 41 init.

    [5] It is here assumed that this is Kant's normal view of the
    phenomenal character of our knowledge. Cf. p. 75.

The above may be said to represent the train of thought by which Kant
arrived at his doctrine of time and the inner sense. It was reached by
combining recognition of the fact that we come to be aware not only of
the details of the physical world, but also of the successive process
on our part by which we have attained this knowledge, with the view
that our apprehension of this successive process is based on 'sense',
just as is our apprehension of the world. But the question remains
whether Kant is, on his own principles, entitled to speak of an inner
sense at all. According to him, knowledge begins with the production
in us of sensations, or, as we ought to say in the present context,
appearances by the action of things in themselves. These sensations or
appearances can reasonably be ascribed to external sense. They may be
ascribed to sense, because they arise through our being _affected_ by
things in themselves. The sense may be called external, because the
object affecting it is external to the mind, i. e. independent of it.
In conformity with this account, internal sense must be the power of
being affected by something internal to the mind, i. e. dependent upon
the mind itself, and since being affected implies the activity of
affecting, it will be the power of being affected by the mind's own
activity.[6] The activity will presumably be that of arranging
spatially the sensations or appearances due to things in
themselves.[7] This activity must be said to produce an affection in
us, the affection being an appearance due to ourselves. Lastly, the
mind must be said to arrange these appearances temporally. Hence it
will be said to follow that we know only the appearances due to
ourselves and not ourselves, and that time is only a determination of
these appearances.[8]

    [6] B. 68 init., M. 41 init.

    [7] The precise nature of the activity makes no difference to
    the argument.

    [8] In B. 152 fin., M. 93 fin. Kant expresses his conclusion
    in the form that we know ourselves only as we appear to
    ourselves, and not as we are in ourselves (cf. p. 75). The
    above account, and the criticism which immediately follows,
    can be adapted, _mutatis mutandis_, to this form of the view.

The weakness of the position just stated lies on the surface. It
provides no means of determining whether any affection produced in us
is produced by ourselves rather than by the thing in itself;
consequently we could never say that a given affection was an
appearance due to _ourselves_, and therefore to _inner_ sense. On the
contrary, we should ascribe all affections to things in themselves,
and should, therefore, be unable to recognize an _inner_ sense at all.
In order to recognize an inner sense we must know that certain
affections are due to _our_ activity, and, to do this, we must know
what the activity consists in--for we can only be aware that we are
active by being aware of an activity of ours of a particular
kind--and, therefore, we must know ourselves. Unless, then, we know
ourselves, we cannot call any affections internal.

If, however, the doctrine of an internal sense is obviously untenable
from Kant's own point of view, why does he hold it? The answer is
that, inconsistently with his general view, he continues to think of
the facts as they really are, and that he is deceived by an ambiguity
into thinking that the facts justify a distinction between internal
and external sense.

He brings forward only one argument to show that time is the form of
the internal sense. "Time is nothing else than the form of the
internal sense, i. e. of the perception of ourselves and our inner
state. For time cannot be any determination of external phenomena; it
has to do neither with a shape nor a position; on the contrary, it
determines the relation of representations in our internal state."[9]

    [9] B. 49 (b), M. 30 (b).

To follow this argument it is first necessary to realize a certain
looseness and confusion in the expression of it. The term 'external',
applied to phenomena, has a double meaning. It must mean (1) that of
which the parts are external to one another, i. e. spatial; for the
ground on which time is denied to be a determination of external
phenomena is that it has nothing to do with a shape or a position. It
must also mean (2) external to, in the sense of independent of, the
mind; for it is contrasted with our internal state, and if 'internal',
applied to 'our state', is not to be wholly otiose, it can only serve
to emphasize the contrast between our state and something external to
in the sense of independent of us. Again, 'phenomena,' in the phrase
'external phenomena', can only be an unfortunate expression for
things independent of the mind, these things being here called
phenomena owing to Kant's view that bodies in space are phenomena.
Otherwise, 'phenomena' offers no contrast to 'our state' and to
'representations'. The passage, therefore, presupposes a distinction
between states of ourselves and things in space, the former being
internal to, or dependent upon, and the latter external to, or
independent of, the mind.

It should now be easy to see that the argument involves a complete
_non sequitur_. The conclusion which is justified is that time is a
form not of things but of our own states. For the fact to which he
appeals is that while things, as being spatial, are not related
temporally, our states are temporally related; and if 'a form' be
understood as a mode of relation, this fact can be expressed by the
formula 'Time is a form not of things but of our own states', the
corresponding formula in the case of space being 'Space is a form not
of our states but of things'. But the conclusion which Kant desires
to draw--and which he, in fact, actually draws--is the quite different
conclusion that time is a form of _perception_ of our states, the
corresponding conclusion in the case of space being that space is a
form of perception of things. For time is to be shown to be the form
of inner sense, i. e. the form of the perception of what is internal
to ourselves, i. e. of our own states.[10] The fact is that the same
unconscious transition takes place in Kant's account of time which, as
we saw,[11] takes place in his account of space. In the case of space,
Kant passes from the assertion that space is a form of things, in the
sense that all things are spatially related--an assertion which he
expresses by saying that space is the form of phenomena--to the quite
different assertion that space is a form of perception, in the sense
of a way in which we perceive things as opposed to a way in which
things are. Similarly, in the case of time, Kant passes from the
assertion that time is the form of our internal states, in the sense
that all our states are temporally related, to the assertion that time
is a way in which we perceive our states as opposed to a way in which
our states really are. Further, the two positions, which he thus fails
to distinguish, are not only different, but incompatible. For if space
is a form of things, and time is a form of our states, space and time
cannot belong only to our mode of perceiving things and ourselves
respectively, and not to the things and ourselves; for _ex hypothesi_
things _are_ spatially related, and our states _are_ temporally
related.

    [10] Cf. B. 49 (b) line 2, M. 30 (b) line 2

    [11] Cf. pp. 38-40.

Kant's procedure, therefore, may be summed up by saying that he
formulates a view which is true but at the same time inconsistent with
his general position, the view, viz. that while things in space are
not temporally related, the acts by which we come to apprehend them
are so related; and further, that he is deceived by the verbally easy
transition from a legitimate way of expressing this view, viz. that
time is the form of our states, to the desired conclusion that time is
the form of inner sense.

The untenable character of Kant's position with regard to time and the
knowledge of ourselves can be seen in another way. It is not difficult
to show that, in order to prove that we do not know _things_, but only
the appearances which they produce, we must allow that we do know
_ourselves_, and not appearances produced by ourselves, and,
consequently, that time is real and not phenomenal. To show this, it
is only necessary to consider the objection which Kant himself quotes
against his view of time. The objection is important in itself, and
Kant himself remarks that he has heard it so unanimously urged by
intelligent men that he concludes that it must naturally present
itself to every reader to whom his views are novel. According to Kant,
it runs thus: "Changes are real (this is proved by the change of our
own representations, even though all external phenomena, together with
their changes, be denied). Now changes are only possible in time;
therefore time is something real."[12] And he goes on to explain why
this objection is so unanimously brought, even by those who can bring
no intelligible argument against the ideality of space. "The reason is
that men have no hope of proving apodeictically the absolute reality
of space, because they are confronted by idealism, according to which
the reality of external objects is incapable of strict proof, whereas
the reality of the object of our internal senses (of myself and my
state) is immediately clear through consciousness. External objects
might be mere illusion, but the object of our internal senses is to
their mind undeniably something real."[13]

    [12] B. 53, M. 32.

    [13] B. 55, M. 33.

Here, though Kant does not see it, he is faced with a difficulty from
which there is no escape. On the one hand, according to him, we do not
know things in themselves, i. e. things independent of the mind. In
particular, we cannot know that they are spatial; and the objection
quoted concedes this. On the other hand, we do know phenomena or
the appearances produced by things in themselves. Phenomena or
appearances, however, as he always insists, are essentially states or
determinations of the mind. To the question, therefore, 'Why are we
justified in saying that we do know phenomena, whereas we do not know
the things which produce them?' Kant could only answer that it is
because phenomena are dependent upon the mind, as being its own
states.[14] As the objector is made to say, 'the reality of the object
of our internal senses (of myself and my state) is immediately clear
through consciousness.' If we do not know things in themselves,
because they are independent of the mind, we only know phenomena
because they are dependent upon the mind. Hence Kant is only justified
in denying that we know things in themselves if he concedes that we
really know our own states, and not merely appearances which they
produce.

    [14] Cf. p. 123.

Again, Kant must allow--as indeed he normally does--that these states
of ours are related by way of succession. Hence, since these states
are really our states and not appearances produced by our states,
these being themselves unknown, time, as a relation of these states,
must itself be real, and not a way in which we apprehend what is real.
It must, so to say, be really in what we apprehend about ourselves,
and not put into it by us as perceiving ourselves.

The objection, then, comes to this. Kant must at least concede that
we undergo a succession of changing states, even if he holds that
_things_, being independent of the mind, cannot be shown to undergo
such a succession; consequently, he ought to allow that time is not a
way in which we apprehend ourselves, but a real feature of our real
states. Kant's answer[15] does not meet the point, and, in any case,
proceeds on the untenable assumption that it is possible for the
characteristic of a thing to belong to it as perceived, though not
in itself.[16]

    [15] B. 55, M. 33 med.

    [16] Cf. pp. 71-3.




CHAPTER VI

KNOWLEDGE AND REALITY


Kant's theory of space, and, still more, his theory of time, are
bewildering subjects. It is not merely that the facts with which he
deals are complex; his treatment of them is also complicated by his
special theories of 'sense' and of 'forms of perception'. Light,
however, may be thrown upon the problems raised by the _Aesthetic_,
and upon Kant's solution of them, in two ways. In the first place, we
may attempt to vindicate the implication of the preceding criticism,
that the very nature of knowledge presupposes the independent
existence of the reality known, and to show that, in consequence, all
idealism is of the variety known as subjective. In the second place,
we may point out the way in which Kant is misled by failing to realize
(1) the directness of the relation between the knower and the reality
known, and (2) the impossibility of transferring what belongs to one
side of the relation to the other.

The question whether any reality exists independently of the knowledge
of it may be approached thus. The standpoint of the preceding
criticism of Kant may be described as that of the plain man. It is the
view that the mind comes by a temporal process to apprehend or to know
a spatial world which exists independently of it or of any other mind,
and that the mind knows it as it exists in the independence. 'Now this
view,' it may be replied, 'is exposed to at least one fatal objection.
It presupposes the possibility of knowing the thing in itself, i. e.
something which exists independently of the mind which comes to know
it. Whatever is true, this is not. Whatever be the criticism to which
Kant's doctrine is exposed in detail, it contains one inexpugnable
thesis, viz. that the thing in itself cannot be known. Unless the
physical world stands in essential relation to the mind, it is
impossible to understand how it can be known. This position being
unassailable, any criticism of an idealistic theory must be compatible
with it, and therefore confined to details. Moreover, Kant's view can
be transformed into one which will defy criticism. Its unsatisfactory
character lies in the fact that in regarding the physical world as
dependent on the mind, it really alters the character of the world by
reducing the world to a succession of 'appearances' which, as such,
can only be mental, i. e. can only belong to the mind's own being.
Bodies, as being really appearances in the mind, are regarded as on
the level of transitory mental occurrences, and as thereby at least
resembling feelings and sensations. This consequence, however, can be
avoided by maintaining that the real truth after which Kant was
groping was that knower and known form an inseparable unity, and that,
therefore, any reality which is not itself a knower, or the knowing of
a knower, presupposes a mind which knows it. In that case nothing is
suggested as to the special nature of the reality known, and, in
particular, it is not implied to be a transitory element of the mind's
own being. The contention merely attributes to any reality, conceived
to have the special nature ordinarily attributed to it, the additional
characteristic that it is known. Consequently, on this view, the
physical world can retain the permanence ordinarily attributed to it.
To the objection that, at any rate, _our_ knowledge is transitory,
and that if the world is relative to it the world also must be
transitory, it may be replied--though with some sense of
uneasiness--that the world must be considered relative not to us as
knowers, but to a knower who knows always and completely, and whose
knowing is in some way identical with ours. Further, the view so
transformed has two other advantages. In the first place, it renders
it possible to dispense with what has been called the Mrs. Harris of
philosophy, the thing in itself. As Kant states his position, the
thing in itself must be retained, for it is impossible to believe that
there is no reality other than what is mental. But if the physical
world need not be considered to be a succession of mental occurrences,
it can be considered to be the reality which is not mental. In the
second place, knowledge proper is vindicated, for on this view we do
not know 'only' phenomena; we know the reality which is not mental,
and we know it as it is, for it is as object of knowledge.'

'Moreover, the contention must be true, and must form the true basis
of idealism. For the driving force of idealism is furnished by the
question, 'How can the mind and reality come into the relation which
we call knowledge?' This question is unanswerable so long as reality
is thought to stand in no essential relation to the knowing mind.
Consequently, in the end, knowledge and reality must be considered
inseparable. Again, even if it be conceded that the mind in some way
gains access to an independent reality, it is impossible to hold that
the mind can really know it. For the reality cannot in the relation of
knowledge be what it is apart from this relation. It must become in
some way modified or altered in the process. Hence the mind cannot on
this view know the reality as it is. On the other hand, if the reality
is essentially relative to a knower, the knower knows it as it is, for
what it is is what it is in this relation.'

The fundamental objection, however, to this line of thought is that it
contradicts the very nature of knowledge. Knowledge unconditionally
presupposes that the reality known exists independently of the
knowledge of it, and that we know it as it exists in this
independence. It is simply _impossible_ to think that any reality
depends upon our knowledge of it, or upon any knowledge of it. If
there is to be knowledge, there must first _be_ something to be known.
In other words, knowledge is essentially discovery, or the finding of
what already is. If a reality could only be or come to be in virtue of
some activity or process on the part of the mind, that activity or
process would not be 'knowing', but 'making' or 'creating', and to
make and to know must in the end be admitted to be mutually
exclusive.[1]

    [1] Cf. pp. 235-6.

This presupposition that what is known exists independently of being
known is quite general, and applies to feeling and sensation just as
much as to parts of the physical world. It must in the end be conceded
of a toothache as much as of a stone that it exists independently of
the knowledge of it. There must be a pain to be attended to or
noticed, which exists independently of our attention or notice. The
true reason for asserting feeling and sensation to be dependent on the
mind is that they presuppose not a knowing, but a feeling and a
sentient subject respectively. Again, it is equally presupposed that
knowing in no way alters or modifies the thing known. We can no more
think that in apprehending a reality we do not apprehend it as it is
apart from our knowledge of it, than we can think that its existence
depends upon our knowledge of it. Hence, if 'things in themselves'
means 'things existing independently of the knowledge of them',
knowledge is essentially of 'things in themselves'. It is, therefore,
unnecessary to consider whether idealism is assisted by the
supposition of a non-finite knowing mind, correlated with reality as a
whole. For reality must equally be independent of it. Consequently, if
the issue between idealism and realism is whether the physical world
is or is not dependent on the mind, it cannot turn upon a dependence
in respect of knowledge.

That the issue does not turn upon knowledge is confirmed by our
instinctive procedure when we are asked whether the various realities
which we suppose ourselves to know depend upon the mind. Our natural
procedure is not to treat them simply as realities and to ask whether,
as realities, they involve a mind to know them, but to treat them as
realities of the particular kind to which they belong, and to consider
relation to the mind of some kind other than that of knowledge. We
should say, for instance, that a toothache or an emotion, as being a
feeling, presupposes a mind capable of feeling, whose feeling it is;
for if the mind be thought of as withdrawn, the pain or the feeling
must also be thought of as withdrawn. We should say that an act of
thinking presupposes a mind which thinks. We should, however,
naturally deny that an act of thinking or knowing, in order to be,
presupposes that it is known either by the thinker whose act it is, or
by any other mind. In other words, we should say that knowing
presupposes a mind, not as something which _knows_ the knowing, but
as something which _does_ the knowing. Again, we should naturally say
that the shape or the weight of a stone is _not_ dependent on the mind
which perceives the stone. The shape, we should say, would disappear
with the disappearance of the stone, but would not disappear with the
disappearance of the mind which perceives the stone. Again, we should
assert that the stone itself, so far from depending on the mind which
perceives it, has an independent being of its own. We might, of
course, find difficulty in deciding whether a reality of some
particular kind, e. g. a colour, is dependent on a mind. But, in any
case, we should think that the ground for decision lay in the special
character of the reality in question, and should not treat it merely
as a reality related to the mind as something known. We should ask,
for instance, whether a colour, as a colour, involves a mind which
sees, and not whether a colour, as a reality, involves its being
known. Our natural procedure, then, is to divide realities into two
classes, those which depend on a mind, and may therefore be called
mental, and those which do not, and to conclude that some realities
depend upon the mind, while others do not. We thereby ignore a
possible dependence of realities on their being known; for not only is
the dependence which we recognize of some other kind, e. g. in respect
of feeling or sentience, but if the dependence were in respect of
knowledge, we could not distinguish in respect of dependence between
one reality and another.

Further, if reality be allowed to exist independently of knowledge, it
is easy to see that, from the idealist's point of view, Kant's
procedure was essentially right, and that all idealism, when pressed,
must prove subjective; in other words, that the idealist must hold
that the mind can only know what is mental and belongs to its own
being, and that the so-called physical world is merely a succession of
appearances. Moreover, our instinctive procedure[2] is justified. For,
in the first place, since it is impossible to think that a reality
depends for its existence upon being known, it is impossible to reach
an idealistic conclusion by taking into account relation by way of
knowledge; and if this be the relation considered, the only conclusion
can be that all reality is independent of the mind. Again, since
knowledge is essentially of reality as it is apart from its being
known, the assertion that a reality is dependent upon the mind is an
assertion of the kind of thing which it is in itself, apart from its
being known.[3] And when we come to consider what we mean by saying of
a reality that it depends upon the mind, we find we mean that it is in
its own nature of such a kind as to disappear with the disappearance
of the mind, or, more simply, that it is of the kind called mental.
Hence, we can only decide that a particular reality depends upon the
mind by appeal to its special character. We cannot treat it simply as
a reality the relation of which to the mind is solely that of
knowledge. And we can only decide that all reality is dependent upon
the mind by appeal to the special character of all the kinds of
reality of which we are aware. Hence, Kant in the _Aesthetic_, and
Berkeley before him, were essentially right in their procedure. They
both ignored consideration of the world simply as a reality, and
appealed exclusively to its special character, the one arguing that in
its special character as spatial and temporal it presupposed a
percipient, and the other endeavouring to show that the primary
qualities are as relative to perception as the secondary.
Unfortunately for their view, in order to think of bodies in space as
dependent on the mind, it is necessary to think of them as being in
the end only certain sensations or certain combinations of sensations
which may be called appearances. For only sensations or combinations
of them can be thought of as at once dependent on the mind, and
capable with any plausibility of being identified with bodies in
space. In other words, in order to think of the world as dependent on
the mind, we have to think of it as consisting only of a succession of
appearances, and in fact Berkeley, and, at certain times, Kant, did
think of it in this way.

    [2] Cf. p. 119.

    [3] Though not apart from relation to the mind of some other
    kind.

That this is the inevitable result of idealism is not noticed, so long
as it is supposed that the essential relation of realities to the mind
consists in their being known; for, as we have seen, nothing is
thereby implied as to their special nature. To say of a reality that
it is essentially an object of knowledge is merely to add to the
particular nature ordinarily attributed to the existent in question
the further characteristic that it must be known.[4] Moreover,
since in fact, though contrary to the theory, any reality exists
independently of the knowledge of it, when the relation thought of
between a reality and the mind is _solely_ that of knowledge, the
realities can be thought of as independent of the mind. Consequently,
the physical world can be thought to have that independence of the
mind which the ordinary man attributes to it, and, therefore, need not
be conceived as only a succession of appearances. But the advantage of
this form of idealism is really derived from the very fact which it
is the aim of idealism in general to deny. For the conclusion that the
physical world consists of a succession of appearances is only avoided
by taking into account the relation of realities to the mind by way of
knowledge, and, then, without being aware of the inconsistency, making
use of the independent existence of the reality known.

    [4] Cf. p. 116.

Again, that the real contrary to realism is _subjective_ idealism is
confirmed by the history of the theory of knowledge from Descartes
onwards. For the initial supposition which has originated and
sustained the problem is that in knowledge the mind is, at any rate in
the first instance, confined within itself. This supposition granted,
it has always seemed that, while there is no difficulty in
understanding the mind's acquisition of knowledge of what belongs to
its own being, it is difficult, if not impossible, to understand how
it can acquire knowledge of what does not belong to its own being.
Further, since the physical world is ordinarily thought of as
something which does not belong to the mind's own being, the problem
has always been not 'How is it possible to know anything?' but 'How is
it possible to know a particular kind of reality, viz. the physical
world?' Moreover, in consequence of the initial supposition, any
answer to this question has always presupposed that our apprehension
of the physical world is indirect. Since _ex hypothesi_ the mind is
confined within itself, it can only apprehend a reality independent of
it through something within the mind which 'represents' or 'copies'
the reality; and it is perhaps Hume's chief merit that he showed that
no such solution is possible, or, in other words, that, on the given
supposition, knowledge of the physical world is impossible.

Now the essential weakness of this line of thought lies in the initial
supposition that the mind can only apprehend what belongs to its own
being. It is as much a fact of our experience that we directly
apprehend bodies in space, as that we directly apprehend our feelings
and sensations. And, as has already been shown,[5] what is spatial
cannot be thought to belong to the mind's own being on the ground that
it is relative to perception. Further, if it is legitimate to ask,
'How can we apprehend what does not belong to our being?' it is
equally legitimate to ask, 'How can we apprehend what does belong to
our own being?' It is wholly arbitrary to limit the question to the
one kind of reality. If a question is to be put at all, it should take
the form, 'How is it possible to apprehend anything?' But this
question has only to be put to be discarded. For it amounts to a
demand to _explain_ knowledge; and any answer to it would involve the
derivation of knowledge from what was not knowledge, a task which must
be as impossible as the derivation of space from time or of colour
from sound. Knowledge is _sui generis_, and, as such, cannot be
explained.[6]

    [5] Cf. pp. 89-91.

    [6] This assertion, being self-evident, admits of no direct
    proof. A 'proof' can only take the form of showing that
    any supposed 'derivation' or 'explanation' of knowledge
    presupposes knowledge in that from which it derives it.
    Professor Cook Wilson has pointed out that we must understand
    what knowing is in order to explain anything at all, so
    that any proposed explanation of knowing would necessarily
    presuppose that we understood what knowing is. For the
    general doctrine, cf. p. 245.

Moreover, it may be noted that the support which this form of idealism
sometimes receives from an argument which uses the terms 'inside' and
'outside' the mind is unmerited. At first sight it seems a refutation
of the plain man's view to argue thus: 'The plain man believes the
spatial world to exist whether any one knows it or not. Consequently,
he allows that the world is outside the mind. But, to be known, a
reality must be inside the mind. Therefore, the plain man's view
renders knowledge impossible.' But, as soon as it is realized that
'inside the mind' and 'outside the mind' are metaphors, and,
therefore, must take their meaning from their context, it is easy to
see that the argument either rests on an equivocation or assumes the
point at issue. The assertion that the world is outside the mind,
being only a metaphorical expression of the plain man's view, should
only mean that the world is something independent of the mind, as
opposed to something inside the mind, in the sense of dependent upon
it, or mental. But the assertion that, to be known, a reality must be
inside the mind, if it is to be incontestably true, should only mean
that a reality, to be apprehended, must really be object of
apprehension. And in this case 'being inside the mind', since it only
means 'being object of apprehension', is not the opposite of 'being
outside the mind' in the previous assertion. Hence, on this
interpretation, the second assertion is connected with the first only
apparently and by an equivocation; there is really no argument at all.
If, however, the equivocation is to be avoided, 'inside the mind' in
the second assertion must be the opposite of 'outside the mind' in the
first, and consequently the second must mean that a reality, to be
known, must be dependent on the mind, or mental. But in that case the
objection to the plain man's view is a _petitio principii_, and not an
argument.

Nevertheless, the tendency to think that the only object or, at least,
the only direct object of the mind is something mental still requires
explanation. It seems due to a tendency to treat self-consciousness as
similar to consciousness of the world. When in reflection we turn our
attention away from the world to the activity by which we come to know
it, we tend to think of our knowledge of the world as a reality to be
apprehended similar to the world which we apprehended prior to
reflection. We thereby implicitly treat this knowledge as something
which, like the world, merely _is_ and is not the knowledge of
anything; in other words, we imply that, so far from being knowledge,
i. e. the knowing of a reality, it is precisely that which we
distinguish from knowledge, viz. a reality to be known,
although--since knowledge must be mental--we imply that it is a
reality of the special kind called mental. But if the knowledge upon
which we reflect is thus treated as consisting in a mental reality
which merely _is_, it is implied that in this knowledge the world is
not, at any rate directly, object of the mind, for _ex hypothesi_ a
reality which merely _is_ and is not the knowledge of anything has no
object. Hence it comes to be thought that the only object or, at
least, the only direct object of the mind is this mental reality
itself, which is the object of reflection; in other words, that the
only immediate object of the mind comes to be thought of as its own
idea. The root of the mistake lies in the initial supposition--which,
it may be noted, seems to underlie the whole treatment of knowledge by
empirical psychology--that knowledge can be treated as a reality to be
apprehended, in the way in which any reality which is not knowledge is
a reality to be apprehended.

We may now revert to that form of idealism which maintains that the
essential relation of reality to the mind is that of _being known_,
in order to consider two lines of argument by which it may be
defended.

According to the first of these, the view of the plain man either is,
or at least involves, materialism; and materialism is demonstrably
absurd. The plain man's view involves the existence of the physical
world prior to the existence of the knowledge of it, and therefore
also prior to the existence of minds which know it, since it is
impossible to separate the existence of a knowing mind from its actual
knowledge. From this it follows that mere matter, having only the
qualities considered by the physicist, must somehow have originated or
produced knowing and knowing minds. But this production is plainly
impossible. For matter, possessing solely, as it does, characteristics
bound up with extension and motion, cannot possibly have originated
activities of a wholly different kind, or beings capable of exercising
them.

It may, however, be replied that the supposed consequence, though
absurd, does not really follow from the plain man's realism.
Doubtless, it would be impossible for a universe consisting solely of
the physical world to originate thought or beings capable of thinking.
But the real presupposition of the coming into existence of human
knowledge at a certain stage in the process of the universe is to be
found in the pre-existence, not of a mind or minds which always
actually knew, but simply of a mind or minds in which, under certain
conditions, knowledge is necessarily actualized. A mind cannot be the
product of anything or, at any rate, of anything but a mind. It cannot
be a new reality introduced at some time or other into a universe of
realities of a wholly different order. Therefore, the presupposition
of the present existence of knowledge is the pre-existence of a mind
or minds; it is not implied that its or their knowledge must always
have been actual. In other words, knowing implies the ultimate or
unoriginated existence of beings possessed of the capacity to know.
Otherwise, knowledge would be a merely derivative product, capable of
being stated in terms of something else, and in the end in terms of
matter and motion. This implication is, however, in no wise traversed
by the plain man's realism. For that implies, not that the existence
of the physical world is prior to the existence of a mind, but only
that it is prior to a mind's actual knowledge of the world.

The second line of thought appeals to the logic of relation. It may be
stated thus. If a term is relative, i. e. is essentially 'of' or
relative to another, that other is essentially relative to it. Just as
a doctor, for instance, is essentially a doctor of a patient, so a
patient is essentially the patient of a doctor. As a ruler implies
subjects, so subjects imply a ruler. As a line essentially has points
at its ends, so points are essentially ends of a line. Now knowledge
is essentially 'of' or relative to reality. Reality, therefore, is
essentially relative to or implies the knowledge of it. And this
correlativity of knowledge and reality finds linguistic confirmation
in the terms 'subject' and 'object'. For, linguistically, just as a
subject is always the subject of an object, so an object is always the
object of a subject.

Nevertheless, further analysis of the nature of relative terms, and in
particular of knowledge, does not bear out this conclusion. To take
the case of a doctor. It is true that if some one is healing, some one
else is receiving treatment, i. e. is being healed; and 'patient'
being the name for the recipient of treatment, we can express this
fact by saying that a doctor is essentially the doctor of a patient.
Further, it is true that a recipient of treatment implies a giver of
it, as much as a giver of it implies a recipient. Hence we can truly
say that since a doctor is the doctor of a patient, a patient is the
patient of a doctor, meaning thereby that since that to which a doctor
is relative is a patient, a patient must be similarly relative to a
doctor. There is, however, another statement which can be made
concerning a doctor. We can say that a doctor is a doctor of a human
being who is ill, i. e. a sick man. But in this case we cannot go on
to say that since a doctor is a doctor of a sick man, a sick man
implies or is relative to a doctor. For we mean that the kind of
reality capable of being related to a doctor as his patient is a sick
man; and from this it does not follow that a reality of this kind does
stand in this relation. Doctoring implies a sick man; a sick man does
not imply that some one is treating him. We can only say that since a
doctor is the doctor of a sick man, a sick man implies the possibility
of doctoring. In the former case the terms, viz. 'doctor' and
'patient', are inseparable because they signify the relation in
question in different aspects. The relation is one fact which has two
inseparable 'sides', and, consequently, the terms must be inseparable
which signify the relation respectively from the point of view of the
one side and from the point of view of the other. Neither term
signifies the nature of the elements which can stand in the relation.
In the latter case, however, the terms, viz. 'doctor' and 'sick man',
signify respectively the relation in question (in one aspect), and the
nature of one of the elements capable of entering into it;
consequently they are separable.

Now when it is said that knowledge is essentially knowledge of
reality, the statement is parallel to the assertion that a doctor is
essentially the doctor of a sick man, and not to the assertion that a
doctor is essentially the doctor of a patient. It should mean that
that which is capable of being related to a knower as his object is
something which is or exists; consequently it cannot be said that
since knowledge is of reality, reality must essentially be known. The
parallel to the assertion that a doctor is the doctor of a patient is
the assertion that knowledge is the knowledge of an object; for just
as 'patient' means that which receives treatment from a doctor, so
'object' means that which is known. And here we _can_ go on to make
the further parallel assertion that since knowledge is essentially the
knowledge of an object, an object is essentially an object of
knowledge. Just as 'patient' means a recipient of treatment, or, more
accurately, a sick man under treatment, so 'object' means something
known, or, more accurately, a reality known. And 'knowledge' and
'object of knowledge', like 'doctor' and 'patient', indicate the same
relation, though from different points of view, and, consequently,
when we can use the one term, we can use the other. But to say that an
object (i. e. a reality known) implies the knowledge of it is not to
say that reality implies the knowledge of it, any more than to say
that a patient implies a doctor is to say that a sick man implies a
doctor.

But a doctor, it might be objected, is not a fair parallel to
knowledge or a knower. A doctor, though an instance of a relative
term, is only an instance of one kind of relative term, that in which
the elements related are capable of existing apart from the relation,
the relation being one in which they can come to stand and cease to
stand. But there is another kind of relative term, in which the
elements related presuppose the relation, and any thought of these
elements involves the thought of the relation. A universal, e. g.
whiteness, is always the universal of certain individuals, viz.
individual whites; an individual, e. g. this white, is always an
individual of a universal, viz. whiteness. A genus is the genus of a
species, and vice versa. A surface is the surface of a volume, and a
volume implies a surface. A point is the end of a line, and a line is
bounded by points. In such cases the very being of the elements
related involves the relation, and, apart from the relation,
disappears. The difference between the two kinds of relative terms can
be seen from the fact that only in the case of the former kind can two
elements be found of which we can say significantly that their
relation is of the kind in question. We can say of two men that they
are related as doctor and patient, or as father and son, for we can
apprehend two beings as men without being aware of them as so related.
But of no two elements is it possible to say that their relation is
that of universal and individual, or of genus and species, or of
surface and volume; for to apprehend elements which are so related we
must apprehend them so related.[7] To apprehend a surface is to
apprehend a surface of a volume. To apprehend a volume is to apprehend
a volume bounded by a surface. To apprehend a universal is to
apprehend it as the universal of an individual, and vice versa.[8] In
the case of relations of this kind, the being of either element which
stands in the relation is relative to that of the other; neither can
be real without the other, as we see if we try to think of one without
the other. And it is at least possible that knowledge and reality or,
speaking more strictly, a knower and reality, are related in this way.

    [7] It is, of course, possible to say significantly that two
    elements, A and B, are related as universal and individual,
    or as surface and volume, if we are trying to explain what we
    mean by 'universal and individual' or 'surface and volume';
    but in that case we are elucidating the relationship through
    the already known relation of A and B, and are not giving
    information about the hitherto unknown relation of A and B.

    [8] Professor Cook Wilson has pointed out that the
    distinction between these two kinds of relation is marked
    in language in that, for instance, while we speak of the
    'relation _of_ universal _and_ individual', we speak of
    'the relation _between_ one man _and_ another', or of 'the
    relation _of_ one man _to_ another', using, however, the
    phrase 'the relation _of_ doctor _and_ patient', when we
    consider two men only as in that relation.

    I owe to him recognition of the fact that the use of the word
    'relation' in connexion with such terms as 'universal and
    individual' is really justified.

What is, however, at least a strong presumption against this view is
to be found in the fact that while relations of the second kind are
essentially non-temporal, the relation of knowing is essentially
temporal. The relation of a universal and its individuals, or of a
surface and the volume which it bounds, does not either come to be, or
persist, or cease. On the other hand, it is impossible to think of a
knowing which is susceptible of no temporal predicates and is not
bound up with a process; and the thought of knowing as something which
comes to be involves the thought that the elements which become thus
related exist independently of the relation. Moreover, the real
refutation of the view lies in the fact that, when we consider what we
really think, we find that we think that the relation between a knower
and reality is not of the second kind. If we consider what we mean by
'a reality', we find that we mean by it something which is not
correlative to a mind knowing it. It does not mean something the
thought of which disappears with the thought of a mind actually
knowing it, but something which, though it can be known by a mind,
need not be actually known by a mind. Again, just as we think of a
reality as something which _can_ stand as object in the relation of
knowledge, without necessarily being in this relation, so, as we see
when we reflect, we think of a knowing mind as something which _can_
stand as subject in this relation without necessarily being in the
relation. For though we think of the capacities which constitute the
nature of a knowing mind as only recognized through their
actualizations, i. e. through actual knowing, we think of the mind
which is possessed of these capacities as something apart from their
actualization.

It is now possible to direct attention to two characteristics of
perception and knowledge with which Kant's treatment of space and time
conflicts, and the recognition of which reveals his procedure in its
true light.

It has been already urged that both knowledge and perception--which,
though not identical with knowledge, is presupposed by it--are
essentially of _reality_. Now, in the _first_ place, it is thereby
implied that the relation between the mind and reality in knowledge or
in perception is essentially direct, i. e. that there is no _tertium
quid_ in the form of an 'idea' or a 'representation' between us as
perceiving or knowing and what we perceive or know. In other words, it
is implied that Locke's view is wrong in principle, and, in fact, the
contrary of the truth. In the _second_ place, it is implied that while
the whole fact of perception includes the reality perceived and the
whole fact of knowledge includes the reality known, since both
perception and knowledge are 'of', and therefore inseparable from a
reality, yet the reality perceived or known is essentially distinct
from, and cannot be stated in terms of, the perception or the
knowledge. Just as neither perception nor knowledge can be stated in
terms of the reality perceived or known from which they are
distinguished, so the reality perceived or known cannot be stated in
terms of the perception or the knowledge. In other words, the terms
'perception' and 'knowledge' ought to stand for the activities of
perceiving and knowing respectively, and not for the reality perceived
or known. Similarly, the terms 'idea' and 'representation'--the latter
of which has been used as a synonym for Kant's _Vorstellung_--ought to
stand not for something thought of or represented, but for the act of
thinking or representing.

Further, this second implication throws light on the proper meaning of
the terms 'form of perception' and 'form of knowledge or of thought'.
For, in accordance with this implication, a 'form of perception' and a
'form of knowledge' ought to refer to the nature of our acts of
perceiving and knowing or thinking respectively, and not to the nature
of the realities perceived or known. Consequently, Kant was right in
making the primary antithesis involved in the term 'form of
perception' that between a way in which we perceive and a way in which
things are, or, in other words, between a characteristic of our
perceiving nature and a characteristic of the reality perceived.
Moreover, Kant was also right in making this distinction a real
antithesis and not a mere distinction within one and the same thing
regarded from two points of view. That which is a form of perception
cannot also be a form of the reality and vice versa. Thus we may
illustrate a perceived form of perception by pointing out that our
apprehension of the physical world (1) is a temporal process, and (2)
is conditioned by perspective. Both the succession and the conditions
of perspective belong to the act of perception, and do not form part
of the nature of the world perceived. And it is significant that in
our ordinary consciousness it never occurs to us to attribute either
the perspective or the time to the reality perceived. Even if it be
difficult in certain cases, as in that of colour, to decide whether
something belongs to our act of perception or not, we never suppose
that it can be _both_ a form of perception _and_ a characteristic of
the reality perceived. We think that if it be the one, it cannot be
the other.

Moreover, if we pass from perception to knowledge or thought--which in
this context may be treated as identical--and seek to illustrate a
form of knowledge or of thought, we may cite the distinction of
logical subject and logical predicate of a judgement. The distinction
as it should be understood--for it does not necessitate a difference
of grammatical form--may be illustrated by the difference between the
judgements 'Chess is the _most trying of games_' and '_Chess_ is the
most trying of games'. In the former case 'chess' is the logical
subject, in the latter case it is the logical predicate. Now this
distinction clearly does not reside in or belong to the reality about
which we judge; it relates solely to the order of our approach in
thought to various parts of its nature. For, to take the case of the
former judgement, in calling 'chess' its subject, and 'most trying of
games' its predicate, we are asserting that in this judgement we begin
by apprehending the reality of which we are thinking as chess, and
come to apprehend it as the most trying of games. In other words, the
distinction relates solely to the order of our apprehension, and not
to anything in the thing apprehended.

In view of the preceding, it is possible to make clear the nature of
certain mistakes on Kant's part. In the first place, space, and time
also, so far as we are thinking of the world, and not of our
apprehension of it, as undergoing a temporal process, are essentially
characteristics not of perception but of the reality perceived, and
Kant, in treating space, and time, so regarded, as forms of
perception, is really transferring to the perceiving subject that
which in the whole fact 'perception of an object' or 'object
perceived' belongs to the object.

Again, if we go on to ask how Kant manages to avoid drawing the
conclusion proper to this transference, viz. that space and time are
not characteristics of any realities at all, but belong solely to the
process by which we come to apprehend them, we see that he does so
because, in effect, he contravenes both the characteristics of
perception referred to. For, in the first place, although in
conformity with his theory he almost always _speaks_ of space and time
in terms of perception,[9] he consistently _treats_ them as features
of the reality perceived, i. e. of phenomena. Thus in arguing that
space and time belong not to the understanding but to the sensibility,
although he uniformly speaks of them as perceptions, his argument
implies that they are objects of perception; for its aim, properly
stated, is to show that space and time are not objects of thought but
objects of perception. Consequently, in his treatment of space and
time, he refers to what are both to him and in fact objects of
perception in terms of perception, and thereby contravenes the second
implication of perception to which attention has been drawn. Again, in
the second place, if we go on to ask how Kant is misled into doing
this, we see that it is because he contravenes the first implication
of perception. In virtue of his theory of perception[10] he interposes
a _tertium quid_ between the reality perceived and the percipient, in
the shape of an 'appearance'. This _tertium quid_ gives him something
which can plausibly be regarded as at once a perception and something
perceived. For, though from the point of view of the thing in itself
an appearance is an appearance or a perception of it, yet, regarded
from the point of view of what it is in itself, an appearance is a
reality perceived of the kind called mental. Hence space and time,
being characteristics of an appearance, can be regarded as at once
characteristics of our perception of a reality, viz. of a thing in
itself, and characteristics of a reality perceived, viz. an
appearance. Moreover, there is another point of view from which the
treatment of bodies in space as appearances or phenomena gives
plausibility to the view that space, though a form of perception, is a
characteristic of a reality. When Kant speaks of space as the form of
phenomena the fact to which he refers is that all bodies are
spatial.[11] He means, not that space is a way in which we perceive
something, but that it is a characteristic of things perceived, which
he _calls_ phenomena, and which _are_ bodies. But, since in his
statement of this fact he substitutes for bodies phenomena, which to
him are perceptions, his statement can be put in the form 'space is
_the form of perceptions_'; and the statement in this form is verbally
almost identical with the statement that space is _a form of
perception_. Consequently, the latter statement, which _should_ mean
that space is a way in which we perceive things, is easily identified
with a statement of which the meaning is that space is a
characteristic of something perceived.[12]

    [9] Cf. p. 51, note 1.

    [10] Cf. p. 30 and ff.

    [11] Cf. p. 39.

    [12] It can be shown in the same way, _mutatis mutandis_ (cp.
    p. 111), that the view that time, though the form of inner
    perception, is a characteristic of a reality gains
    plausibility from Kant's implicit treatment of our states as
    appearances due to ourselves.

Again, Kant's account of time will be found to treat something
represented or perceived as also a perception. We find two consecutive
paragraphs[13] of which the aim is apparently to establish the
contrary conclusions: (1) that time is only the form of our internal
state and not of external phenomena, and (2) that time is the formal
condition of all phenomena, external and internal.

    [13] B. 49-50 (b) and (c), M. 30 (b) and (c).

To establish the first conclusion, Kant argues that time has nothing
to do with shape or position, but, on the contrary, determines the
relation of representations in our internal state. His meaning is that
we have a succession of perceptions or representations of bodies in
space,[14] and that while the bodies perceived are not related
temporally, our perceptions or representations of them are so
related. Here 'representations' refers to our apprehension, and
is distinguished from what is represented, viz. bodies in space.

    [14] Kant here refers to bodies by the term 'phenomena', but
    their character as phenomena is not relevant to his argument.

How, then, does Kant reach the second result? He remembers that bodies
in space are 'phenomena', i. e. representations. He is, therefore,
able to point out that all representations belong, as determinations
of the mind, to our internal state, whether they have external things,
i. e. bodies in space, for their objects or not, and that,
consequently, they are subject to time. Hence time is concluded to be
the form of all phenomena. In this second argument, however, it is
clear that Kant has passed from his previous treatment of bodies in
space as something represented or perceived to the treatment of them
as themselves representations or perceptions.[15]

    [15] It may be noted that Kant's assertion (B. 50, M. 31)
    that time is the immediate condition of internal phenomena,
    and thereby also mediately the condition of external
    phenomena, does not help to reconcile the two positions.

In conclusion, we may point out an insoluble difficulty in Kant's
account of time. His treatment of space and time as the forms of outer
and inner sense respectively implies that, while spatial relations
apply to the realities which we perceive, temporal relations apply
solely to our perceptions of them. Unfortunately, however, as Kant in
certain contexts is clearly aware, time also belongs to the realities
perceived. The moon, for instance, moves round the earth. Thus there
are what may be called real successions as well as successions in our
perception. Further, not only are we aware of this distinction in
general, but in particular cases we succeed in distinguishing a
succession of the one kind from a succession of the other. Yet from
Kant's standpoint it would be impossible to distinguish them in
particular cases, and even to be aware of the distinction in general.
For the distinction is possible only so long as a distinction is
allowed between our perceptions and the realities perceived. But for
Kant this distinction has disappeared, for in the end the realities
perceived are merely our perceptions; and time, if it be a
characteristic of anything, must be a characteristic only of our
perceptions.




CHAPTER VII

THE METAPHYSICAL DEDUCTION OF THE CATEGORIES


The aim of the _Aesthetic_ is to answer the first question of the
_Critique_ propounded in the Introduction, viz. 'How is pure
mathematics possible?'[1] The aim of the _Analytic_ is to answer the
second question, viz. 'How is pure natural science possible?' It has
previously[2] been implied that the two questions are only verbally of
the same kind. Since Kant thinks of the judgements of mathematics as
self-evident, and therefore as admitting of no reasonable doubt[3],
he takes their truth for granted. Hence the question, 'How is pure
mathematics possible?' means 'Granted the truth of mathematical
judgements, what inference can we draw concerning the nature of the
reality to which they relate?'; and the inference is to proceed from
the truth of the judgements to the nature of the reality to which
they relate. Kant, however, considers that the principles underlying
natural science, of which the law of causality is the most prominent,
are not self-evident, and consequently need proof.[4] Hence, the
question, 'How is pure natural science possible?' means 'What
justifies the assertion that the presuppositions of natural science
are true?' and the inference is to proceed from the nature of the
objects of natural science to the truth of the _a priori_ judgements
which relate to them.

    [1] B. 20, M. 13.

    [2] pp. 23-5.

    [3] Cf. p. 24, note 1.

    [4] Cf. p. 24, notes 2 and 3.

Again, as Kant rightly sees, the vindication of the presuppositions
of natural science, to be complete, requires the discovery upon a
definite principle of _all_ these presuppositions. The clue to this
discovery he finds in the view that, just as the perceptions of space
and time originate in the sensibility, so the _a priori_ conceptions
and laws which underlie natural science originate in the
understanding; for, on this view, the discovery of all the conceptions
and laws which originate in the understanding will be at the same time
the discovery of all the presuppositions of natural science.

Kant therefore in the _Analytic_ has a twofold problem to solve.
He has firstly to discover the conceptions and laws which belong to
the understanding as such, and secondly to vindicate their application
to individual things. Moreover, although it is obvious that the
conceptions and the laws of the understanding must be closely
related,[5] he reserves them for separate treatment.

    [5] E. g. the conception of 'cause and effect', and the law
    that 'all changes take place according to the law of the
    connexion between cause and effect'.

The _Analytic_ is accordingly subdivided into the _Analytic of
Conceptions_ and the _Analytic of Principles_. The _Analytic of
Conceptions_, again, is divided into the _Metaphysical Deduction of
the Categories_, the aim of which is to discover the conceptions
of the understanding, and the _Transcendental Deduction of the
Categories_, the aim of which is to vindicate their validity,
i. e. their applicability to individual things.

It should further be noticed that, according to Kant, it is the
connexion of the _a priori_ conceptions and laws underlying natural
science with the _understanding_ which constitutes the main difficulty
of the vindication of their validity, and renders necessary an answer
of a different kind to that which would have been possible, if the
validity of mathematical judgements had been in question.

"We have been able above, with little trouble, to make comprehensible
how the conceptions of space and time, although _a priori_ knowledge,
must necessarily relate to objects and render possible a synthetic
knowledge of them independently of all experience. For since an object
can appear to us, i. e. be an object of empirical perception, only by
means of such pure forms of sensibility, space and time are pure
perceptions, which contain _a priori_ the condition of the possibility
of objects as phenomena, and the synthesis in space and time has
objective validity."

"On the other hand, the categories of the understanding do not
represent the conditions under which objects are given in perception;
consequently, objects can certainly appear to us without their
necessarily being related to functions of the understanding, and
therefore without the understanding containing _a priori_ the
conditions of these objects. Hence a difficulty appears here, which
we did not meet in the field of sensibility, viz. how _subjective
conditions of thought_ can have _objective validity_, i. e. can
furnish conditions of the possibility of all knowledge of objects;
for phenomena can certainly be given us in perception without the
functions of the understanding. Let us take, for example, the
conception of cause, which indicates a peculiar kind of synthesis in
which on A something entirely different B is placed[6] according to a
law. It is not _a priori_ clear why phenomena should contain something
of this kind ... and it is consequently doubtful _a priori_, whether
such a conception is not wholly empty, and without any corresponding
object among phenomena. For that objects of sensuous perception must
conform to the formal conditions of the sensibility which lie _a
priori_ in the mind is clear, since otherwise they would not be
objects for us; but that they must also conform to the conditions
which the understanding requires for the synthetical unity of thought
is a conclusion the cogency of which it is not so easy to see. For
phenomena might quite well be so constituted that the understanding
did not find them in conformity with the conditions of its unity, and
everything might lie in such confusion that, e. g. in the succession
of phenomena, nothing might present itself which would offer a rule of
synthesis, and so correspond to the conception of cause and effect, so
that this conception would be quite empty, null, and meaningless.
Phenomena would none the less present objects to our perception, for
perception does not in any way require the functions of thinking."[7]

    [6] _Gesetzt._

    [7] B. 121-3, M. 75-6.

This passage, if read in connexion with that immediately preceding
it,[8] may be paraphrased as follows: 'The argument of the _Aesthetic_
assumes the validity of mathematical judgements, which as such relate
to space and time, and thence it deduces the phenomenal character of
space and time, and of what is contained therein. At the same time the
possibility of questioning the validity of the law of causality, and
of similar principles, may lead us to question even the validity of
mathematical judgements. In the case of mathematical judgements,
however, in consequence of their relation to perception, an answer is
readily forthcoming. We need only reverse the original argument and
appeal directly to the phenomenal character of space and time and of
what is contained in them. Objects in space and time, being
appearances, must conform to the laws according to which we have
appearances; and since space and time are only ways in which we
perceive, or have appearances, mathematical laws, which constitute the
general nature of space and time, are the laws according to which we
have appearances. Mathematical laws, then, constitute the general
structure of appearances, and, as such, enter into the very being
of objects in space and time. But the case is otherwise with the
conceptions and principles underlying natural science. For the law of
causality, for instance, is a law not of our perceiving but of our
thinking nature, and consequently it is not presupposed in the
presentation to us of objects in space and time. Objects in space
and time, being appearances, need conform only to the laws of our
perceiving nature. We have therefore to explain the possibility of
saying that a law of our thinking nature must be valid for objects
which, as conditioned merely by our perceiving nature, are independent
of the laws of our thinking; for phenomena might be so constituted as
not to correspond to the necessities of our thought.'

    [8] B. 120-1, M. 73-4.

No doubt Kant's _solution_ of this problem in the _Analytic_ involves
an emphatic denial of the central feature of this statement of it,
viz. that phenomena may be given in perception without any help from
the activity of the understanding.[9] Hence it may be urged that this
passage merely expresses a temporary aberration on Kant's part, and
should therefore be ignored. Nevertheless, in spite of this
inconsistency, the view that phenomena may be given in perception
without help from the activity of the understanding forms the basis
of the difference of treatment which Kant thinks necessary for the
vindication of the judgements underlying natural science and for that
of the judgements of mathematics.

    [9] Cf. B. 137-8, M. 85, and B. 160 note, M. 98 note.

We may now consider how Kant 'discovers' the categories or conceptions
which belong to the understanding as such.[10] His method is sound in
principle. He begins with an account of the understanding in general.
He then determines its essential differentiations. Finally, he argues
that each of these differentiations involves a special conception,
and that therefore these conceptions taken together constitute an
exhaustive list of the conceptions which belong to the understanding.

    [10] B. 91-105, M. 56-63.

His account of the understanding is expressed thus: "The understanding
was explained above only negatively, as a non-sensuous faculty of
knowledge. Now, independently of sensibility, we cannot have any
perception; consequently, the understanding is no faculty of
perception. But besides perception there is no other kind of
knowledge, except through conceptions. Consequently, the knowledge of
every understanding, or at least of every human understanding, is a
knowledge through conceptions,--not perceptive, but discursive. All
perceptions, as sensuous, depend on affections; conceptions,
therefore, upon functions. By the word function, I understand the
unity of the act of arranging different representations under one
common representation. Conceptions, then, are based on the spontaneity
of thinking, as sensuous perceptions are on the receptivity of
impressions. Now the understanding cannot make any other use of these
conceptions than to judge by means of them. Since no representation,
except only the perception, refers immediately to the object, a
conception is never referred immediately to an object, but to some
other representation thereof, be that a perception or itself a
conception. A judgement, therefore, is the mediate knowledge of an
object, consequently the representation of a representation of it. In
every judgement there is a conception which is valid for many
representations, and among these also comprehends a given
representation, this last being then immediately referred to the
object. For example, in the judgement 'All bodies are divisible', our
conception of the divisible refers to various other conceptions; among
these, however, it is herein particularly referred to the conception
of body, and this conception of body is referred to certain phenomena
which present themselves to us. These objects, therefore, are
mediately represented by the conception of divisibility. Accordingly,
all judgements are functions of unity in our representations, since,
instead of an immediate, a higher representation, which comprehends
this and several others, is used for the knowledge of the object, and
thereby many possible items of knowledge are collected into one. But
we can reduce all acts of the understanding to judgements, so that the
_understanding_ in general can be represented as a _faculty of
judging_."[11]

    [11] B. 92-4, M. 56-7.

It is not worth while to go into all the difficulties of this confused
and artificial passage. Three points are clear upon the surface. In
the first place, the account of the understanding now given differs
from that given earlier in the _Critique_[12] in that, instead of
merely distinguishing, it separates the sensibility and the
understanding, and treats them as contributing, not two inseparable
factors involved in all knowledge, but two kinds of knowledge. In the
second place, the guise of argument is very thin, and while Kant
ostensibly _proves_, he really only _asserts_ that the understanding
is the faculty of judgement. In the third place, in describing
judgement Kant is hampered by trying to oppose it as the mediate
knowledge of an object to perception as the immediate knowledge of an
object. A perception is said to relate immediately to an object; in
contrast with this, a conception is said to relate immediately only to
another conception or to a perception, and mediately to an object
through relation to a perception, either directly or through another
conception. Hence a judgement, as being the use of a conception, viz.
the predicate of the judgement, is said to be the mediate knowledge of
an object. But if this distinction be examined, it will be found that
two kinds of immediate relation are involved, and that the account of
perception is not really compatible with that of judgement. When a
perception is said to relate immediately to an object, the relation in
question is that between a sensation or appearance produced by an
object acting upon or affecting the sensibility and the object which
produces it. But when a conception is said to relate immediately to
another conception or to a perception, the relation in question is
that of universal and particular, i. e. that of genus and species or
of universal and individual. For the conception is said to be 'valid
for' (i. e. to 'apply to') and to 'comprehend' the conception or
perception to which it is immediately related; and again, when a
conception is said to relate mediately to an object, the relation
meant is its 'application' to the object, even though in this case
the application is indirect. Now if a perception to which a
conception is related--either directly or indirectly through another
conception--were an appearance produced by an object, the conception
could never be related to the object in the sense required, viz. that
it applies to it; for an appearance does not _apply to_ but is
_produced_ by the object. Consequently, when Kant is considering a
conception, and therefore also when he is considering a judgement,
which is the use of a conception, he is really thinking of the
perception to which it is related as an _object of_ perception, i. e.
as a perceived individual, and he has ceased to think of a perception
as an appearance produced by an object.[13] Hence in considering
Kant's account of a conception and of judgement, we should ignore his
account of perception, and therefore also his statement that judgement
is the mediate knowledge of an object.

    [12] B. 74-6, M. 45-6.

    [13] Kant, in _illustrating_ the nature of a judgement,
    evades the difficulty occasioned by his account of
    perception, by illustrating a 'perception' by the 'conception
    of body', and 'objects' by 'certain phenomena'. He thereby
    covertly substitutes the relation of universal and individual
    for the relation of an appearance and the object which causes
    it.

If we do so, we see that Kant's account of judgement simply amounts to
this: 'Judgement is the use of a conception or 'universal'; the use of
a conception or universal consists in bringing under it corresponding
individuals or species. Consequently, judgement is a function
producing unity. If, for instance, we judge 'All bodies are
divisible', we thereby unify 'bodies' with other kinds of divisible
things by bringing them under the conception of divisibility; and if
we judge 'This body is divisible' we thereby unify this divisible
body with others by bringing it and them under the conception of
divisibility.'[14] Again, since 'the understanding in general can be
represented as a _faculty of judging_', it follows that the activity
of the understanding consists in introducing unity into our
representations, by bringing individuals or species--both these being
representations--under the corresponding universal or conception.[15]

    [14] It is not Kant's general account of judgement given in
    this passage, but the account of perception incompatible with
    it, which leads him to confine his illustrations to universal
    judgements.

    [15] We may note three minor points. (1) Kant's definition of
    function as 'the unity of the act of arranging [i. e. the act
    which produces unity by arranging] different representations
    under a common representation' has no justification in its
    immediate context, and is occasioned solely by the
    forthcoming description of judgement. (2) Kant has no right
    to distinguish the activity which _originates_ conceptions,
    or upon which they depend, from the activity which _uses_
    conceptions, viz. judgement. For the act of arranging diverse
    representations under a common representation which
    originates conceptions is the act of judgement as Kant
    describes it. (3) It is wholly artificial to speak of
    judgement as 'the representation of a representation of an
    object'.

Having explained the nature of the understanding, Kant proceeds to
take the next step. His aim being to connect the understanding with
the categories, and the categories being a plurality, he has to show
that the activity of judgement can be differentiated into several
kinds, each of which must subsequently be shown to involve a special
category. Hence, solely in view of the desired conclusion, and in
spite of the fact that he has described the activity of judgement as
if it were always of the same kind, he passes in effect from the
singular to the plural and asserts that 'all the functions of the
understanding can be discovered, when we can completely exhibit the
functions of unity in judgements'. After this preliminary transition,
he proceeds to assert that, if we abstract in general from all content
of a judgement and fix our attention upon the mere form of the
understanding, we find that the function of thinking in a judgement
can be brought under four heads, each of which contains three
subdivisions. These, which are borrowed with slight modifications from
Formal Logic, are expressed as follows.[16]

    I. _Quantity._
       Universal
       Particular
       Singular.

   II. _Quality._
       Affirmative
       Negative
       Infinite.

  III. _Relation._
       Categorical
       Hypothetical
       Disjunctive.

   IV. _Modality._
       Problematic
       Assertoric
       Apodeictic.

These distinctions, since they concern only the form of judgements,
belong, according to Kant, to the activity of judgement as such, and
in fact constitute its essential differentiations.

    [16] B. 95, M. 58.

Now, before we consider whether this is really the case, we should
ask what answer Kant's account of judgement would lead us to expect
to the question 'What are all the functions of unity in judgement?'
The question must mean 'What are the kinds of unity produced by
judgement?' To this question three alternative answers are prima facie
possible. (1) There is only one kind of unity, that of a group of
particulars unified through relation to the corresponding universal.
The special unity produced will differ for different judgements, since
it will depend upon the special universal involved. The kind or form
of unity, however, will always be the same, viz. that of particulars
related through the corresponding universal. For instance, 'plants'
and 'trees' are unified respectively by the judgements 'This body is a
plant' and 'This body is a tree'; for 'this body' is in the one case
related to other 'plants' and in the other case to other 'trees'. And
though the unity produced is different in each case, the kind of unity
is the same; for plants and trees are, as members of a kind, unities
of a special kind distinct from unities of another kind, such as the
parts of a spatial or numerical whole. (2) There are as many kinds of
unity as there are universals. Every group of particulars forms a
unity of a special kind through relation to the corresponding
universal. (3) There are as many kinds of unity as there are highest
universals or _summa genera_. These _summa genera_ are the most
general sources of unity through which individuals are related in
groups, directly or indirectly. The kinds of unity are therefore in
principle the Aristotelian categories, i. e. the highest forms of
being under which all individuals fall.

Nevertheless, it is easy to see that the second and third answers
should be rejected in favour of the first. For though, according to
Kant, a judgement unifies particulars by bringing them under a
universal, the special universal involved in a given judgement belongs
not to the judgement as such, but to the particulars unified. What
belongs to the judgement as such is simply the fact that the
particulars are brought under a universal. In other words, the
judgement as such determines the kind of unity but not the particular
unity. The judgements 'Gold is a metal' and 'Trees are green',
considered merely as judgements and not as the particular judgements
which they are, involve the same kind of unity, viz. that of
particulars as particulars of a universal; for the distinction between
'metal' and 'green' is a distinction not of kinds of unity but of
unities. Moreover, to anticipate the discussion of Kant's final
conclusion, the moral is that Kant's account of judgement should have
led him to recognize that judgement involves the reality, not of any
special universals or--in Kant's language--conceptions, but of
universality or conception as such. In other words, on his view of
judgement the activity of the understanding implies simply that there
_are_ universals or conceptions; it does not imply the existence of
special conceptions which essentially belong to the understanding,
e. g. that of 'cause' or 'plurality'.[17]

    [17] To this failure in Kant's argument is due the difficulty
    in following his transition from 'function' to 'functions' of
    judgements. The judgement, as Kant describes it, always does
    one and the same thing; it unifies particulars by bringing
    them under a universal. This activity does not admit of
    differentiation.

If we now turn to the list of the activities of thought in judgement,
borrowed from Formal Logic, we shall see that it is not in any way
connected with Kant's account of judgement.[18] For if the kinds of
judgement distinguished by Formal Logic are to be regarded as
different ways of unifying, the plurality unified must be allowed to
be not a special kind of group of particulars, but the two conceptions
which constitute the terms of the judgement[19]; and the unity
produced must be allowed to be in no case a special form of the unity
of particulars related through the corresponding universal. Thus the
particular judgement 'Some coroners are doctors' must be said to unify
the conceptions of 'coroner' and of 'doctor', and presumably by means
of the conception of 'plurality'. Again, the hypothetical judgement
'If it rains, the ground will be wet' must be said to unify the
judgements 'It rains' and 'The ground will be wet', and presumably by
means of the conception of 'reason and consequence'. In neither case
can the act of unification be considered a special form of the act of
recognizing particulars as particulars of the corresponding universal.
The fact is that the distinctions drawn by Formal Logic are based on a
view of judgement which is different from, and even incompatible with,
Kant's, and they arise from the attempt to solve a different problem.
The problem before Kant in describing judgement is to distinguish the
understanding from the sensibility, i. e. thought from perception.
Hence he regards judgement as the act of unifying a manifold given in
perception, directly, or indirectly by means of a conception. But this
is not the problem with which Formal Logic is occupied. Formal Logic
assumes judgement to be an act which relates material given to it in
the shape of 'conceptions' or 'judgements' by analysis of this
material, and seeks to discover the various modes of relation thereby
effected. The work of judgement, however, cannot consist _both_ in
relating particulars through a conception _and_ in relating two
conceptions or judgements.

    [18] Moreover, the forms of judgement clearly lack the
    systematic character which Kant claims for them. Even if it
    be allowed that the subdivisions within the four main heads
    of quantity, quality, relation, and modality are based upon
    single principles of division, it cannot be said that the
    four heads themselves originate from a common principle.

    [19] In the case of the third division, the plurality unified
    will be two prior judgements.

It may be urged that this criticism only affects Kant's argument, but
not his conclusion. Possibly, it may be said, the list of types of
judgement borrowed from Formal Logic really expresses the essential
differentiations of judgement, and, in that case, Kant's only mistake
is that he bases them upon a false or at least inappropriate account
of judgement.[20] Moreover, since this list furnishes Kant with the
'clue' to the categories, provided that it expresses the essential
differentiations of judgement, the particular account of judgement
upon which it is based is a matter of indifference.

    [20] It may be noted that the account cannot be merely
    inappropriate to the general problem, if it be _incompatible_
    with that assumed by Formal Logic.

This contention leads us to consider the last stage of Kant's
argument, in which he deduces the categories in detail from his list
of the forms of judgement. For it is clear that unless the forms of
judgement severally involve the categories, it will not matter whether
these forms are or are not the essential differentiations of
judgement.

Kant's mode of connecting the categories in detail with the forms of
judgement discovered by Formal Logic is at least as surprising as his
mode of connecting the latter with the nature of judgement in general.
Since the twelve distinctions within the form of judgement are to
serve as a clue to the conceptions which belong to the understanding,
we naturally expect that each distinction will be found directly to
involve a special conception or category, and that therefore, to
discover the categories, we need only look for the special conception
involved in each form of judgement.[21] Again, since the plurality
unified in a judgement of each form is the two conceptions or
judgements which form the matter of the judgement, we should expect
the conception involved in each form of judgement to be merely the
type of relationship established between these conceptions or
judgements. This expectation is confirmed by a cursory glance at the
table of categories.[22]

    I. _Of Quantity._
       Unity
       Plurality
       Totality.

   II. _Of Quality._
       Reality
       Negation
       Limitation.

  III. _Of Relation._
       Inherence and Subsistence (_Substantia et Accidens_)
       Causality and Dependence (_Cause and Effect_)
       Community (_Reciprocity between the agent and patient._)

   IV. _Of Modality._
       Possibility--Impossibility
       Existence--Non-existence
       Necessity--Contingence.

If we compare the first division of these categories with the first
division of judgements we naturally think that Kant conceived
singular, particular, and universal judgements to unify their terms
by means of the conceptions of 'one', of 'some', and of 'all'
respectively; and we form corresponding, though less confident,
expectations in the case of the other divisions.

    [21] This expectation is confirmed by Kant's view that
    judgement introduces unity into a plurality by means of a
    conception. This view leads us to expect that different forms
    of judgement--if there be any--will be distinguished by the
    different conceptions through which they unify the plurality;
    for it will naturally be the different conceptions involved
    which are responsible for the different kinds of unity
    effected.

    [22] B. 106, M. 64.

Kant, however, makes no attempt to show that each form of judgement
distinguished by Formal Logic involves a special conception. In fact,
his view is that the activities of thought studied by Formal Logic do
not originate or use any special conceptions at all. For his actual
deduction of the categories[23] is occupied in showing that although
thought, when exercised under the conditions under which it is studied
by Formal Logic, does not originate and use conceptions of its own, it
is able under certain other conditions to originate and use such
conceptions, i. e. categories.[24] Hence if we attend only to the
professed procedure of the deduction, we are compelled to admit that
the deduction not only excludes any use of the 'clue' to the
categories, supposed to be furnished by Formal Logic, but even fails
to deduce them at all. For it does not even nominally attempt to
discover the categories in detail, but reverts to the prior task of
showing merely that there are categories. Doubtless Kant thinks that
the forms of judgement formulated by Formal Logic in some way
_suggest_ the conceptions which become operative in thought under
these other conditions. Nevertheless, it is impossible to see how
these forms of judgement can suggest these conceptions, unless they
actually presuppose them.

It is clear, however, that the professed link[25] between the forms of
judgement and the categories does not represent the actual process by
which Kant reached his list of categories; for he could never have
reached any list of categories by an argument which was merely
directed to show that there are categories. Moreover, an inspection of
the list shows that he actually reached it partly by noticing the
conceptions which the forms of judgement seemed to presuppose, and
partly by bearing in mind the general conceptions underlying physics
which it was his ultimate aim to vindicate. Since this is the case,
and since the categories can only be connected with the forms of
judgement by showing that they are presupposed in them, the proper
question to be considered from the point of view of the metaphysical
deduction is simply whether the forms of judgement really presuppose
the categories.[26]

    [23] B. 102-5, M. 62-3.

    [24] Cf. p. 166.

    [25] B. 102-5, M. 62-3.

    [26] As we shall see later, the real importance of the
    passage in which Kant professes to effect the transition from
    the forms of judgement to the categories (B. 102-5, M. 62-3)
    lies in its introduction of a new and important line of
    thought, on which the transcendental deduction turns.
    Consideration of it is therefore deferred to the next
    chapter.

If, however, we examine the forms of judgement distinguished by Formal
Logic, we find that they do not presuppose the categories. To see
this, it is only necessary to examine the four main divisions of
judgement _seriatim_.

The first division of judgements is said to be a division in respect
of quantity into singular, particular, and universal. So stated, the
division is numerical. It is a division of judgements according as
they make an assertion about one, more than one, or all the members of
a kind. Each species may be said to presuppose (1) the conception of
quantity, and (2) a conception peculiar to itself: the first
presupposing the conception of one member of a kind, the second that
of more than one but less than all members of a kind, the third that
of all members of a kind. Moreover, a judgement of each kind may
perhaps be said to relate the predicate conception to the subject
conception by means of one of these three conceptions.

The fundamental division, however, into which universal and singular
judgements enter is not numerical at all, and ignores particular
judgements altogether. It is that between such judgements as
'Three-sided figures, as such, are three-angled' and 'This man is
tall'. The essential distinction is that in the universal judgement
the predicate term is apprehended to belong to the subject through
our insight that it is necessitated by the nature of the subject term,
while in the singular judgement our apprehension that the predicate
term belongs to the subject is based upon the perception or experience
of the coexistence of predicate and subject terms in a common subject.
In other words, it is the distinction between an _a priori_ judgement
and a judgement of perception.[27] The merely numerically universal
judgement, and the merely numerically particular judgement[28] are
simply aggregates of singular judgements, and therefore are
indistinguishable in principle from the singular judgement. If then we
ask what conceptions are really presupposed by the kinds of judgement
which Kant seeks to distinguish in the first division, we can only
reply that the universal judgement presupposes the conception of a
connected or systematic whole of attributes, and that the singular
judgement presupposes the conception of the coexistence of two
attributes in a common subject. Neither kind of judgement presupposes
the conception of quantity or the conceptions of unity, plurality, and
totality.

    [27] I owe this view of the distinction to Professor Cook
    Wilson's lectures on logic.

    [28] 'Some coroners are doctors' of course in some contexts
    means, 'it is possible for a coroner to be a doctor,' and is
    therefore not numerical; but understood in this sense it is
    merely a weakened form of the universal judgement in which
    the connexion apprehended between subject and predicate terms
    is incomplete.

The second division of judgements is said to be a division in respect
of quality into affirmative, negative, and infinite, i. e. into
species which may be illustrated by the judgements, 'A college is a
place of education,' 'A college is not a hotel,' and 'A college is a
not-hotel'. The conceptions involved are said to be those of reality,
of negation, and of limitation respectively. The conception of
limitation may be ignored, since the infinite judgement said to
presuppose it is a fiction. On the other hand, the conceptions of
reality and negation, even if their existence be conceded, cannot be
allowed to be the conceptions presupposed. For when we affirm or deny,
we affirm or deny of something not mere being, but being of a
particular kind. The conceptions presupposed are rather those of
identity and difference. It is only because differences fall within an
identity that we can affirm, and it is only because within an identity
there are differences that we can deny.

The third division of judgements is said to be in respect of relation
into categorical, hypothetical, and disjunctive judgements. Here,
again, the conclusion which Kant desires is clearly impossible. The
categorical judgement may be said to presuppose the conception of
subject and attribute, but not that of substance and accident. The
hypothetical judgement may be conceded to presuppose the conception of
reason and consequence, but it certainly does not presuppose the
conception of cause and effect.[29] Lastly, while the disjunctive
judgement may be said to presuppose the conception of mutually
exclusive species of a genus, it certainly does not presuppose the
conception of reciprocal action between physical things.

    [29] No doubt, as the schematism of the categories shows,
    Kant does not think that the hypothetical judgement
    _directly_ involves the conception of cause and effect, i. e.
    of the relation of necessary succession between the various
    states of physical things. The point is, however, that the
    hypothetical judgement does not involve it at all.

The fourth division of judgement is said to be in respect of modality
into assertoric, problematic, and apodeictic, the conceptions
involved being respectively those of possibility and impossibility, of
actuality and non-actuality, and of necessity and contingence. Now,
from the point of view of Kant's argument, these conceptions, like
those which he holds to be involved in the other divisions of
judgement, must be considered to relate to reality and not to our
attitude towards it. Considered in this way, they resolve themselves
into the conceptions of--

(1) the impossible (impossibility);
(2) the possible but not actual (possibility, nonexistence);
(3) the actual but not necessary (existence, contingence);
(4) the necessary (necessity).

But since it must, in the end, be conceded that all fact is necessary,
it is impossible to admit the reality of the conception of the
possible but not actual, and of the actual but not necessary. There
remain, therefore, only the conceptions of the necessary and of the
impossible. In fact, however, the distinctions between the assertoric,
the problematic, and the apodeictical judgement relate to our attitude
to reality and not to reality, and therefore involve no different
conceptions relating to reality. It must, therefore, be admitted
that the 'metaphysical' deduction of the categories breaks down
doubly. Judgement, as Kant describes it, does not involve the
forms of judgement borrowed from Formal Logic as its essential
differentiations; and these forms of judgement do not involve the
categories.




CHAPTER VIII

THE TRANSCENDENTAL DEDUCTION OF THE CATEGORIES


The aim of the _Transcendental Deduction_ is to show that the
categories, though _a priori_ as originating in the understanding, are
valid, i. e. applicable to individual things. It is the part of the
_Critique_ which has attracted most attention and which is the most
difficult to follow. The difficulty of interpretation is increased
rather than diminished by the complete rewriting of this portion in
the second edition. For the second version, though it does not imply
a change of view, is undoubtedly even more obscure than the first.
It indeed makes one new contribution to the subject by adding an
important link in the argument,[1] but the importance of the link
is nullified by the fact that it is not really the link which it
professes to be. The method of treatment adopted here will be to
consider only the minimum of passages necessary to elucidate Kant's
meaning and to make use primarily of the first edition.

    [1] Cf. p. 206-10.

It is necessary, however, first to consider the passage in the
_Metaphysical Deduction_ which nominally connects the list of
categories with the list of forms of judgement.[2] For its real
function is to introduce a new and third account of knowledge, which
forms the keynote of the _Transcendental Deduction_.[3]

    [2] B. 102-5, M. 62-3. Cf. pp. 155-6.

    [3] The first two accounts are (1) that of judgement given B.
    92-4, M. 56-8, and (2) that of judgement implicit in the view
    that the forms of judgement distinguished by Formal Logic are
    functions of unity. In A. 126, Mah. 215, Kant seems to
    imply--though untruly--that this new account coincides with
    the other two, which he does not distinguish.

In this passage, the meaning of which it is difficult to state
satisfactorily, Kant's thought appears to be as follows: 'The activity
of thought studied by Formal Logic relates by way of judgement
conceptions previously obtained by an analysis of perceptions. For
instance, it relates the conceptions of body and of divisibility,
obtained by analysis of perceptions of bodies, in the judgement
'Bodies are divisible'. It effects this, however, merely by analysis
of the conception 'body'. Consequently, the resulting knowledge or
judgement, though _a priori_, is only analytic, and the conceptions
involved originate not from thought but from the manifold previously
analysed. But besides the conceptions obtained by analysis of a given
manifold, there are others which belong to thought or the
understanding as such, and in virtue of which thought originates
synthetic _a priori_ knowledge, this activity of thought being that
studied by Transcendental Logic. Two questions therefore arise.
Firstly, how do these conceptions obtain a matter to which they can
apply and without which they would be without content or empty? And,
secondly, how does thought in virtue of these conceptions originate
synthetic _a priori_ knowledge? The first question is easily answered,
for the manifolds of space and time, i. e. individual spaces and
individual times, afford matter of the kind needed to give these
conceptions content. As perceptions (i. e. as objects of perception),
they are that to which a conception can apply, and as pure or _a
priori_ perceptions, they are that to which those conceptions can
apply which are pure or _a priori_, as belonging to the understanding.
The second question can be answered by considering the process by
which this pure manifold of space and time enters into knowledge. All
synthetic knowledge, whether empirical or _a priori_, requires the
realization of three conditions. In the first place, there must be a
manifold given in perception. In the second place, this manifold must
be 'gone through, taken up, and combined'. In other words, if
synthesis be defined as 'the act of joining different representations
to one another and of including their multiplicity in one knowledge',
the manifold must be subjected to an act of synthesis. This is
effected by the imagination. In the third place, this synthesis
produced by the imagination must be brought to a conception, i. e.
brought under a conception which will constitute the synthesis a
unity. This is the work of the understanding. The realization of _a
priori_ knowledge, therefore, will require the realization of the
three conditions in a manner appropriate to its _a priori_ character.
There must be a pure or _a priori_ manifold; this is to be found in
individual spaces and individual times. There must be an act of pure
synthesis of this manifold; this is effected by the pure imagination.
Finally, this pure synthesis must be brought under a conception. This
is effected by the pure understanding by means of its pure or a priori
conceptions, i. e. the categories. This, then, is the process by which
_a priori_ knowledge is originated. The activity of thought or
understanding, however, which unites two conceptions in a judgement by
analysis of them--this being the act studied by Formal Logic--is the
same as that which gives unity to the synthesis of the pure manifold
of perception--this being the act studied by Transcendental Logic.
Consequently, 'the same understanding, and indeed by the same
activities whereby in dealing with conceptions it unifies them in a
judgement by an act of analysis, introduces by means of the
synthetical unity which it produces in the pure manifold of perception
a content into its own conceptions, in consequence of which these
conceptions are called pure conceptions of the understanding,'[4] and
we are entitled to say _a priori_ that these conceptions apply to
objects because they are involved in the process by which we acquire
_a priori_ knowledge of objects.'

    [4] An interpretation of B. 105 init., M. 63 fin.

A discussion of the various difficulties raised by the general drift
of this passage, as well as by its details,[5] is unnecessary, and
would anticipate discussion of the _Transcendental Deduction_. But it
is necessary to draw attention to three points.

    [5] E. g. Kant's arbitrary assertion that the operation of
    counting presupposes the conception of that number which
    forms the scale of notation adopted as the source of the
    unity of the synthesis. This is of course refuted among other
    ways by the fact that a number of units less than the scale
    of notation can be counted.

In the first place, as has been said, Kant here introduces--and
introduces without warning--a totally new account of knowledge. It has
its origin in his theory of perception, according to which knowledge
begins with the production of sensations in us by things in
themselves. Since the spatial world which we come to know consists in
a multiplicity of related elements, it is clear that the isolated data
of sensation have somehow to be combined and unified, if we are to
have this world before us or, in other words, to know it. Moreover,
since these empirical data are subject to space and time as the forms
of perception, individual spaces and individual times, to which the
empirical data will be related, have also to be combined and unified.
On this view, the process of knowledge consists in combining certain
data into an individual whole and in unifying them through a principle
of combination.[6] If the data are empirical, the resulting knowledge
will be empirical; if the data are _a priori_, i. e. individual spaces
and individual times, the resulting knowledge will be _a priori_.[7]
This account of knowledge is new, because, although it treats
knowledge as a process or act of unifying a manifold, it describes a
different act of unification. As Kant first described the faculty of
judgement,[8] it unifies a group of particulars through relation to
the corresponding universal. As Formal Logic, according to Kant,
treats the faculty of judgement, it unifies two conceptions or two
prior judgements into a judgement. As Kant now describes the faculty
of judgement or thought, it unifies an empirical or an _a priori_
manifold of perception combined into an individual whole, through a
conception which constitutes a principle of unity. The difference
between this last account and the others is also shown by the fact
that while the first two kinds of unification are held to be due to
mere analysis of the material given to thought, the third kind of
unification is held to be superinduced by thought, and to be in no way
capable of being extracted from the material by analysis. Further,
this new account of knowledge does not replace the others, but is
placed side by side with them. For, according to Kant, there exist
_both_ the activity of thought which relates two conceptions in a
judgement,[9] _and_ the activity by which it introduces a unity of its
own into a manifold of perception. Nevertheless, this new account of
knowledge, or rather this account of a new kind of knowledge, must be
the important one; for it is only the process now described for the
first time which produces synthetic as opposed to analytic knowledge.

    [6] Cf. A. 97, Mah. 193, 'Knowledge is a totality of compared
    and connected representations.'

    [7] No doubt Kant would allow that at least some categories,
    e. g. the conception of cause and effect, are principles of
    synthesis of a manifold which at any rate contains an
    empirical element, but it _includes_ just one of the
    difficulties of the passage that it implies that _a priori_
    knowledge either is, or involves, a synthesis of pure or _a
    priori_ elements.

    [8] B. 92-4, M. 56-8.

    [9] Kant, of course, thinks of this activity of thought,
    as identical with that which brings particulars under a
    conception.

In the second place, the passage incidentally explains why, according
to Kant, the forms of judgement distinguished by Formal Logic do not
involve the categories.[10] For its doctrine is that while thought, if
exercised under the conditions under which it is studied by Formal
Logic, can only analyse the manifold given to it, and so has, as it
were, to borrow from the manifold the unity through which it relates
the manifold,[11] yet if an _a priori_ manifold be given to it, it can
by means of a conception introduce into the manifold a unity of its
own which could not be discovered by analysis of the manifold. Thus
thought as studied by Formal Logic merely analyses and consequently
does not and cannot make use of conceptions of its own; it can use
conceptions of its own only when an _a priori_ manifold is given to it
to deal with.

    [10] Cf. pp. 155-6.

    [11] In bringing perceptions under a conception, thought,
    according to Kant, finds the conception _in_ the perceptions
    by analysis of them, and in relating two conceptions in
    judgement, it determines the particular form of judgement by
    analysis of the conceptions.

In the third place, there is great difficulty in following the part in
knowledge assigned to the understanding. The synthesis of the manifold
of perception is assigned to the imagination, a faculty which, like
the new kind of knowledge, is introduced without notice. The business
of the understanding is to 'bring this synthesis to conceptions' and
thereby to 'give unity to the synthesis'. Now the question arises
whether 'the activity of giving unity to the synthesis' really means
what it says, i. e. an activity which _unifies_ or _introduces a unity
into_ the synthesis, or whether it only means an activity which
_recognizes_ a unity already given to the synthesis by the
imagination. Prima facie Kant is maintaining that the understanding
really unifies, or introduces the principle of unity. For the
twice-repeated phrase 'give unity to the synthesis' seems unmistakable
in meaning, and the important rôle in knowledge is plainly meant to be
assigned to the understanding. Kant's language, however, is not
decisive; for he speaks of the synthesis of the manifold as that which
'first produces a knowledge which indeed at first may be crude and
confused and therefore needs _analysis_[12]', and he says of the
conceptions which give unity to the synthesis that 'they consist
solely in the _representation_[13] of this necessary synthetical
unity'.[14] Again, 'to bring the synthesis to a conception' may well
be understood to mean 'to recognize the synthesis as an instance of
the conception'; and, since Kant is speaking of knowledge, 'to give
unity to the synthesis' may only mean 'to give unity to the synthesis
_for us_', i. e. 'to make us aware of its unity'. Moreover,
consideration of what thought can possibly achieve with respect to a
synthesis presented to it by the imagination renders it necessary to
hold that the understanding only recognizes the unity of the
synthesis. For if a synthesis has been effected, it must have been
effected in accordance with a principle of construction or synthesis,
and therefore it would seem that the only work left for the
understanding is to discover the principle latent in the procedure of
the imagination. At any rate, if the synthesis does not involve a
principle of synthesis, it is impossible to see how thought can
subsequently introduce a principle. The imagination, then, must be
considered to have already introduced the principle of unity into the
manifold by combining it in accordance with a conception or principle
of combination, and the work of the understanding must be considered
to consist in recognizing that the manifold has been thereby combined
and unified through the conception. We are therefore obliged to accept
one of two alternatives. _Either_ the understanding merely renders the
mind conscious of the procedure of a faculty different from itself,
viz. the imagination, in which case the important rôle in knowledge,
viz. the effecting of the synthesis according to a principle, is
played by a faculty different from the understanding; _or_ the
imagination is the understanding working unreflectively, and the
subsequent process of bringing the synthesis to a conception is merely
a process by which the understanding becomes conscious of its own
procedure. Moreover, it is the latter alternative which we must accept
as more in accordance with the general tenor of Kant's thought. For
the synthesis of the imagination is essentially the outcome of
activity or spontaneity, and, as such, it belongs to the understanding
rather than to the sensibility; in fact we find Kant in one place
actually saying that 'it is one and the same spontaneity which at one
time under the name of imagination, at another time under that of
understanding, introduces connexion into the manifold of
perception'.[15] Further, it should be noted that since the
imagination must be the understanding working unreflectively, and
since it must be that which introduces unity into the manifold, there
is some justification for his use of language which implies that the
understanding is the source of the unity, though it will not be so in
the sense in which the passage under discussion might at first sight
lead us to suppose.

    [12] The italics are mine.

    [13] The italics are mine.

    [14] Cf. the description of the imagination as 'blind'.

    [15] B. 162 note, M. 99 note. Cf. B. 152, M. 93. Similarly at
    one point in the passage under discussion (B. 102 fin., M. 62
    med.) the synthesis is expressly attributed to the
    spontaneity of thought.

We can now turn to the argument of the _Transcendental Deduction_
itself. Kant introduces it in effect by raising the question, 'How is
it that, beginning with the isolated data of sense, we come to acquire
knowledge?' His aim is to show (1) that knowledge requires the
performance of certain operations by the mind upon the manifold of
sense; (2) that this process is a condition not merely of knowledge,
but also of self-consciousness; and (3) that, since the manifold is
capable of entering into knowledge, and since we are capable of being
self-conscious, the categories, whose validity is implied by this
process, are valid.

Kant begins by pointing out[16] that all knowledge, _a priori_ as well
as empirical, requires the manifold, produced successively in the
mind, to be subjected to three operations.

    [16] A. 95-104, Mah. 194-8.

1. Since the elements of the manifold are as given mere isolated
units, and since knowledge is the apprehension of a unity of connected
elements, the mind must first run through the multiplicity of sense
and then grasp it together into a whole, i. e. into an image.[17]
This act is an act of synthesis; it is called 'the synthesis of
apprehension' and is ascribed to the imagination. It must be carried
out as much in respect of the pure or _a priori_ elements of space and
time as in respect of the manifold of sensation, for individual spaces
and times contain a multiplicity which, to be apprehended, must be
combined.[18] The necessity of this act of synthesis is emphasized in
the second edition. "We cannot represent anything as combined in the
object without having previously combined it ourselves. Of all
representations, _combination_ is the only one which cannot be given
through objects,[19] but can be originated only by the subject itself
because it is an act of its own activity."[20]

    [17] Cf. A. 120, Mah. 211.

    [18] 'Combine' is used as the verb corresponding to
    'synthesis'.

    [19] I. e. given to us through the operation of things in
    themselves upon our sensibility.

    [20] B. 130, M. 80.

2. Since the data of perception are momentary, and pass away with
perception, the act of grasping them together requires that the mind
shall reproduce the past data in order to combine them with the
present datum. "It is plain that if I draw a line in thought, or wish
to think of the time from one midday to another, or even to represent
to myself a certain number, I must first necessarily grasp in thought
these manifold representations one after another. But if I were
continually to lose from my thoughts the preceding representations
(the first parts of the line, the preceding parts of time or the units
successively represented), and were not to reproduce them, while I
proceeded to the succeeding parts, there could never arise a complete
representation, nor any of the thoughts just named, not even the first
and purest fundamental representations of space and time."[21] This
act of reproduction is called 'the synthesis of reproduction in the
imagination'.[22]

    [21] A. 102, Mah. 197.

    [22] The term 'synthesis' is undeserved, and is due to a
    desire to find a verbal parallel to the 'synthesis of
    apprehension in perception'. For the inappropriateness of
    'reproduction' and of 'imagination' see pp. 239-41.

Further, the necessity of reproduction brings to light a
characteristic of the synthesis of apprehension. "It is indeed only an
empirical law, according to which representations which have often
followed or accompanied one another in the end become associated, and
so form a connexion, according to which, even in the absence of the
object, one of these representations produces a transition of the mind
to another by a fixed rule. But this law of reproduction presupposes
that phenomena themselves are actually subject to such a rule, and
that in the manifold of their representations there is a concomitance
or sequence, according to a fixed rule; for, without this, our
empirical imagination would never find anything to do suited to its
capacity, and would consequently remain hidden within the depths of
the mind as a dead faculty, unknown to ourselves. If cinnabar were now
red, now black, now light, now heavy, if a man were changed now into
this, now into that animal shape, if our fields were covered on the
longest day, now with fruit, now with ice and snow, then my empirical
faculty of imagination could not even get an opportunity of thinking
of the heavy cinnabar when there occurred the representation of red
colour; or if a certain name were given now to one thing, now to
another, or if the same thing were called now by one and now by
another name, without the control of some rule, to which the phenomena
themselves are already subject, no empirical synthesis of reproduction
could take place."

"There must then be something which makes this very reproduction of
phenomena possible, by being the _a priori_ foundation of a necessary
synthetical unity of them. But we soon discover it, if we reflect that
phenomena are not things in themselves, but the mere play of our
representations, which in the end resolve themselves into
determinations of our internal sense. For if we can prove that even
our purest _a priori_ perceptions afford us no knowledge, except so
far as they contain such a combination of the manifold as renders
possible a thoroughgoing synthesis of reproduction, then this
synthesis of imagination is based, even before all experience, on _a
priori_ principles, and we must assume a pure transcendental synthesis
of the imagination which lies at the foundation of the very
possibility of all experience (as that which necessarily presupposes
the reproducibility of phenomena)."[23]

    [23] A. 100-2, Mah. 195-7.

In other words, the faculty of reproduction, if it is to get to work,
presupposes that the elements of the manifold are parts of a
necessarily related whole; or, as Kant expresses it later, it
presupposes the _affinity_ of phenomena; and this affinity in turn
presupposes that the synthesis of apprehension by combining the
elements of the manifold on certain principles makes them parts of a
necessarily related whole.[24]

    [24] Cf. A. 113, Mah. 205; A. 121-2, Mah. 211-12; and Caird,
    i. 362-3. For a fuller account of these presuppositions, and
    for a criticism of them, cf. Ch. IX, p. 219 and ff.

3. Kant introduces the third operation, which he calls 'the synthesis
of recognition in the conception',[25] as follows:

    [25] This title also is a misnomer due to the desire to give
    parallel titles to the three operations involved in
    knowledge. There is really only one synthesis referred to,
    and the title here should be 'the recognition of the
    synthesis in the conception'.

"Without consciousness that what we are thinking is identical with
what we thought a moment ago, all reproduction in the series of
representations would be in vain. For what we are thinking would be a
new representation at the present moment, which did not at all belong
to the act by which it was bound to have been gradually produced, and
the manifold of the same would never constitute a whole, as lacking
the unity which only consciousness can give it. If in counting I
forget that the units which now hover before my mind have been
gradually added by me to one another, I should not know the generation
of the group through this successive addition of one to one, and
consequently I should not know the number, for this conception
consists solely in the consciousness of this unity of the synthesis."

"The word 'conception'[26] might itself lead us to this remark. For
it is this _one_ consciousness which unites the manifold gradually
perceived and then also reproduced into one representation. This
consciousness may often be only weak, so that we connect it with the
production of the representation only in the result but not in the act
itself, i. e. immediately; but nevertheless there must always be one
consciousness, although it lacks striking clearness, and without it
conceptions, and with them knowledge of objects, are wholly
impossible."[27]

    [26] _Begriff._

    [27] A. 103-4, Mah. 197-8.

Though the passage is obscure and confused, its general drift is
clear. Kant, having spoken hitherto only of the operation of the
imagination in apprehension and reproduction, now wishes to introduce
the understanding. He naturally returns to the thought of it as that
which recognizes a manifold as unified by a conception, the manifold,
however, being not a group of particulars unified through the
corresponding universal or conception, but the parts of an individual
image, e. g. the parts of a line or the constituent units of a number,
and the conception which unifies it being the principle on which these
parts are combined.[28] His main point is that it is not enough for
knowledge that we should combine the manifold of sense into a whole in
accordance with a specific principle,[29] but we must also be in some
degree conscious of our continuously identical act of combination,[30]
this consciousness being at the same time a consciousness of the
special unity of the manifold. For the conception which forms the
principle of the combination has necessarily two sides; while from our
point of view it is the principle according to which we combine and
which makes our combining activity one, from the point of view of the
manifold it is the special principle[31] by which the manifold is made
_one_. If I am to count a group of five units, I must not only add
them, but also be conscious of my continuously identical act of
addition, this consciousness consisting in the consciousness that I am
successively taking units up to, and only up to, five, and being at
the same time a consciousness that the units are acquiring the unity
of being a group of five. It immediately follows, though Kant does not
explicitly say so, that all knowledge implies self-consciousness. For
the consciousness that we have been combining the manifold on a
certain definite principle is the consciousness of our identity
throughout the process, and, from the side of the manifold, it is just
that consciousness of the manifold as unified by being brought under a
conception which constitutes knowledge. Even though it is Kant's view
that the self-consciousness need only be weak and need only arise
after the act of combination, when we are aware of its result, still,
without it, there will be no consciousness of the manifold as unified
through a conception and therefore no knowledge. Moreover, if the
self-consciousness be weak, the knowledge will be weak also, so that
if it be urged that knowledge in the strictest sense requires the full
consciousness that the manifold is unified through a conception, it
must be allowed that knowledge in this sense requires a full or clear
self-consciousness.

    [28] Cf. pp. 162-9.

    [29] That the combination proceeds on a specific principle
    only emerges in this account of the third operation.

    [30] Kant's example shows that this consciousness is not the
    mere consciousness of the act of combination as throughout
    identical, but the consciousness of it as an identical act of
    a particular kind.

    [31] When Kant says 'this conception [i. e. the conception
    of the number counted] consists in the consciousness of this
    unity of the synthesis', he is momentarily and contrary to
    his usual practice speaking of a conception in the sense
    of the activity of conceiving a universal, and not in the
    sense of the universal conceived. Similarly in appealing to
    the meaning of _Begriff_ (conception) he is thinking of
    'conceiving' as the activity of combining a manifold through
    a conception.

As is to be expected, however, the passage involves a difficulty
concerning the respective functions of the imagination and the
understanding. Is the understanding represented as only recognizing a
principle of unity introduced into the manifold by the imagination, or
as also for the first time introducing a principle of unity? At first
sight the latter alternative may seem the right interpretation. For he
says that unless we were conscious that what we are thinking is
identical with what we thought a moment ago, 'what we are thinking
would _be_ a new representation which _did not at all belong_ to the
act by which it was bound to have been gradually produced, and the
manifold of the same _would never_ constitute a whole, as lacking the
unity which only _consciousness can give it_.'[32] Again, in speaking
of a conception--which of course implies the understanding--he
says that 'it is this one consciousness which _unites_ the
manifold gradually perceived and then reproduced into _one_
representation'.[33] But these statements are not decisive, for he
uses the term 'recognition' in his formula for the work of the
understanding, and he illustrates its work by pointing out that in
counting we must _remember_ that we have added the units. Moreover,
there is a consideration which by itself makes it necessary to accept
the former interpretation. The passage certainly represents the
understanding as recognizing the identical action of the mind in
combining the manifold on a principle, whether or not it also
represents the understanding as the source of this activity. But if
it were the understanding which combined the manifold, there would
be no synthesis which the imagination could be supposed to have
performed,[34] and therefore it could play no part in knowledge at
all, a consequence which must be contrary to Kant's meaning. Further
if, as the general tenor of the deduction shows, the imagination is
really only the understanding working unreflectively,[35] we are able
to understand why Kant should for the moment cease to distinguish
between the imagination and the understanding, and consequently should
use language which implies that the understanding both combines the
manifold on a principle and makes us conscious of our activity in so
doing. Hence we may say that the real meaning of the passage should
be stated thus: 'Knowledge requires one consciousness which,
as imagination, combines the manifold on a definite principle
constituted by a conception,[36] and, as understanding, is to some
extent conscious of its identical activity in so doing, this
self-consciousness being, from the side of the whole produced by the
synthesis, the consciousness of the conception by which the manifold
is unified.'

    [32] The italics are mine. He does not say '_we should not be
    conscious_ of what we are thinking as the same representation
    and as belonging [Greek: ktl]., _and we should not be
    conscious_ of the manifold as constituting a whole.

    [33] The italics are mine.

    [34] There could not, of course, be two syntheses, the one
    being and the other not being upon a principle.

    [35] Cf. pp. 168-9.

    [36] In view of Kant's subsequent account of the function of
    the categories it should be noticed that, according to the
    present passage, the conception involved in an act of
    knowledge is the conception not of an 'object in general',
    but of 'an object of the particular kind which constitutes
    the individual whole produced by the combination a whole of
    the particular kind that it is of', and that, in accordance
    with this, the self-consciousness involved is not the mere
    consciousness that our combining activity is identical
    throughout, but the consciousness that it is an identical
    activity of a particular kind, e. g. that of counting five
    units. Cf. pp. 184 fin.-186, 190-2, and 206-7.

Hitherto there has been no mention of an _object_ of knowledge, and
since knowledge is essentially knowledge of an object, Kant's next
task is to give such an account of an object of knowledge as will show
that the processes already described are precisely those which give
our representations, i. e. the manifold of sense, relation to an
object, and consequently yield knowledge.

He begins by raising the question, 'What do we mean by the phrase 'an
object of representations'?'[37] He points out that a phenomenon, since
it is a mere sensuous representation, and not a thing in itself
existing independently of the faculty of representations, is just not
an object. To the question, therefore, 'What is meant by an object
corresponding to knowledge and therefore distinct from it?' we are
bound to answer from the point of view of the distinction between
phenomena and things in themselves, that the object is something in
general = _x_, i. e. the thing in itself of which we know only
_that_ it is and not _what_ it is. There is, however, another point
of view from which we can say something more about an object of
representations and the correspondence of our representations to it,
viz. that from which we consider what is involved in the thought of
the relation of knowledge or of a representation to its object. "We
find that our thought of the relation of all knowledge to its object
carries with it something of necessity, since its object is regarded
as that which prevents our cognitions[38] being determined at random
or capriciously, and causes them to be determined _a priori_ in a
certain way, because in that they are to relate to an object, they
must necessarily also, in relation to it, agree with one another, that
is to say, they must have that unity which constitutes the conception
of an object."[39]

    [37] _Vorstellung_ in the present passage is perhaps better
    rendered 'idea', but representation has been retained for the
    sake of uniformity.

    [38] _Erkenntnisse._

    [39] A. 104, Mah. 199.

Kant's meaning seems to be this: 'If we think of certain
representations, e. g. certain lines[40] or the representations of
extension, impenetrability, and shape,[41] as related to an object,
e. g. to an individual triangle or an individual body, we think that
they must be mutually consistent or, in other words, that they must
have the unity of being parts of a necessarily related whole or
system, this unity in fact constituting the conception of an object
in general, in distinction from the conception of an object of a
particular kind. The latter thought in turn involves the thought of
the object of representations as that which prevents them being
anything whatever and in fact makes them parts of a system. The
thought therefore of representations as related to an object carries
with it the thought of a certain necessity, viz. the necessary or
systematic unity introduced into the representations by the object.
Hence by an object of representations we mean something which
introduces into the representations a systematic unity which
constitutes the nature of an object in general, and the relatedness of
representations to, or their correspondence with, an object involves
their systematic unity.'[42]

    [40] Cf. A. 105, Mah. 199.

    [41] Cf. A. 106, Mah. 200.

    [42] It may be noticed that possession of the unity of a
    system does not really distinguish 'an object' from any other
    whole of parts, nor in particular from 'a representation'.
    Any whole of parts must be a systematic unity.

Certain points, however, should be noticed. In the _first_ place, Kant
is for the moment tacitly ignoring his own theory of knowledge, in
accordance with which the object proper, i. e. the thing in itself, is
unknowable, and is reverting to the ordinary conception of knowledge
as really _knowledge_ of its object. For the elements which are said,
in virtue of being related to an object, to agree and to have the
unity which constitutes the conception of an object must be elements
of an object which we know; for if the assertion that they agree is
to be significant, they must be determinate parts or qualities of the
object, e. g. the sides of an individual triangle or the
impenetrability or shape of an individual body, and therefore it is
implied that we know that the object has these parts or qualities. In
the _second_ place, both the problem which Kant raises and the clue
which he offers for its solution involve an impossible separation of
knowledge or a representation from its object. Kant begins with the
thought of a phenomenon as a mere representation which, as mental, and
as the representation of an object, is just not an object, and asks,
'What is meant by the object of it?' He finds the clue to the answer
in the thought that though a representation or idea when considered in
itself is a mere mental modification, yet, when considered as related
to an object, it is subject to a certain necessity. In fact, however,
an idea or knowledge is essentially an idea or knowledge of an object,
and we are bound to think of it as such. There is no meaning whatever
in saying that the thought of an idea as related to an object carries
with it something of necessity, for to say so implies that it is
possible to think of it as unrelated to an object. Similarly there is
really no meaning in the question, 'What is meant by an object
corresponding to knowledge or to an idea?' for this in the same way
implies that we can first think of an idea as unrelated to an object
and then ask, 'What can be meant by an object corresponding to
it?'[43] In the _third_ place, Kant only escapes the absurdity
involved in the thought of a mere idea or a mere representation
by treating representations either as parts or as qualities of an
object. For although he speaks of our cognitions,[44] i. e. of our
representations, as being determined by the object, he says that they
must agree, i. e. they must have that unity which constitutes the
conception of an object, and he illustrates representations by the
sides of an individual triangle and the impenetrability and shape of
an individual body, which are just as 'objective' as the objects to
which they relate. The fact is that he really treats a representation
not as his problem requires that it should be treated, i. e. as a
representation of something, but as something represented,[45] i. e.
as something of which we are aware, viz. a part or a quality of an
object. In the _fourth_ place, not only is that which Kant speaks of
as related to an object really not a representation, but also--as we
see if we consider the fact which Kant has in mind--that to which he
speaks of it as related is really not _an_ object but _one and the
same object to which another so-called representation is related_. For
what Kant says is that representations as related to an object must
agree among themselves. But this statement, to be significant, implies
that the object to which various representations are related is _one
and the same_. Otherwise why should the representations agree? In
view, therefore, of these last two considerations we must admit that
the real thought underlying Kant's statement should be expressed thus:
'We find that the thought that _two or more parts or qualities of an
object_ relate to _one and the same object_ carries with it a certain
necessity, since this object is considered to be that which _prevents
these parts or qualities which we know it to possess_ from being
determined at random, because by being related to _one and the same
object_, they must agree among themselves.' The importance of the
correction lies in the fact that what Kant is stating is not what he
thinks he is stating. He is really stating the implication of the
thought that two or more qualities or parts of some object or other,
which, as such, already relate to an object, relate to one and the
same object. He thinks he is stating the implication of the thought
that a representation which in itself has no relation to an object,
has relation to an object. And since his problem is simply to
determine what constitutes the relatedness to an object of that which
in itself is a mere representation, the distinction is important; for
it shows that he really elucidates it by an implication respecting
something which already has relation to an object and is not a mental
modification at all, but a quality or a part of an object.

    [43] Cf. pp. 230-3.

    [44] _Erkenntnisse._

    [45] _Vorgestellt._

Kant continues thus: "But it is clear that, since we have to do only
with the manifold of our representations, and the _x_, which
corresponds to them (the object), since it is to be something distinct
from all our representations, is for us nothing, the unity which the
object necessitates can be nothing else than the formal unity of
consciousness in the synthesis of the manifold of representations."
[I. e. since the object which produces systematic unity in our
representations is after all only the unknown thing in itself, viz.
_x_,[46] any of the parts or qualities of which it is impossible to
know, that to which it gives unity can be only our representations
and not its own parts or qualities. For, since we do not know any
of its parts or qualities, these representations cannot be its
parts or qualities. Consequently, the unity produced by this _x_
can only be the formal unity of the combination of the manifold in
consciousness.[47]] "Then and then only do we say that we know the
object," [i. e. we know that the manifold relates to an object[48]]
"if we have produced synthetical unity in the manifold of perception.
But this unity would be impossible, if the perception could not be
produced by means of such a function of synthesis according to a rule
as renders the reproduction of the manifold a priori necessary, and a
conception in which the manifold unifies itself possible. Thus we
think a triangle as an object, in that we are conscious of the
combination of three straight lines in accordance with a rule by which
such a perception can at any time be presented. This _unity of the
rule_ determines all the manifold and limits it to conditions which
make the unity of apperception possible, and the conception of this
unity is the representation of the object=_x_, which I think through
the aforesaid predicates of a triangle." [I. e., apparently, 'to
conceive this unity of the rule is to represent to myself the object
_x_, i. e. the thing in itself,[49] of which I come to think by means
of the rule of combination.']

    [46] Cf. p. 183, note 2.

    [47] 'The formal unity' means not the unity peculiar to any
    particular synthesis, but the character shared by all
    syntheses of being a systematic whole.

    [48] The final sense is the same whether 'object' be here
    understood to refer to the thing in itself or to a
    phenomenon.

    [49] A comparison of this passage (A. 104-5, Mah. 198-9) with
    A. 108-9, Mah. 201-2 (which seems to reproduce A. 104-5, Mah.
    198-9), B. 522-3, M. 309 and A. 250, Mah. 224, seems to
    render it absolutely necessary to understand by _x_, and by
    the transcendental object, the thing in itself. Cf. also B.
    236, M. 143 ('so soon as I raise my conception of an object
    to the transcendental meaning thereof, the house is not a
    thing in itself but only a phenomenon, i. e. a representation
    of which the transcendental object is unknown'), A. 372, Mah.
    247 and A. 379, Mah. 253.

In this passage several points claim attention. In the _first_ place,
it seems impossible to avoid the conclusion that in the second
sentence the argument is exactly reversed. Up to this point, it is
the thing in itself which produces unity in our representations.
Henceforward it is we who produce the unity by our activity of
combining the manifold. The discrepancy cannot be explained away, and
its existence can only be accounted for by the exigencies of Kant's
position. When he is asking 'What is meant by the object (beyond the
mind) corresponding to our representations?' he has to think of the
unity of the representations as due to the object. But when he is
asking 'How does the manifold of sense become unified?' his view that
all synthesis is due to the mind compels him to hold that the unity is
produced by us. In the _second_ place, the passage introduces a second
object in addition to the thing in itself, viz. the phenomenal object,
e. g. a triangle considered as a whole of parts unified on a definite
principle.[50] It is this object which, as the object that we know, is
henceforward prominent in the first edition, and has exclusive
attention in the second. The connexion between this object and the
thing in itself appears to lie in the consideration that we are only
justified in holding that the manifold of sense is related to a thing
in itself when we have unified it and therefore know it to be a unity,
and that to know it to be a unity is _ipso facto_ to be aware of it as
related to a phenomenal object; in other words, the knowledge that the
manifold is related to an object beyond consciousness is acquired
through our knowledge of its relatedness to an object within
consciousness. In the _third_ place, in view of Kant's forthcoming
vindication of the categories, it is important to notice that the
process by which the manifold is said to acquire relation to an
object is illustrated by a synthesis on a particular principle which
constitutes the phenomenal object an object of a particular kind. The
synthesis which enables us to recognize three lines as an object is
not a synthesis based on general principles constituted by the
categories, but a synthesis based on the particular principle that the
three lines must be so put together as to form an enclosed space.
Moreover, it should be noticed that the need of a particular principle
is really inconsistent with his view that relation to an object gives
the manifold the systematic unity which constitutes the conception of
an object, or that at least a [Greek: hysteron proteron] is involved.
For if the knowledge that certain representations form a systematic
unity justifies our holding that they relate to an object, it would
seem that in order to know that they relate to an object we need not
know the special character of their unity. Yet, as Kant states the
facts, we really have to know the special character of their unity in
order to know that they possess systematic unity in general.[51]
_Lastly_, it is easy to see the connexion of this account of an object
of representations with the preceding account of the synthesis
involved in knowledge. Kant had said that knowledge requires a
synthesis of the imagination in accordance with a definite principle,
and the recognition of the principle of the synthesis by the
understanding. From this point of view it is clear that the aim of the
present passage is to show that this process yields knowledge of an
object; for it shows that this process yields knowledge of a
phenomenal object of a particular kind, e. g. of a triangle or of a
body, and that this object as such refers to what after all is _the_
object, viz. the thing in itself.

    [50] Compare 'The object of our perceptions is merely that
    something of which the conception expresses such a necessity
    of synthesis' (A. 106, Mah. 200), and 'An object is that in
    the conception of which the manifold of a given perception is
    united' (B. 137, M. 84). Cf. also A. 108, Mah. 201.

    [51] Kant's position is no doubt explained by the fact that
    since the object corresponding to our representations is the
    thing in itself, and since we only know that this is of the
    same kind in the case of every representation, it can only be
    thought of as producing systematic unity, and not a unity of
    a particular kind. The position is also in part due to the
    fact that the principles of synthesis involved by the
    phenomenal object are usually thought of by Kant as the
    categories; these of course can only contribute a general
    kind of unity, and not the special kind of unity belonging to
    an individual object.

The position reached by Kant so far is this. Knowledge, as being
knowledge of an object, consists in a process by which the manifold of
perception acquires relation to an object. This process again is a
process of combination of the manifold into a systematic whole upon a
definite principle, accompanied by the consciousness in some degree of
the act of combination, and therefore also of the acquisition by the
manifold of the definite unity which forms the principle of
combination. In virtue of this process there is said to be 'unity of
consciousness in the synthesis of the manifold', a phrase which the
context justifies us in understanding as a condensed expression for a
situation in which (1) the manifold of sense is a unity of necessarily
related parts, (2) there is _consciousness_ of this unity, and (3) the
consciousness which combines and is conscious of combining the
manifold, as being necessarily one and the same throughout this
process, is itself a unity.

Kant then proceeds to introduce what he evidently considers the
keystone of his system, viz. 'transcendental apperception.'

"There is always a transcendental condition at the basis of any
necessity. Hence we must be able to find a transcendental ground of
the unity of consciousness in the synthesis of the manifold of all our
perceptions, and therefore also of the conceptions of objects in
general, consequently also of all objects of experience, a ground
without which it would be impossible to think any object for our
perceptions; for this object is no more than that something, the
conception of which expresses such a necessity of synthesis."

"Now this original and transcendental condition is no other than
_transcendental apperception_. The consciousness of self according to
the determinations of our state in internal sense-perception is merely
empirical, always changeable; there can be no fixed or permanent self
in this stream of internal phenomena, and this consciousness is
usually called _internal sense_ or _empirical apperception_. That
which is _necessarily_ to be represented as numerically identical
cannot be thought as such by means of empirical data. The condition
which is to make such a transcendental presupposition valid must be
one which precedes all experience, and makes experience itself
possible."

"Now no cognitions[52] can occur in us, no combination and unity of
them with one another, without that unity of consciousness which
precedes all data of perception, and by relation to which alone all
representation of objects is possible. This pure original unchangeable
consciousness I shall call _transcendental apperception_. That it
deserves this name is clear from the fact that even the purest
objective unity, viz. that of _a priori_ conceptions (space and time)
is only possible by relation of perceptions to it. The numerical unity
of this apperception therefore forms the _a priori_ foundation of all
conceptions, just as the multiplicity of space and time is the
foundation of the perceptions of the sensibility."[53]

    [52] _Erkenntnisse._

    [53] A. 106-7, Mah. 200-1.

The argument is clearly meant to be 'transcendental' in character; in
other words, Kant continues to argue from the existence of knowledge
to the existence of its presuppositions. We should therefore expect
the passage to do two things: firstly, to show what it is which is
presupposed by the 'unity of consciousness in the synthesis of the
manifold'[54]; and secondly, to show that this presupposition deserves
the title 'transcendental apperception'. Unfortunately Kant introduces
'transcendental apperception' after the manner in which he introduced
the 'sensibility', the 'imagination' and the 'understanding', as if it
were a term with which every one is familiar, and which therefore
needs little explanation. To interpret the passage, it seems necessary
to take it in close connexion with the preceding account of the three
'syntheses' involved in knowledge, and to bear in mind that, as a
comparison of passages will show, the term 'apperception', which Kant
borrows from Leibniz, always has for Kant a reference to consciousness
of self or self-consciousness. If this be done, the meaning of the
passage seems to be as follows:

    [54] We should have expected this to have been already
    accomplished. For according to the account already
    considered, it is we who by our imagination introduce
    necessity into the synthesis of the manifold and by our
    understanding become conscious of it. We shall therefore not
    be surprised to find that 'transcendental apperception' is
    really only ourselves as exercising imagination and
    understanding in a new guise.

'To vindicate the existence of a self which is necessarily one and the
same throughout its representations, and which is capable of being
aware of its own identity throughout, it is useless to appeal to that
consciousness of ourselves which we have when we reflect upon our
successive states. For, although in being conscious of our states we
are conscious of ourselves we are not conscious of ourselves as
unchanging. The self as going through successive states is changing,
and even if in fact its states did not change, its identity would be
only contingent; it need not continue unchanged. Consequently, the
only course possible is to show that the self-consciousness in
question is presupposed in any experience or knowledge. Now it is so
presupposed. For, as we have already shown, the relation of
representations to an object presupposes one consciousness which
combines and unifies them, and is at the same time conscious of the
identity of its own action in unifying them. This consciousness is the
ground of the unity of consciousness in the synthesis of the manifold.
It may fairly be called transcendental, because even a conception
which relates to space or time, and therefore is the most remote from
sensation, presupposes one consciousness which combines and unifies
the manifold of space and time through the conception, and is
conscious of the identity of its own action in so doing. It may,
therefore, be regarded as the presupposition of _all_ conceiving or
bringing a manifold under a conception, and therefore of all
knowledge. Consequently, since knowledge is possible, i. e. since the
manifold of representations can be related to an object, there must be
one self capable of being aware of its own identity throughout its
representations.'

At this point of Kant's argument, however, there seems to occur an
inversion of the thought. Hitherto, Kant has been arguing from the
possibility of knowledge to the possibility of the consciousness of
our own identity. But in the next paragraph he appears to reverse this
procedure and to argue from the possibility of self-consciousness to
the possibility of knowledge.

"But it is just this transcendental unity of apperception[55] which
forms, from all possible phenomena which can be together in one
experience, a connexion of them according to laws. For this unity of
consciousness would be impossible, if the mind in the knowledge of the
manifold could not become conscious of the identity of the function
whereby it unites the manifold synthetically in one knowledge.
Consequently, the original and necessary consciousness of the identity
of oneself is at the same time a consciousness of an equally necessary
unity of the synthesis of all phenomena according to conceptions,
i. e. according to rules which not only make them necessarily
reproducible, but thereby determine an object for their perception,
i. e. determine the conception of something in which they are
necessarily connected. For the mind could not possibly think the
identity of itself in the manifold of its representations, and this
indeed _a priori_, if it had not before its eyes the identity of its
action which subjects all synthesis of apprehension (which is
empirical) to a transcendental unity, and first makes possible its
connexion according to rules."

    [55] Kant seems here and elsewhere to use the phrase
    'transcendental unity of apperception' as synonymous with
    'transcendental apperception', the reason, presumably, being
    that transcendental apperception is a unity.

The argument seems indisputably to be as follows: 'The mind is
necessarily able to be aware of its own identity throughout its
manifold representations. To be aware of this, it must be aware of the
identity of the activity by which it combines the manifold of
representations into a systematic whole. Therefore it must be capable
of combining, and of being conscious of its activity in combining, all
phenomena which can be its representations into such a whole. But
this process, from the point of view of the representations combined,
is the process by which they become related to an object and so enter
into knowledge. Therefore, since we are capable of being conscious of
our identity with respect to all phenomena which can be our
representations, the process of combination and consciousness of
combination which constitutes knowledge must be possible with respect
to them.' Thus the thought of this and the preceding paragraph seems
to involve a circle. First the possibility of self-consciousness is
deduced from the possibility of knowledge, and then the possibility of
knowledge is deduced from the possibility of self-consciousness.

An issue therefore arises, the importance of which can be seen by
reference to the final aim of the 'deduction', viz. the vindication of
the categories. The categories are 'fundamental conceptions which
enable us to think objects in general[56] for phenomena'[57]; in other
words, they are the principles of the synthesis by which the manifold
of sense becomes related to an object. Hence, if this be granted, the
proof that the categories are applicable to objects consists in
showing that the manifold can be subjected to this synthesis. The
question therefore arises whether Kant's real starting-point for
establishing the possibility of this synthesis and therefore the
applicability of the categories, is to be found in the possibility
of knowledge, or in the possibility of self-consciousness, or in
both. In other words, does Kant start from the position that all
representations must be capable of being related to an object, or
from the position that we must be capable of being conscious of our
identity with respect to all of them, or from both?

    [56] _Objecte überhaupt_, i. e. objects of any kind in
    distinction not from objects of a particular kind but from no
    objects at all.

    [57] A. 111, Mah. 204

Prima facie the second position is the more plausible basis for the
desired conclusion. On the one hand, it does not seem obvious that the
manifold _must_ be capable of being related to an object; for even if
it be urged that otherwise we should have only 'a random play of
representations, less than a dream'[58], it may be replied, that this
might be or might come to be the case. On the other hand, the fact
that our representations are ours necessarily seems to presuppose that
we are identical subjects of these representations, and recognition of
this fact is the consciousness of our identity.

    [58] A. 112, Mah. 204.

If we turn to the text for an answer to this question, we find that
Kant seems not only to use both starting-points, but even to regard
them as equivalents. Thus in introducing the categories[59] Kant
begins by appealing to the necessity for knowledge that
representations should relate to an object.

    [59] A. 110-12, Mah. 203-4.

"Unity of synthesis according to empirical conceptions would be purely
contingent, and were these not based on a transcendental ground of
unity, it would be possible for a confused crowd of phenomena to fill
our soul, without the possibility of experience ever arising
therefrom. But then also all relation of knowledge to objects would
fall away, because knowledge would lack connexion according to
universal and necessary laws; it would be thoughtless perception but
never knowledge, and therefore for us as good as nothing."

"The _a priori_ conditions of any possible experience whatever are at
the same time conditions of the possibility of the objects of
experience. Now I assert that the above mentioned _categories_ are
nothing but _the conditions of thinking in any possible experience_,
just as _space and time_ are the _conditions of perception_ requisite
for the same. The former therefore are also fundamental conceptions by
which we think objects in general for phenomena, and are therefore
objectively valid _a priori_--which is exactly what we wished to
know."

The next sentence, however, bases the necessity of the categories on
the possibility of self-consciousness, without giving any indication
that a change of standpoint is involved.

"But the possibility, nay, even the necessity, of these categories
rests on the relation which the whole sensibility, and with it also
all possible phenomena, have to original apperception, a relation
which forces everything to conform to the conditions of the
thoroughgoing unity of self-consciousness, i. e. to stand under
universal functions of synthesis, i. e. of synthesis according to
conceptions, as that wherein alone apperception can prove _a priori_
its thorough-going and necessary identity."

Finally, the conclusion of the paragraph seems definitely to treat
both starting-points as really the same.[60] "Thus the conception of a
cause is nothing but a synthesis (of the consequent in the time series
with other phenomena) _according to conceptions_; and without such a
unity, which has its _a priori_ rule and subjects phenomena to itself,
thorough-going and universal and therefore necessary unity of
consciousness in the manifold of sense-perceptions would not be met
with. But then also these perceptions would belong to no experience,
consequently they would have no object, and would be nothing but a
blind play of representations, less than a dream."

    [60] Cf. A. 113, Mah. 205-6 and A. 108-10, Mah. 202-3.

The fact is that since for Kant the synthesis of representations in
accordance with the categories, accompanied by the consciousness of
it, is at once the necessary and sufficient condition of the
relatedness of representations to an object and of the consciousness
of our identity with respect to them, it seems to him to be one and
the same thing whether, in vindicating the synthesis, we appeal to the
possibility of knowledge or to the possibility of self-consciousness,
and it even seems possible to argue, _via_ the synthesis, from
knowledge to self-consciousness and vice versa.

Nevertheless, it remains true that the vindication of the categories
is different, according as it is based upon the possibility of
relating representations to an object or upon the possibility of
becoming self-conscious with respect to them. It also remains true
that Kant vindicates the categories in both ways. For while, in
expounding the three so-called syntheses involved in knowledge, he is
vindicating the categories from the point of view of knowledge, when
he comes to speak of transcendental apperception, of which the central
characteristic is the consciousness of self involved, there is a
shifting of the centre of gravity. Instead of treating representations
as something which can become related to an object, he now treats
them as something of which, as belonging to a self, the self must
be capable of being conscious as its own, and argues that a
synthesis in accordance with the categories is required for this
self-consciousness. It must be admitted then--and the admission is
only to be made with reluctance--that when Kant reaches transcendental
apperception, he really adopts a new starting-point,[61] and that the
passage which introduces transcendental apperception by showing it to
be implied in knowledge[62] only serves to conceal from Kant the fact
that, from the point of view of the deduction of the categories, he is
really assuming without proof the possibility of self-consciousness
with respect to all our representations, as a new basis for argument.

    [61] The existence of this new starting-point is more
    explicit, A. 116-7 (and note), Mah. 208 (and note), and A.
    122, Mah. 212.

    [62] A. 107, Mah. 200.

The approach to the categories from the side of self-consciousness is,
however, more prominent in the second edition, and consequently we
naturally turn to it for more light on this side of Kant's position.
There Kant vindicates the necessity of the synthesis from the side of
self-consciousness as follows:[63]

    [63] The main clauses have been numbered for convenience of
    reference.

"[1.] It must be possible that the 'I think' should accompany all my
representations; for otherwise something would be represented in me
which could not be thought; in other words, the representation would
be either impossible or at least for me nothing. [2.] That
representation which can be given before all thought is called
_perception_. All the manifold of perception has therefore a necessary
relation to the 'I think' in the same subject in which this manifold
is found. [3.] But this representation[64] [i. e. the 'I think'] is an
act of _spontaneity_, i. e. it cannot be regarded as belonging to
sensibility. I call it _pure apperception_, to distinguish it from
_empirical apperception_, or _original apperception_ also, because it
is that self-consciousness which, while it gives birth to the
representation 'I think', which must be capable of accompanying all
others and is one and the same in all consciousness, cannot itself be
accompanied by any other.[65] [4.] I also call the unity of it the
_transcendental_ unity of self-consciousness, in order to indicate the
possibility of _a priori_ knowledge arising from it. For the manifold
representations which are given in a perception would not all of them
be _my_ representations, if they did not all belong to one
self-consciousness, that is, as my representations (even though I am
not conscious of them as such), they must necessarily conform to the
condition under which alone they _can_ stand together in a universal
self-consciousness, because otherwise they would not all belong to me.
From this original connexion much can be concluded."

    [64] This is an indisputable case of the use of
    representation in the sense of something represented or
    presented.

    [65] I. e. consciousness of our identity is final; we cannot,
    for instance, go further back to a consciousness of the
    consciousness of our identity.

[5.] "That is to say, this thorough-going identity of the apperception
of a manifold given in perception contains a synthesis of
representations,[66] and is possible only through the consciousness of
this synthesis.[67] [6.] For the empirical consciousness which
accompanies different representations is in itself fragmentary, and
without relation to the identity of the subject. [7.] This relation,
therefore, takes place not by my merely accompanying every
representation with consciousness, but by my _adding_ one
representation to another, and being conscious of the synthesis of
them. [8.] Consequently, only because I can connect a manifold of
given representations _in one consciousness_, is it possible for me to
represent to myself the _identity of consciousness in these
representations_; i. e. the _analytical_ unity of apperception is
possible only under the presupposition of a _synthetical_ unity. [9.]
The thought, 'These representations given in perception belong all of
them to me' is accordingly just the same as, 'I unite them in one
self-consciousness, or at least can so unite them;' [10.] and although
this thought is not itself as yet the consciousness of the _synthesis_
of representations, it nevertheless presupposes the possibility of
this synthesis; that is to say, it is only because I can comprehend
the manifold of representations in one consciousness, that I call them
all _my_ representations; for otherwise I should have as many-coloured
and varied a self as I have representations of which I am conscious.
[11.] Synthetical unity of the manifold of perceptions, as given _a
priori_, is therefore the ground of the identity of apperception
itself, which precedes _a priori_ all _my_ determinate thinking. [12.]
But connexion does not lie in the objects, nor can it be borrowed from
them through perception and thereby first taken up into the
understanding, but it is always an operation of the understanding
which itself is nothing more than the faculty of connecting _a
priori_, and of bringing the manifold of given representations under
the unity of apperception, which principle is the highest in all human
knowledge."

    [66] I understand this to mean 'This through and through
    identical consciousness of myself as the identical subject of
    a manifold given in perception involves a synthesis of
    representations'.

    [67] The drift of the passage as a whole (cf. especially
    § 16) seems to show that here 'the synthesis of
    representations' means 'their connectedness' and not
    'the act of connecting them'.

[13.] "Now this principle of the necessary unity of apperception is
indeed an identical, and therefore an analytical, proposition, but
nevertheless it declares a synthesis of the manifold given in a
perception to be necessary, without which the thorough-going identity
of self-consciousness cannot be thought. [14.] For through the Ego, as
a simple representation, is given no manifold content; in perception,
which is different from it, a manifold can only be given, and through
_connexion_ in one consciousness it can be thought. An understanding,
through whose self-consciousness all the manifold would _eo ipso_ be
given, would _perceive_; our understanding can only _think_ and must
seek its perception in the senses. [15.] I am, therefore, conscious of
the identical self, in relation to the manifold of representations
given to me in a perception, because I call all those representations
_mine_, which constitute _one_. [16.] But this is the same as to say
that I am conscious _a priori_ of a necessary synthesis of them, which
is called the original synthetic unity of apperception, under which
all representations given to me stand, but also under which they must
be brought through a synthesis."[68]

    [68] B. 131-5, M. 81-4.

Though this passage involves many difficulties, the main drift of it
is clear. Kant is anxious to establish the fact that the manifold of
sense must be capable of being combined on principles, which
afterwards turn out to be the categories, by showing this to be
involved in the fact that we must be capable of being conscious of
ourselves as the identical subject of all our representations. To do
this, he seeks to prove in the first paragraph that self-consciousness
in this sense must be possible, and in the second that this
self-consciousness presupposes the synthesis of the manifold.

Examination of the argument, however, shows that the view that
self-consciousness must be possible is, so far as Kant is
concerned,[69] an assumption for which Kant succeeds in giving no
reason at all, and that even if it be true, it cannot form a basis
from which to deduce the possibility of the synthesis.

    [69] Cf. p. 204, note 3.

Before, however, we attempt to prove this, it is necessary to draw
attention to three features of the argument. In the _first_ place, it
implies a somewhat different account of self-consciousness to that
implied in the passages of the first edition which we have already
considered. Self-consciousness, instead of being the consciousness of
the identity of our activity in combining the manifold, is now
primarily the consciousness of ourselves as identical subjects of all
our representations, i. e. it is what Kant calls the analytical unity
of apperception; and consequently it is somewhat differently related
to the activity of synthesis involved in knowledge. Instead of being
regarded as the consciousness of this activity, it is regarded as
presupposing the consciousness of the product of this activity, i. e.
of the connectedness[70] of the manifold produced by the activity,
this consciousness being what Kant calls the synthetical unity of
apperception.[71] In the _second_ place, it is plain that Kant's view
is not that self-consciousness involves the consciousness of our
representations as a connected whole, but that it involves the
consciousness of them as capable of being connected by a synthesis.
Yet, if it is only because I can connect (and therefore apprehend as
connected) a manifold of representations in one consciousness, that I
can represent to myself the identity of consciousness in these
representations, self-consciousness really requires the consciousness
of our representations as _already_ connected; the mere consciousness
of our representations as _capable_ of being connected would not be
enough. The explanation of the inconsistency seems to lie in the fact
that the synthetic unity of which Kant is thinking is the unity
of nature. For, as Kant of course was aware, in our ordinary
consciousness we do not apprehend the interconnexion of the parts
of nature in detail, but only believe that there is such an
interconnexion; consequently he naturally weakened the conclusion
which he ought to have drawn, viz. that self-consciousness presupposes
consciousness of the synthesis, in order to make it conform to the
facts of our ordinary consciousness. Yet, if his _argument_ is
to be defended, its conclusion must be taken in the form that
self-consciousness presupposes consciousness of the actual synthesis
or connexion and not merely of the possibility of it. In the _third_
place, Kant twice in this passage[72] definitely makes the act of
synthesis, which his argument maintains to be the condition of
_consciousness of the identity_ of ourselves, the condition of the
_identity_ of ourselves. The fact is that, on Kant's view, the act of
synthesis of the representations is really a condition of their
belonging to one self, the self being presupposed to be a self capable
of self-consciousness.[73]

    [70] More accurately, 'of the possibility of the
    connectedness'.

    [71] The same view seems implied A. 117-8, Mah. 208. Kant
    apparently thinks of this consciousness as also a
    self-consciousness (cf. § 9), though it seems that he should
    have considered it rather as a condition of
    self-consciousness, cf. p. 204, note 2.

    [72] Sections 6 and 10.

    [73] Cf. pp. 202-3.

We may now turn to the first of the two main points to be considered,
viz. the reason given by Kant for holding that self-consciousness must
be possible. In the first paragraph (§§ 1-4) Kant appears twice to
state a reason, viz. in §§ 1 and 4. What is meant by the first
sentence, "It must be possible that the 'I think' should accompany all
my representations; for otherwise something would be represented in me
which could not be thought; in other words, the representation would
either be impossible or at least for me nothing"? It is difficult to
hold that 'my representations' here means objects of which I am aware,
and that the thesis to be established is that I must be capable of
being conscious of my own identity throughout all awareness or thought
of objects. For the next sentence refers to perceptions as
representations which can be given previously to all thought, and
therefore, presumably, as something of which I am not necessarily
aware. Again, the ground adduced for the thesis would be in part a
mere restatement of it, and in part nonsense. It would be 'otherwise
something would be apprehended with respect to which I could not be
aware that I was apprehending it; in other words, I could not
apprehend it [since otherwise I could be aware that I was apprehending
it]', the last words being incapable of any interpretation. It is much
more probable that though Kant is leading up to self-consciousness,
the phrase 'I think' here refers not to 'consciousness that I am
thinking', but to 'thinking'. He seems to mean 'It must be possible to
apprehend all my 'affections' (i. e. sensations or appearances in me),
for otherwise I should have an affection of which I could not be
aware; in other words, there could be no such affection, or at least
it would be of no possible importance to me.'[74] And on this
interpretation self-consciousness is not introduced till § 3, and
then only surreptitiously. On neither interpretation, however, does
Kant give the vestige of a _reason_ for the possibility of
self-consciousness. Again, it seems clear that in § 4 'my
representations', and 'representations which belong to me' mean
objects of which I am aware (i. e. something presented); for he says
of my representations, not that I may not be conscious of them--which
he should have said if 'my representations' meant my mental affections
of which I could become conscious--but that I may not be conscious of
them as my representations. Consequently in § 4 he is merely asserting
that I must be able to be conscious of my identity throughout my
awareness of objects. So far, then, we find merely the _assertion_
that self-consciousness must be possible.[75]

    [74] A third alternative is to understand Kant to be thinking
    of all thought as self-conscious, i. e. as thinking
    accompanied by the consciousness of thinking. But since in
    that case Kant would be arguing from thinking as _thinking_,
    i. e. as apprehending objects, the possibility of
    self-consciousness would only be glaringly assumed.

    [75] The same is true of A. 116 and A. 117 note, Mah. 208,
    where Kant also appears to be offering what he considers to
    be an argument.

In the next paragraph[76]--which is clearly meant to be the important
one--Kant, though he can hardly be said to be aware of it, seems to
_assume_ that it is the very nature of a knowing self, not only to be
identical throughout its thoughts or apprehendings, but to be capable
of being conscious of its own identity. § 6 runs: "The empirical
consciousness which accompanies different representations is in itself
fragmentary, and without relation to the identity of the subject."
Kant is saying that if there existed merely a consciousness of A which
was not at the same time a consciousness of B and a consciousness
of B which was not at the same time a consciousness of A, these
consciousnesses would not be the consciousnesses belonging to one
self. But this is only true, if the one self to which the
consciousness of A and the consciousness of B are to belong must be
capable of being aware of its own identity. Otherwise it might be one
self which apprehended A and then, forgetting A, apprehended B. No
doubt in that case the self could not be aware of its own identity in
apprehending A and in apprehending B, but none the less it would _be_
identical in so doing. We reach the same conclusion if we consider the
concluding sentence of § 10. "It is only because I can comprehend the
manifold of representations in one consciousness, that I call them all
my representations; for otherwise I should have as many-coloured and
varied a self as I have representations of which I am conscious."
Doubtless if I am to _be aware of_ myself as the same in apprehending
A and B, then, in coming to apprehend B, I must continue to apprehend
A, and therefore must apprehend A and B as related; and such a
consciousness on Kant's view involves a synthesis. But if I am merely
to _be_ the same subject which apprehends A and B, or rather if the
apprehension of A and that of B are merely to _be_ apprehensions on
the part of one and the same subject, no such consciousness of A and B
as related and, therefore, no synthesis is involved.

    [76] §§ 5-11.

Again, the third paragraph assumes the possibility of
self-consciousness as the starting-point for argument. The thought[77]
seems to be this: 'For a self to be aware of its own identity, there
must be a manifold in relation to which it can apprehend itself as one
and the same throughout. An understanding which was perceptive, i. e.
which originated objects by its own act of thinking, would necessarily
by its own thinking originate a manifold in relation to which it could
be aware of its own identity in thinking, and therefore its
self-consciousness would need no synthesis. But our understanding,
which is not perceptive, requires a manifold to be given to it, in
relation to which it can be aware of its own identity by means of a
synthesis of the manifold.' If this be the thought, it is clearly
presupposed that _any_ understanding must be capable of being
conscious of its own identity.[78]

    [77] Cf. B. 138 fin.-139 init., M. 85 fin.

    [78] B. 139 init., M. 85 fin. also assumes that it is
    impossible for a mind to be a unity without being able to be
    conscious of its unity.

Further, it is easy to see how Kant came to take for granted the
possibility of self-consciousness, in the sense of the consciousness
of ourselves as the identical subject of all our representations. He
approaches self-consciousness with the presupposition derived from his
analysis of knowledge that our apprehension of a manifold does not
consist in separate apprehensions of its elements, but is one
apprehension or consciousness of the elements as related.[79] He
thinks of this as a general presupposition of all apprehension of a
manifold, and, of course, to discover this presupposition is to be
self-conscious. To recognize the oneness of our apprehension is to be
conscious of our own identity.[80]

    [79] It is in consequence of this that the statement that 'a
    manifold of representations belongs to me' means, with the
    probable exception of § 1, not, 'I am aware of A, I am aware
    of B, I am aware of C,' but, 'I am aware, in one act of
    awareness, of A B C as related' (= ABC are 'connected in' or
    'belong to' one consciousness). Cf. §§ 4, 8 ('in one
    consciousness'), 9, 10 ('in one consciousness'), and A. 116,
    Mah. 208 ('These representations only represent anything in
    me by belonging with all the rest to one consciousness
    [accepting Erdmann's emendation _mit allen anderen_], in
    which at any rate they can be connected').

    [80] The above criticism of Kant's thought has not implied
    that it may not be true that a knowing mind is, as such,
    capable of being aware of its own unity; the argument has
    only been that Kant's proof is unsuccessful.

Again, to pass to the second main point to be considered,[81]
Kant has no justification for arguing from the possibility of
self-consciousness to that of the synthesis. This can be seen from the
mere form of his argument. Kant, as has been said, seems first to
establish the possibility of self-consciousness, and thence to
conclude that a synthesis must be possible. But if, as it is his point
to urge, consciousness of our identity only takes place through
consciousness of the synthesis, this method of argument must be
invalid. It would clearly be necessary to know that the synthesis is
possible, _before_ and _in order that_ we could know that
self-consciousness is possible. An objector has only to urge that the
manifold might be such that it could not be combined into a systematic
whole, in order to secure the admission that in that case
self-consciousness would not be possible.

    [81] Cf. p. 198.

Nevertheless, the passage under consideration may be said to lay bare
an important presupposition of self-consciousness. It is true that
self-consciousness would be impossible, if we merely apprehended the
parts of the world in isolation. To be conscious that I who am
perceiving C perceived B and A, I must be conscious at once of A, B,
and C, in one act of consciousness or apprehension. To be conscious
separately of A and B and C is not to be conscious of A and B and C.
And, to be conscious of A and B and C in one act of consciousness, I
must apprehend A, B, and C as related, i. e. as forming parts of a
whole or system. Hence it is only because our consciousness of A, B,
and C is never the consciousness of a mere A, a mere B, and a mere C,
but is always the consciousness of A B C as elements in one world that
we can be conscious of our identity in apprehending A, B, and C. If
_per impossibile_ our apprehension be supposed to cease to be an
apprehension of a plurality of objects in relation, self-consciousness
must be supposed to cease also. At the same time, it is impossible to
argue from the consciousness of our identity in apprehending to the
consciousness of what is apprehended as a unity, and thence to the
existence of that unity. For, apart from the consideration that in
fact all thinking presupposes the relatedness or--what is the same
thing--the necessary relatedness of objects to one another, and that
therefore any assertion to the contrary is meaningless, the
consciousness of objects as a unity is a condition of the
consciousness of our identity, and therefore any doubt that can be
raised in regard to the former can be raised equally with regard to
the latter.

We may now pass to the concluding portion of the deduction. For the
purpose of considering it, we may sum up the results of the preceding
discussion by saying that Kant establishes the synthesis of the
manifold on certain principles by what are really two independent
lines of thought. The manifold may be regarded either as something
which, in order to enter into knowledge, must be given relation to an
object, or as something with respect to which self-consciousness must
be possible. Regarded in either way, the manifold, according to Kant,
involves a process of synthesis on certain principles, which makes it
a systematic unity. Now Kant introduces the categories by maintaining
that they are the principles of synthesis in question. "I assert that
the above mentioned _categories_ are nothing but the _conditions of
thinking in a possible experience_.... They are fundamental
conceptions by which we think objects in general for phenomena."[82]
A synthesis according to the categories is 'that wherein alone
apperception can prove _a priori_ its thorough-going and necessary
identity'.[83] In the first edition this identification is simply
asserted, but in the second Kant offers a proof.[84]

    [82] A. 111, Mah. 204. Cf. A. 119, Mah. 210.

    [83] A. 112, Mah. 204.

    [84] Cf. p. 161.

Before, however, we consider the proof, it is necessary to refer
to a difficulty which seems to have escaped Kant altogether. The
preceding account of the synthesis involved in knowledge and in
self-consciousness implies, as his illustrations conclusively show,
that the synthesis requires a particular principle which constitutes
the individual manifold a whole of a particular kind.[85] But, if this
be the case, it is clear that the categories, which are merely
conceptions of an object in general, and are consequently quite
general, cannot possibly be sufficient for the purpose. And since the
manifold in itself includes no synthesis and therefore no principle of
synthesis, Kant fails to give any account of the source of the
particular principles of synthesis required for particular acts of
knowledge.[86] This difficulty--which admits of no solution--is
concealed from Kant in two ways. In the first place, when he describes
what really must be stated as the process by which parts or qualities
of an object become related to an object of a particular kind, he
thinks that he is describing a process by which representations become
related to an object in general.[87] Secondly, he thinks of the
understanding as the source of general principles of synthesis,
individual syntheses and the particular principles involved being
attributed to the imagination; and so, when he comes to consider the
part played in knowledge by the understanding, he is apt to ignore the
need of particular principles.[88] Hence, Kant's proof that the
categories are the principles of synthesis can at best be taken only
as a proof that the categories, though not sufficient for the
synthesis, are involved in it.

    [85] Cf. p. 177, note 2, and p. 185.

    [86] Cf. pp. 215-17.

    [87] Cf. pp. 181-2.

    [88] Cf. p. 217.

The proof runs thus:

"I could never satisfy myself with the definition which logicians
give of a judgement in general. It is, according to them, the
representation of a relation between two conceptions...."

"But if I examine more closely the relation of given
representations[89] in every judgement, and distinguish it, as
belonging to the understanding, from their relation according to the
laws of the reproductive imagination (which has only subjective
validity), I find that a judgement is nothing but the mode of bringing
given representations under the _objective_ unity of apperception.
This is what is intended by the term of relation 'is' in judgements,
which is meant to distinguish the objective unity of given
representations from the subjective. For this term indicates the
relation of these representations to the original apperception, and
also their _necessary unity_, even though the judgement itself is
empirical, and therefore contingent, e. g. 'Bodies are heavy.' By this
I do not mean that these representations _necessarily_ belong _to each
other_ in empirical perception, but that they belong to each other _by
means of the necessary unity_ of apperception in the synthesis of
perceptions, that is, according to principles of the objective
determination of all our representations, in so far as knowledge can
arise from them, these principles being all derived from the principle
of the transcendental unity of apperception. In this way alone can
there arise from this relation _a judgement_, that is, a relation
which is _objectively valid_, and is adequately distinguished from the
relation of the very same representations which would be only
subjectively valid, e. g. according to laws of association. According
to these laws, I could only say, 'If I carry a body, I feel an
impression of weight', but not 'It, the body, _is_ heavy'; for this is
tantamount to saying, 'These two representations are connected in the
object, that is, without distinction as to the condition of the
subject, and are not merely connected together in the perception,
however often it may be repeated.'"[90]

    [89] _Erkenntnisse_ here is clearly used as a synonym for
    representations. Cf. A. 104, Mah. 199.

    [90] B. 140-2, M. 86-8; cf. _Prol._, §§ 18-20.

This ground for the identification of the categories with the
principles of synthesis involved in knowledge may be ignored, as on
the face of it unsuccessful. For the argument is that since the
activity by which the synthesis is affected is that of judgement, the
conceptions shown by the _Metaphysical Deduction_ to be involved in
judgement must constitute the principles of synthesis. But it is
essential to this argument that the present account of judgement and
that which forms the basis of the _Metaphysical Deduction_ should be
the same; and this is plainly not the case.[91] Judgement is now
represented as an act by which we relate the manifold of sense in
certain necessary ways as parts of the physical world,[92] whereas in
the _Metaphysical_ _Deduction_ it was treated as an act by which we
relate conceptions; and Kant now actually says that this latter
account is faulty. Hence even if the metaphysical deduction had
successfully derived the categories from the account of judgement
which it presupposed, the present argument would not justify the
identification of the categories so deduced with the principles of
synthesis. The fact is that Kant's vindication of the categories is in
substance independent of the _Metaphysical Deduction_. Kant's real
thought, as opposed to his formal presentation of it, is simply that
when we come to consider what are the principles of synthesis involved
in the reference of the manifold to an object, we find that they are
the categories.[93] The success, then, of this step in Kant's
vindication of the categories is independent of that of the
metaphysical deduction, and depends solely upon the question whether
the principles of synthesis involved in knowledge are in fact the
categories.

    [91] Cf. Caird, i. 348-9 note.

    [92] We may notice in passing that this passage renders
    explicit the extreme difficulty of Kant's view that 'the
    objective unity of apperception' is the unity of the parts of
    nature or of the physical world. How can the 'very same
    representations' stand at once in the subjective relation of
    association and in the objective relation which consists in
    their being related as parts of nature? There is plainly
    involved a transition from representation, in the sense of
    the apprehension of something, to representation, in the
    sense of something apprehended. It is objects apprehended
    which are objectively related; it is our apprehensions of
    objects which are associated, cf. pp. 233 and 281-2. Current
    psychology seems to share Kant's mistake in its doctrine of
    association of ideas, by treating the elements associated,
    which are really apprehensions of objects, as if they were
    objects apprehended.

    [93] Cf. A. 112, Mah. 204; B. 162, M. 99.

The substance of Kant's vindication of the categories may therefore be
epitomized thus: 'We may take either of two starting-points. On the
one hand, we may start from the fact that our experience is no mere
dream, but an intelligent experience in which we are aware of a world
of individual objects. This fact is conceded even by those who, like
Hume, deny that we are aware of any necessity of relation between
these objects. We may then go on to ask how it comes about that,
beginning as we do with a manifold of sense given in succession, we
come to apprehend this world of individual objects. If we do so, we
find that there is presupposed a synthesis on our part of the manifold
upon principles constituted by the categories.

To deny, therefore, that the manifold is so connected is implicitly to
deny that we have an apprehension of objects at all. But the existence
of this apprehension is plainly a fact which even Hume did not
dispute. On the other hand, we may start with the equally obvious fact
that we must be capable of apprehending our own identity throughout
our apprehension of the manifold of sense, and look for the
presupposition of this fact. If we do this, we again find that there
is involved a combination of the manifold according to the
categories.'

In conclusion, attention may be drawn to two points. In the first
place, Kant completes his account by at once emphasizing and
explaining the paradoxical character of his conclusion. "Accordingly,
the order and conformity to law in the phenomena which we call
_nature_ we ourselves introduce, and we could never find it there,
if we, or the nature of our mind, had not originally placed it
there."[94] "However exaggerated or absurd then it may sound to say
that the understanding itself is the source of the laws of nature and
consequently of the formal unity of nature, such an assertion is
nevertheless correct and in accordance with the object, i. e. with
experience."[95] The explanation of the paradox is found in the fact
that objects of nature are phenomena. "But if we reflect that this
nature is in itself nothing else than a totality[96] of phenomena and
consequently no thing in itself but merely a number of representations
of the mind, we shall not be surprised that only in the radical
faculty of all our knowledge, viz. transcendental apperception, do we
see it in that unity through which alone it can be called object of
all possible experience, i. e. nature."[97] "It is no more surprising
that the laws of the phenomena in nature must agree with the
understanding and with its _a priori_ form, that is, its faculty of
connecting the manifold in general, than that the phenomena themselves
must agree with the _a priori_ form of our sensuous perception. For
laws exist in the phenomena as little as phenomena exist in
themselves; on the contrary, laws exist only relatively to the subject
in which the phenomena inhere, so far as it has understanding, just as
phenomena exist only relatively to the subject, so far as it has
senses. To things in themselves their conformity to law would
necessarily also belong independently of an understanding which knows
them. But phenomena are only representations of things which exist
unknown in respect of what they may be in themselves. But, as mere
representations, they stand under no law of connexion except that
which the connecting faculty prescribes."[98]

    [94] A. 125, Mah. 214.

    [95] A. 127, Mah. 216.

    [96] _Inbegriff._

    [97] A. 114, Mah. 206.

    [98] B. 164, M. 100.

In the second place, this last paragraph contains the real reason from
the point of view of the deduction[99] of the categories for what may
be called the negative side of his doctrine, viz. that the categories
only apply to objects of experience and not to things in themselves.
According to Kant, we can only say that certain principles of
connexion apply to a reality into which we introduce the connexion.
Things in themselves, if connected, are connected in themselves and
apart from us. Hence there can be no guarantee that any principles of
connexion which we might assert them to possess are those which they
do possess.

    [99] The main passage (B. 146-9, M. 90-2), in which he argues
    that the categories do not apply to things in themselves,
    ignores the account of a conception as a principle of
    synthesis, upon which the deduction turns, and returns to the
    earlier account of a conception as something opposed to a
    perception, i. e. as that by which an object is thought as
    opposed to a perception by which an object is given.
    Consequently, it argues merely that the categories, as
    conceptions, are empty or without an object, unless an object
    is given in perception, and that, since things in themselves
    are not objects of perception, the categories are no more
    applicable to things in themselves than are any other
    conceptions.




CHAPTER IX

GENERAL CRITICISM OF THE TRANSCENDENTAL DEDUCTION OF THE CATEGORIES


The preceding account of Kant's vindication of the categories has
included much criticism. But the criticism has been as far as possible
restricted to details, and has dealt with matters of principle only so
far as has been necessary in order to follow Kant's thought. We must
now consider the position as a whole, even though this may involve
some repetition.[1] The general difficulties of the position may be
divided into two kinds, (1) difficulties involved in the working out
of the theory, even if its main principles are not questioned, and (2)
difficulties involved in accepting its main principles at all.

    [1] Difficulties connected with Kant's view of
    self-consciousness will be ignored, as having been
    sufficiently considered.

The initial difficulty of the first kind, which naturally strikes the
reader, concerns the possibility of performing the synthesis. The mind
has certain general ways of combining the manifold, viz. the
categories. But on general grounds we should expect the mind to
possess only one mode of combining the manifold. For the character of
the manifold to be combined cannot affect the mind's power of
combination, and, if the power of the mind consists in combining, the
combining should always be of the same kind. Thus, suppose the
manifold given to the mind to be combined consisted of musical notes,
we could think of the mind's power of combination as exercised in
combining the notes by way of succession, _provided that_ this be
regarded as the only mode of combination. But if the mind were thought
also capable of combining notes by way of simultaneity, we should at
once be confronted with the insoluble problem of determining why the
one mode of combination was exercised in any given case rather than
the other. If, several kinds of synthesis being allowed, this
difficulty be avoided by the supposition that, not being incompatible,
they are all exercised together, we have the alternative task of
explaining how the same manifold can be combined in each of these
ways. As a matter of fact, Kant thinks of manifolds of different kinds
as combined or related in different ways; thus events are related
causally and quantities quantitatively. But since, on Kant's view, the
manifold as given is unrelated and all combination comes from the
mind, the mind should not be held capable of combining manifolds of
different kinds differently. Otherwise the manifold would in its own
nature imply the need of a particular kind of synthesis, and would
therefore not be unrelated.

Suppose, however, we waive the difficulty involved in the plurality of
the categories. There remains the equally fundamental difficulty that
any single principle of synthesis contains in itself no ground for the
different ways of its application.[2] Suppose it to be conceded that
in the apprehension of definite shapes we combine the manifold in
accordance with the conception of figure, and, for the purpose of the
argument, that the conception of figure can be treated as equivalent
to the category of quantity. It is plain that we apprehend different
shapes, e. g. lines[3] and triangles[4], of which, if we take into
account differences of relative length of sides, there is an infinite
variety, and houses,[5] which may also have an infinite variety of
shape. But there is nothing in the mind's capacity of relating the
manifold by way of figure to determine it to combine a given manifold
into a figure of one kind rather than into a figure of any other kind;
for to combine the manifold into a particular shape, there is needed
not merely the thought of a figure in general, but the thought of a
definite figure. No 'cue' can be furnished by the manifold itself, for
any such cue would involve the conception of a particular figure, and
would therefore imply that the particular synthesis was implicit in
the manifold itself, in which case it would not be true that all
synthesis comes from the mind.

    [2] Cf. p. 207.

    [3] B. 137, M. 85.

    [4] A. 105, Mah. 199.

    [5] B. 162, M. 99.

This difficulty takes a somewhat different form in the case of the
categories of relation. To take the case of cause and effect,
the conception of which, according to Kant, is involved in our
apprehension of a succession, Kant's view seems to be that we become
aware of two elements of the manifold A B as a succession of events in
the world of nature by combining them as necessarily successive in a
causal order, in which the state of affairs which precedes B and which
contains A contains something upon which B must follow (i. e. a cause
of B), which therefore makes it necessary that B must follow A.[6] But
if we are to do this, we must in some way succeed in selecting or
picking out from among the elements of the manifold that element A
which is to be thus combined with B. We therefore need something more
than the category. It is not enough that we should think that B has a
cause; we must think of something in particular as the cause of B,
and we must think of it either as coexistent with, or as identical
with, A.

    [6] Cf. pp. 291-3.

Kant fails to notice this second difficulty,[7] and up to a certain
point avoids it owing to his distinction between the imagination and
the understanding. For he thinks of the understanding as the source of
general principles of synthesis, viz. the categories, and attributes
individual syntheses to the imagination. Hence the individual
syntheses, which involve particular principles, are already effected
before the understanding comes into play. But to throw the work of
effecting individual syntheses upon the imagination is only to evade
the difficulty. For in the end, as has been pointed out,[8] the
imagination must be the understanding working unreflectively, and,
whether this is so or not, some account must be given of the way in
which the imagination furnishes the particular principles of synthesis
required.

    [7] We should have expected Kant to have noticed this
    difficulty in A. 105, Mah. 199, where he describes what is
    involved in the relation of representations to an object, for
    his instance of representations becoming so related is the
    process of combining elements into a triangle, which plainly
    requires a synthesis of a very definite kind. For the reasons
    of his failure to notice the difficulty cf. p. 207.

    [8] Pp. 168-9.

The third and last main difficulty of the first kind concerns the
relation of the elements of the manifold and the kinds of synthesis
by which they are combined. This involves the distinction between
relating in general and terms to be related. For to perform a
synthesis is in general to relate, and the elements to be combined
are the terms to be related.[9] Now it is only necessary to take
instances to realize that the possibility of relating terms in certain
ways involves two presuppositions, which concern respectively the
general and the special nature of the terms to be related.

    [9] 'To relate' is used rather than 'to recognize as
    related', in order to conform to Kant's view of knowledge.
    But if it be desired to take the argument which follows in
    connexion with knowledge proper (cf. p. 242), it is only
    necessary to substitute throughout 'to recognize as related'
    for 'to relate' and to make the other changes consequent
    thereon.

In the first place, it is clear that the general nature of the terms
must correspond with or be adapted to the general nature of the
relationship to be effected. Thus if two terms are to be related as
more or less loud, they must be sounds, since the relation in question
is one in respect of sound and not, e. g., of time or colour or space.
Similarly, terms to be related as right and left must be bodies in
space, right and left being a spatial relation. Again, only human
beings can be related as parent and child. Kant's doctrine, however,
does not conform to this presupposition. For the manifold to be
related consists solely of sensations, and of individual spaces, and
perhaps individual times, as elements of pure perception; and such a
manifold is not of the kind required. Possibly individual spaces may
be regarded as adequate terms to be related or combined into
geometrical figures, e. g. into lines or triangles. But a house as a
synthesis of a manifold cannot be a synthesis of spaces, or of times,
or of sensations. Its parts are bodies, which, whatever they may be,
are neither sensations nor spaces nor times, nor combinations of them.
In reality they are substances of a special kind. Again, the relation
of cause and effect is not a relation of sensations or spaces or
times, but of successive states of physical things or substances, the
relation consisting in the necessity of their succession.

In the second place, it is clear that the special nature of the
relation to be effected presupposes a special nature on the part of
the terms to be related. If one sound is to be related to another by
way of the octave, that other must be its octave. If one quantity is
to be related to another as the double of it, that quantity must be
twice as large as the other. In the same way, proceeding to Kant's
instances, we see that if we are to combine or relate a manifold into
a triangle, and therefore into a triangle of a particular size and
shape, the elements of the manifold must be lines, and lines of a
particular size. If we are to combine a manifold into a house, and
therefore into a house of a certain shape and size, the manifold must
consist of bodies of a suitable shape and size. If we are to relate a
manifold by way of necessary succession, the manifold must be such
that it can be so related; in other words, if we are to relate an
element X of the manifold with some other Y as the necessary
antecedent of X, there must be some definite element Y which is
connected with, and always occurs along with, X. To put the matter
generally, we may say that the manifold must be adapted to or 'fit'
the categories not only, as has been pointed out, in the sense that it
must be of the right kind, but also in the sense that its individual
elements must have that orderly character which enables them to be
related according to the categories.

Now it is plain from Kant's vindication of what he calls the affinity
of phenomena,[10] that he recognizes the existence of this
presupposition. But the question arises whether this vindication can
be successful. For since the manifold is originated by the thing in
itself, it seems prima facie impossible to prove that the elements of
the manifold must have affinity, and so be capable of being related
according to the categories. Before, however, we consider the chief
passage in which Kant tries to make good his position, we may notice a
defence which might naturally be offered on his behalf. It might be
said that he establishes the conformity of the manifold to the
categories at least hypothetically, i. e. upon the supposition that
the manifold is capable of entering into knowledge, and also upon the
supposition that we are capable of being conscious of our identity
with respect to it; for upon either supposition any element of the
manifold must be capable of being combined with all the rest into one
world of nature. Moreover, it might be added that these suppositions
are justified, for our experience is not a mere dream, but is
throughout the consciousness of a world, and we are self-conscious
throughout our experience; and therefore it is clear that the manifold
does in fact 'fit' the categories. But the retort is obvious. Any
actual conformity of the manifold to the categories would upon this
view be at best but an empirical fact, and, although, if the
conformity ceased, we should cease to be aware of a world and of
ourselves, no reason has been or can be given why the conformity
should not cease.

    [10] Cf. A. 100-2, Mah. 195-7 (quoted pp. 171-2); A. 113,
    Mah. 205; A. 121-2, Mah. 211-2.

The passage in which Kant vindicates the affinity of phenomena in the
greatest detail is the following:

"We will now try to exhibit the necessary connexion of the
understanding with phenomena by means of the categories, by beginning
from below, i. e. from the empirical end. The first that is given us
is a phenomenon, which if connected with consciousness is called
perception[11].... But because every phenomenon contains a manifold,
and consequently different perceptions are found in the mind scattered
and single, a connexion of them is necessary, which they cannot have
in mere sense. There is, therefore, in us an active power of synthesis
of this manifold, which we call imagination, and the action of which,
when exercised immediately upon perceptions, I call apprehension. The
business of the imagination, that is to say, is to bring the manifold
of intuition[12] into an _image_; it must, therefore, first receive
the impressions into its activity, i. e. apprehend them."

    [11] _Wahrnehmung._

    [12] _Anschauung._

"But it is clear that even this apprehension of the manifold would not
by itself produce an image and a connexion of the impressions, unless
there were a subjective ground in virtue of which one perception, from
which the mind has passed to another, is summoned to join that which
follows, and thus whole series of perceptions are presented, i. e. a
reproductive power of imagination, which power, however, is also only
empirical."

"But if representations reproduced one another at haphazard just as
they happened to meet together, once more no determinate connexion
would arise, but merely chaotic heaps of them, and consequently no
knowledge would arise; therefore the reproduction of them must have a
rule, according to which a representation enters into connexion with
this rather than with another in the imagination. This subjective and
_empirical_ ground of reproduction according to rules is called the
_association_ of representations."

"But now, if this unity of association had not also an objective
ground, so that it was impossible that phenomena should be apprehended
by the imagination otherwise than under the condition of a possible
synthetic unity of this apprehension, it would also be a pure accident
that phenomena were adapted to a connected system of human knowledge.
For although we should have the power of associating perceptions, it
would still remain wholly undetermined and accidental whether they
were associable; and in the event of their not being so, a multitude
of perceptions and even perhaps a whole sensibility would be possible,
in which much empirical consciousness would be met with in my mind,
but divided and without belonging to _one_ consciousness of myself,
which however is impossible. For only in that I ascribe all
perceptions to one consciousness (the original apperception) can I say
of all of them that I am conscious of them. There must therefore be an
objective ground, i. e. a ground to be recognized _a priori_ before
all empirical laws of the imagination, on which rests the possibility,
nay even the necessity, of a law which extends throughout all
phenomena, according to which we regard them without exception as such
data of the senses, as are in themselves associable and subjected to
universal rules of a thorough-going connexion in reproduction. This
objective ground of all association of phenomena I call the _affinity_
of phenomena. But we can meet this nowhere else than in the principle
of the unity of apperception as regards all cognitions which are to
belong to me. According to it, all phenomena without exception must so
enter into the mind or be apprehended as to agree with the unity of
apperception, which agreement would be impossible without synthetical
unity in their connexion, which therefore is also objectively
necessary."

"The objective unity of all (empirical) consciousness in one
consciousness (the original apperception) is therefore the necessary
condition even of all possible perception, and the affinity of all
phenomena (near or remote) is a necessary consequence of a synthesis
in the imagination, which is _a priori_ founded upon rules."

"The imagination is therefore also a power of _a priori_ synthesis,
for which reason we give it the name of the productive imagination;
and so far as it, in relation to all the manifold of the phenomenon,
has no further aim than the necessary unity in the synthesis of the
phenomenon, it can be called the transcendental function of the
imagination. It is therefore strange indeed, but nevertheless clear
from the preceding, that only by means of this transcendental function
of the imagination does even the affinity of phenomena, and with it
their association and, through this, lastly their reproduction
according to laws, and consequently experience itself become possible,
because without it no conceptions of objects would ever come together
into one experience."[13]

    [13] A. 119-23, Mah. 210-3.

If it were not for the last two paragraphs[14], we should understand
this difficult passage to be substantially identical in meaning with
the defence of the affinity of phenomena just given.[15] We should
understand Kant to be saying (1) that the synthesis which knowledge
requires presupposes not merely a faculty of association on our part
by which we reproduce elements of the manifold according to rules, but
also an affinity on the part of the manifold to be apprehended, which
enables our faculty of association to get to work, and (2) that this
affinity can be vindicated as a presupposition at once of knowledge
and of self-consciousness.

    [14] And also the first and last sentence of the fourth
    paragraph, where Kant speaks not of 'phenomena which are to
    be apprehended', but of the 'apprehension of phenomena' as
    necessarily agreeing with the unity of apperception.

    [15] p. 220.

In view, however, of the fact that, according to the last two
paragraphs, the affinity is due to the imagination,[16] it seems
necessary to interpret the passage thus:

    [16] It should be noted that in the last paragraph but one
    Kant does not say '_our knowledge_ that phenomena must have
    affinity is a consequence of _our knowledge_ that there must
    be a synthesis of the imagination', but 'the affinity of all
    phenomena is a consequence of a synthesis in the
    imagination'. And the last paragraph precludes the view that
    in making the latter statement he meant the former. Cf. also
    A. 101, Mah. 196.

'Since the given manifold of sense consists of isolated elements, this
manifold, in order to enter into knowledge, must be combined into an
image. This combination is effected by the imagination, which however
must first apprehend the elements one by one.'

'But this apprehension of the manifold by the imagination could
produce no image, unless the imagination also possessed the power of
reproducing past elements of the manifold, and, if knowledge is to
arise, of reproducing them according to rules. This faculty of
reproduction by which, on perceiving the element A, we are led to
think of or reproduce a past element B--B being reproduced according
to some rule--rather than C or D is called the faculty of association;
and since the rules according to which it works depend on empirical
conditions, and therefore cannot be anticipated _a priori_, it may be
called the subjective ground of reproduction.'

'But if the image produced by association is to play a part in
knowledge, the empirical faculty of reproduction is not a sufficient
condition or ground of it. A further condition is implied, which may
be called objective in the sense that it is _a priori_ and prior to
all empirical laws of imagination. This condition is that the act by
which the data of sense enter the mind or are apprehended, i. e. the
act by which the imagination _apprehends and combines_ the data of
sense into a sensuous image, must _make_ the elements such that they
have affinity, and therefore such that they can subsequently be
recognized as parts of a necessarily related whole.[17] Unless this
condition is satisfied, even if we possessed the faculty of
association, our experience would be a chaos of disconnected elements,
and we could not be self-conscious, which is impossible. Starting,
therefore, with the principle that we must be capable of being
self-conscious with respect to all the elements of the manifold, we
can lay down _a priori_ that this condition is a fact.'

    [17] On this interpretation 'entering the mind' or 'being
    apprehended' in the fourth paragraph does not refer merely to
    the apprehension of elements one by one, which is preliminary
    to the act of combining them, but includes the act by which
    they are combined. If so, Kant's argument formally involves a
    circle. For in the second and third paragraphs he argues that
    the synthesis of perceptions involves reproduction according
    to rules, and then, in the fourth paragraph, he argues that
    this reproduction presupposes a synthesis of perceptions. We
    may, however, perhaps regard his argument as being in
    substance that knowledge involves _re_production by the
    imagination of elements capable of connexion, and that this
    reproduction involves _pro_duction by the imagination of the
    data of sense, which are to be reproduced, into an image.

'It follows, then, that the affinity or connectedness of the data of
sense presupposed by the _re_production which is presupposed in
knowledge, is actually produced by the _pro_ductive faculty of
imagination, which, in combining the data into a sensuous image,
gives them the unity required.'

If, as it seems necessary to believe, this be the correct
interpretation of the passage,[18] Kant is here trying to carry out
to the full his doctrine that _all_ unity or connectedness comes from
the mind's activity. He is maintaining that the imagination, acting
_pro_ductively on the data of sense and thereby combining them into an
image, gives the data a connectedness which the understanding can
subsequently recognize. But to maintain this is, of course, only to
throw the problem one stage further back. If reproduction, in order to
enter into knowledge, implies a manifold which has such connexion that
it is capable of being reproduced according to rules, so the
production of sense-elements into a coherent image in turn implies
sense-elements capable of being so combined. The act of combination
cannot confer upon them or introduce into them a unity which they do
not already possess.

    [18] If the preceding interpretation (pp. 223-4) be thought
    the correct one, it must be admitted that Kant's vindication
    of the affinity breaks down for the reason given, p. 220.

The fact is that this step in Kant's argument exhibits the final
breakdown of his view that all unity or connectedness or relatedness
is conferred upon the data of sense by the activity of the mind.
Consequently, this forms a convenient point at which to consider what
seems to be the fundamental mistake of this view. The mistake stated
in its most general form appears to be that, misled by his theory of
perception, he regards 'terms' as given by things in themselves
acting on the sensibility, and 'relations' as introduced by the
understanding,[19] whereas the fact is that in the sense in which terms
can be said to be given, relations can and must also be said to be
given.

    [19] The understanding being taken to include the
    imagination, as being the faculty of _spontaneity_ in
    distinction from the _passive_ sensibility.

To realize that this is the case, we need only consider Kant's
favourite instance of knowledge, the apprehension of a straight line.
According to him, this presupposes that there is given to us a
manifold, which--whether he admits it or not--must really be parts of
the line, and that we combine this manifold on a principle involved in
the nature of straightness. Now suppose that the manifold given is the
parts AB, BC, CD, DE of the line AE. It is clearly only possible to
recognize AB and BC as contiguous parts of a straight line, if we
immediately apprehend that AB and BC form one line of which these
parts are identical in direction. Otherwise, we might just as well
join AB and BC at a right angle, and in fact at any angle; we need not
even make AB and BC contiguous.[20] Similarly, the relation of BC to
CD and of CD to DE must be just as immediately apprehended as the
parts themselves. Is there, however, any relation of which it could be
said that it is not given, and to which therefore Kant's doctrine
might seem to apply? There is. Suppose AB, BC, CD to be of such a size
that, though we can see AB and BC, or BC and CD, together, we cannot
see AB and CD together. It is clear that in this case we can only
learn that AB and CD are parts of the same straight line through an
inference. We have to infer that, because each is in the same straight
line with BC, the one is in the same straight line with the other.
Here the fact that AB and CD are in the same straight line is not
immediately apprehended. This relation, therefore, may be said not to
be given; and, from Kant's point of view, we could say that we
introduce this relation into the manifold through our activity of
thinking, which combines AB and CD together in accordance with the
principle that two straight lines which are in the same line with a
third are in line with one another. Nevertheless, this case is no
exception to the general principle that relations must be given
equally with terms; for we only become aware of the relation between
AB and CD, which is not given, because we are already aware of other
relations, viz. those between AB and BC, and BC and CD, which are
given. Relations then, or, in Kant's language, particular syntheses
must be said to be given, in the sense in which the elements to be
combined can be said to be given.

    [20] In order to meet a possible objection, it may be pointed
    out that if AB and BC be given in isolation, the contiguity
    implied in referring to them as A_B_ and _B_C will not be
    known.

Further, we can better see the nature of Kant's mistake in this
respect, if we bear in mind that Kant originally and rightly
introduced the distinction between the sensibility and the
understanding as that between the passive faculty by which an
individual is given or presented to us and the active faculty by which
we bring an individual under, or recognize it as an instance of a
universal.[21] For we then see that Kant in the _Transcendental
Deduction_, by treating what is given by the sensibility as terms and
what is contributed by the understanding as relations, is really
confusing the distinction between a relation and its terms with that
between universal and individual; in other words, he says of terms
what ought to be said of individuals, and of relations what ought to
be said of universals. That the confusion is a confusion, and not a
legitimate identification, it is easy to see. For, on the one hand, a
relation between terms is as much an individual as either of the
terms. That a body A is to the right of a body B is as much an
individual fact as either A or B.[22] And if terms, as being
individuals, belong to perception and are given, in the sense that
they are in an immediate relation to us, relations, as being
individuals, equally belong to perception and are given. On the other
hand, individual terms just as much as individual relations imply
corresponding universals. An individual body implies 'bodiness', just
as much as the fact that a body A is to the right of a body B implies
the relationship of 'being to the right of something'. And if, as is
the case, thinking or conceiving in distinction from perceiving, is
that activity by which we recognize an individual, given in
perception, as one of a kind, conceiving is involved as much in the
apprehension of a term as in the apprehension of a relation. The
apprehension of 'this red body' as much involves the recognition of an
individual as an instance of a kind, i. e. as much involves an act of
the understanding, as does the apprehension of the fact that it is
brighter than some other body.

    [21] Cf. pp. 27-9.

    [22] I can attach no meaning to Mr. Bertrand Russell's
    assertion that relations have no instances. See _The
    Principles of Mathematics_, § 55.

Kant has failed to notice this confusion for two reasons. In the first
place, beginning in the _Analytic_ with the thought that the thing in
itself, by acting on our sensibility, produces isolated sense data, he
is led to adopt a different view of the understanding from that which
he originally gave, and to conceive its business as consisting in
relating these data. In the second place, by distinguishing the
imagination from the understanding, he is able to confine the
understanding to being the source of universals or principles of
relation in distinction from individual relations.[23] Since, however,
as has been pointed out, and as Kant himself sees at times, the
imagination is the understanding working unreflectively, this
limitation cannot be successful.

    [23] Cf. p. 217.

There remain for consideration the difficulties of the second kind,
i. e. the difficulties involved in accepting its main principles at
all. These are of course the most important. Throughout the deduction
Kant is attempting to formulate the nature of knowledge. According to
him, it consists in an activity of the mind by which it combines the
manifold of sense on certain principles and is to some extent aware
that it does so, and by which it thereby gives the manifold relation
to an object. Now the fundamental and final objection to this account
is that what it describes is not knowledge at all. The justice of this
objection may be seen by considering the two leading thoughts
underlying the view, which, though closely connected, may be treated
separately. These are the thought of knowledge as a process by which
representations acquire relation to an object, and the thought of
knowledge as a process of synthesis.

It is in reality meaningless to speak of 'a process by which
representations or ideas acquire relation to an object'.[24] The
phrase must mean a process by which a mere apprehension, which, as
such, is not the apprehension of an object, becomes the apprehension
of an object. Apprehension, however, is essentially and from the very
beginning the apprehension of an object, i. e. of a reality
apprehended. If there is no object which the apprehension is 'of',
there is no apprehension. It is therefore wholly meaningless to speak
of a process by which an apprehension _becomes_ the apprehension of an
object. If when we reflected we were not aware of an object, i. e. a
reality apprehended, we could not be aware of our apprehension; for
our apprehension is the apprehension of it, and is itself only
apprehended in relation to, though in distinction from, it. It is
therefore impossible to suppose a condition of mind in which, knowing
what 'apprehension' means, we proceed to ask, 'What is meant by an
object of it?' and 'How does an apprehension become related to an
object?'; for both questions involve the thought of a mere
representation, i. e. of an apprehension which as yet is not the
apprehension of anything.

    [24] Cf. p. 180, and pp. 280-3.

These questions, when their real nature is exhibited, are plainly
absurd. Kant's special theory, however, enables him to evade the real
absurdity involved. For, according to his view, a representation is
the representation or apprehension of something only from the point of
view of the thing in itself. As an appearance or perhaps more strictly
speaking as a sensation, it has also a being of its own which is not
relative[25]; and from this point of view it _is_ possible to speak of
'mere' representations and to raise questions which presuppose their
reality.[26]

    [25] Cf. p. 137 init.

    [26] The absurdity of the problem really propounded is also
    concealed from Kant in the way indicated, pp. 180 fin.-181
    init.

But this remedy, if remedy it can be called, is at least as bad as the
disease. For, in the first place, the change of standpoint is
necessarily illegitimate. An appearance or sensation is not from any
point of view a representation in the proper sense, i. e. a
representation or apprehension of something. It is simply a reality to
be apprehended, of the special kind called mental. If it be called a
representation, the word must have a new meaning; it must mean
something represented, or presented,[27] i. e. object of apprehension,
with the implication that what is presented, or is object of
apprehension, is mental or a modification of the mind. Kant therefore
only avoids the original absurdity by an illegitimate change of
standpoint, the change being concealed by a tacit transition in the
meaning of representation. In the second place, the change of
standpoint only saves the main problem from being absurd by rendering
it insoluble. For if a representation be taken to be an appearance or
a sensation, the main problem becomes that of explaining how it is
that, beginning with the apprehension of mere appearances or
sensations, we come to apprehend an object, in the sense of an object
in nature, which, as such, is not an appearance or sensation but a
part of the physical world. But if the immediate object of
apprehension were in this way confined to appearances, which are, to
use Kant's phrase, determinations of our mind, our apprehension would
be limited to these appearances, and any apprehension of an object in
nature would be impossible.[28] In fact, it is just the view that the
immediate object of apprehension consists in a determination of the
mind which forms the basis of the solipsist position. Kant's own
solution involves an absurdity at least as great as that involved in
the thought of a mere representation, in the proper sense of
representation. For the solution is that appearances or sensations
become related to an object, in the sense of an object in nature, by
being combined on certain principles. Yet it is plainly impossible to
combine appearances or sensations into an object in nature. If a
triangle, or a house, or 'a freezing of water'[29] is the result of
any process of combination, the elements combined must be respectively
lines, and bricks, and physical events; these are objects in the sense
in which the whole produced by the combination is an object, and are
certainly not appearances or sensations. Kant conceals the difficulty
from himself by the use of language to which he is not entitled. For
while his instances of objects are always of the kind indicated, he
persists in calling the manifold combined 'representations', i. e.
presented mental modifications. This procedure is of course
facilitated for him by his view that nature is a phenomenon or
appearance, but the difficulty which it presents to the reader
culminates when he speaks of the very same representations as having
both a subjective and an objective relation, i. e. as being both
modifications of the mind and parts of nature.[30]

    [27] _Vorgestellt._

    [28] Cf. p. 123.

    [29] B. 162, M. 99.

    [30] B. 139-42, M. 87-8. Cf. 209, note 3, and pp. 281-2.

We may now turn to Kant's thought of knowledge as a process of
synthesis. When Kant speaks of synthesis, the kind of synthesis of
which he usually is thinking is that of spatial elements into a
spatial whole; and although he refers to other kinds, e. g. of units
into numbers, and of events into a temporal series, nevertheless it is
the thought of spatial synthesis which guides his view. Now we must in
the end admit that the spatial synthesis of which he is thinking is
really the _construction_ or _making_ of spatial objects in the
literal sense. It would be rightly illustrated by making figures out
of matches or spelicans, or by drawing a circle with compasses, or by
building a house out of bricks. Further, if we extend this view of the
process of which Kant is thinking, we have to allow that the process
of synthesis in which, according to Kant, knowledge consists is that
of making or constructing parts of the physical world, and in fact the
physical world itself, out of elements given in perception.[31] The
deduction throughout presupposes that the synthesis is really
_manufacture_, and Kant is at pains to emphasize the fact. "The order
and conformity to law in the phenomena which we call _nature_ we
ourselves introduce, and we could not find it there, if we or the
nature of our mind had not originally placed it there."[32] He
naturally rejoices in the manufacture, because it is just this which
makes the categories valid. If knowing is really making, the
principles of synthesis must apply to the reality known, because it is
by these very principles that the reality is made. Moreover,
recognition of this fact enables us to understand certain features of
his view which would otherwise be inexplicable. For if the synthesis
consists in literal construction, we are able to understand why Kant
should think (1) that in the process of knowledge the mind
_introduces_ order into the manifold, (2) that the mind is limited in
its activity of synthesis by having to conform to certain principles
of construction which constitute the nature of the understanding, and
(3) that the manifold of phenomena must possess affinity. If, for
example, we build a house, it can be said (1) that we introduce into
the materials a plan or principle of arrangement which they do not
possess in themselves, (2) that the particular plan is limited by, and
must conform to, the laws of spatial relation and to the general
presuppositions of physics, such as the uniformity of nature, and (3)
that only such materials are capable of the particular combination as
possess a nature suitable to it. Moreover, if, for Kant, knowing is
really making, we are able to understand two other prominent features
of his view. We can understand why Kant should lay so much stress upon
the 'recognition' of the synthesis, and upon the self-consciousness
involved in knowledge. For if the synthesis of the manifold is really
the making of an object, it results merely in the existence of the
object; knowledge of it is still to be effected. Consequently,
knowledge of the object only finds a place in Kant's view by the
_recognition_ (on the necessity of which he insists) of the manifold
as combined on a principle. This recognition, which Kant considers
only an element in knowledge, is really the knowledge itself. Again,
since the reality to be known is a whole of parts which we construct
on a principle, we know that it is such a whole, and therefore that
'the manifold is related to one object', because, and only because, we
know that we have combined the elements on a principle.
Self-consciousness therefore _must_ be inseparable from consciousness
of an object.

    [31] It is for this reason that the mathematical
    illustrations of the synthesis are the most plausible for his
    theory. While we can be said to construct geometrical
    figures, and while the construction of geometrical figures
    can easily be mistaken for the apprehension of them, we
    cannot with any plausibility be said to construct the
    physical world.

    [32] A. 125, Mah. 214. Cf. the other passages quoted pp.
    211-12.

The fundamental objection to this account of knowledge seems so
obvious as to be hardly worth stating; it is of course that knowing
and making are not the same. The very nature of knowing presupposes
that the thing known is already made, or, to speak more accurately,
already exists.[33] In other words, knowing is essentially the
discovery of what already is. Even if the reality known happens to be
something which we make, e. g. a house, the knowing it is distinct
from the making it, and, so far from being identical with the making,
presupposes that the reality in question is already made. Music and
poetry are, no doubt, realities which in some sense are 'made' or
'composed', but the apprehension of them is distinct from and
presupposes the process by which they are composed.

    [33] Cf. Ch. VI.

How difficult it is to resolve knowing into making may be seen by
consideration of a difficulty in the interpretation of Kant's phrase
'relation of the manifold to an object', to which no allusion has yet
been made. When it is said that a certain manifold is related to, or
stands[34] in relation to, an object, does the relatedness referred to
consist in the fact that the manifold is combined into a whole, or in
the fact that we are conscious of the combination, or in both? If we
accept the first alternative we must allow that, while relatedness to
an object implies a process of synthesis, yet the relatedness, and
therefore the synthesis, have nothing to do with knowledge. For the
relatedness of the manifold to an object will be the combination of
the elements of the manifold as parts of an object constructed, and
the process of synthesis involved will be that by which the object is
constructed. This process of synthesis will have nothing to do with
knowledge; for since it is merely the process by which the object is
constructed, knowledge so far is not effected at all, and no clue is
given to the way in which it comes about. If, however, we accept the
second alternative, we have to allow that while relatedness to an
object has to do with knowledge, yet it in no way implies a process of
synthesis. For since in that case it consists in the fact that we are
conscious of the manifold as together forming an object, it in no way
implies that the object has been produced by a process of synthesis.
Kant, of course, would accept the third alternative. For, firstly,
since it is knowledge which he is describing, the phrase 'relatedness
to an object' cannot refer simply to the _existence_ of a combination
of the manifold, and of a process by which it has been produced; its
meaning must include _consciousness_ of the combination. In the second
place, it is definitely his view that we cannot represent anything as
combined in the object without having previously combined it
ourselves.[35] Moreover, it is just with respect to this connexion
between the synthesis and the consciousness of the synthesis that his
reduction of knowing to making helps him; for to make an object, e. g.
a house, is to make it consciously, i. e. to combine materials on a
principle of which we are aware. Since, then, the combining of which
he speaks is really making, it seems to him impossible to combine a
manifold without being aware of the nature of the act of combination,
and therefore of the nature of the whole thereby produced.[36] But
though this is clearly Kant's view, it is not justified. In the first
place, 'relatedness of the manifold to an object' ought not to refer
_both_ to its combination in a whole _and_ to our consciousness of the
combination; and in strictness it should refer to the former only. For
as referring to the former it indicates a relation of the manifold _to
the object_, as being the parts of the object, and as referring to the
latter it indicates a relation of the manifold _to us_, as being
apprehended by us as the parts of the object. But two relations which,
though they are of one and the same thing, are nevertheless relations
of it to two different things, should not be referred to by the same
phrase. Moreover, since the relatedness is referred to as relatedness
to an object, the phrase properly indicates the relation of the
manifold to an object, and not to us as apprehending it. Again, in the
second place, Kant cannot successfully maintain that the phrase is
primarily a loose expression for our consciousness of the manifold as
related to an object, and that since this implies a process of
synthesis, the phrase may fairly include in its meaning the thought of
the combination of the manifold by us into a whole. For although Kant
asserts--and with some plausibility--that we can only apprehend as
combined what we have ourselves combined, yet when we consider this
assertion seriously we see it to be in no sense true.

    [34] A. 109, Mah. 202.

    [35] B. 130, M. 80.

    [36] To say that 'combining', in the sense of making,
    _really_ presupposes consciousness of the nature of the whole
    produced, would be inconsistent with the previous assertion
    that even where the reality known is something made, the
    knowledge of it presupposes that the reality is already made.
    Strictly speaking, the activity of combining presupposes
    consciousness not of the whole which we _succeed_ in
    producing, but of the whole which we _want_ to produce.

    It may be noted that, from the point of view of the above
    argument, the activity of combining presupposes actual
    consciousness of the act of combination and of its principle,
    and does not imply merely the possibility of it. Kant, of
    course, does not hold this.

The general conclusion, therefore, to be drawn is that the process of
synthesis by which the manifold is said to become related to an object
is a process not of knowledge but of construction in the literal
sense, and that it leaves knowledge of the thing constructed still to
be effected. But if knowing is obviously different from making, why
should Kant have apparently felt no difficulty in resolving knowing
into making? Three reasons may be given.

In the first place, the very question, 'What does the process of
knowing consist in?' at least suggests that knowing can be resolved
into and stated in terms of something else. In this respect it
resembles the modern phrase '_theory_ of knowledge'. Moreover, since
it is plain that in knowing we are active, the question is apt to
assume the form, 'What do we _do_ when we know or think?' and since
one of the commonest forms of doing something is to perform a physical
operation on physical things, whereby we effect a recombination of
them on some plan, it is natural to try to resolve knowing into this
kind of doing, i. e. into making in a wide sense of the word.

In the second place, Kant never relaxed his hold upon the thing in
itself. Consequently, there always remained for him a reality which
existed in itself and was not made by us. This was to him the
fundamental reality, and the proper object of knowledge, although
unfortunately inaccessible to _our_ faculties of knowing. Hence to
Kant it did not seriously matter that an inferior reality, viz. the
phenomenal world, was made by us in the process of knowing.

In the third place, it is difficult, if not impossible, to read the
_Deduction_ without realizing that Kant failed to distinguish knowing
from that formation of mental imagery which accompanies knowing. The
process of synthesis, if it is even to seem to constitute knowledge
and to involve the validity of the categories, must really be a
process by which we construct, and recognize our construction of,
an individual reality in nature out of certain physical data.
Nevertheless, it is plain that what Kant normally describes as the
process of synthesis is really the process by which we construct an
imaginary picture of a reality in nature not present to perception,
i. e. by which we imagine to ourselves what it would look like if we
were present to perceive it. This is implied by his continued use of
the terms 'reproduction' and 'imagination' in describing the
synthesis. To be aware of an object of past perception, it is
necessary, according to him, that the object should be _re_produced.
It is thereby implied that the object of our present awareness is not
the object of past perception, but a mental image which copies or
reproduces it. The same implication is conveyed by his use of the term
'imagination' to describe the faculty by which the synthesis is
effected; for 'imagination' normally means the power of making a
mental image of something not present to perception, and this
interpretation is confirmed by Kant's own description of the
imagination as 'the faculty of representing an object even without
its presence in perception'.[37] Further, that Kant really fails
to distinguish the construction of mental imagery from literal
construction is shown by the fact that, although he insists that
the formation of an image and reproduction are both necessary for
knowledge, he does not consistently adhere to this. For his general
view is that the elements combined and recognized as combined are the
original data of sense, and not reproductions of them which together
form an image, and his instances imply that the elements retained in
thought, i. e. the elements of which we are aware subsequently to
perception, are the elements originally perceived, e. g. the parts of
a line or the units counted.[38] Moreover, in one passage Kant
definitely describes certain _objects_ of _perception_ taken together
as an _image_ of that 'kind' of which, when taken together, they are
an instance. "If I place five points one after another, . . . . . this
is an image of the number five."[39] Now, if it be granted that Kant
has in mind normally the process of imagining, we can see why he found
no difficulty in the thought of knowledge as construction. For while
we cannot reasonably speak of making _an object of knowledge_, we can
reasonably speak of making _a mental image_ through our own activity,
and also of making it in accordance with the categories and the
empirical laws which presuppose them. Moreover, the ease with which it
is possible to take the imagining which accompanies knowing for
knowing[40]--the image formed being taken to be the object known and
the forming it being taken to be the knowing it--renders it easy to
transfer the thought of construction to the knowledge itself. The only
defect, however, under which the view labours is the important one
that, whatever be the extent to which imagination must accompany
knowledge, it is distinct from knowledge. To realize the difference we
have only to notice that the process by which we present to ourselves
in imagination realities not present to perception presupposes, and is
throughout guided by, the knowledge of them. It should be noted,
however, that, although the process of which Kant is normally thinking
is doubtless that of constructing mental imagery, his real view must
be that knowledge consists in constructing a world out of the data of
sense, or, more accurately, as his instances show, out of the objects
of isolated perceptions, e. g. parts of a line or units to be counted.
Otherwise the final act of recognition would be an apprehension not of
the world of nature, but of an image of it.

    [37] B. 152, M. 93; cf. also Mah. 211, A. 120.

    [38] Cf. A. 102-3, Mah. 197-8. The fact is that the appeal to
    reproduction is a useless device intended by Kant--and by
    'empirical psychologists'--to get round the difficulty of
    allowing that in the apprehension (in memory or otherwise) of
    a reality not present to perception, we are really aware of
    the reality. The difficulty is in reality due to a
    sensationalistic standpoint, avowed or unavowed, and the
    device is useless, because the assumption has in the end to
    be made, covertly or otherwise, that we are really aware of
    the reality in question.

    [39] B. 179, M. 109. Cf. the whole passage B. 176-81, M.
    107-10 (part quoted pp. 249-51), and p. 251.

    [40] Cf. Locke and Hume.

'This criticism,' it may be said, 'is too sweeping. It may be true
that the process which Kant describes is really making in the literal
sense and not knowing, but Kant's mistake may have been merely that of
thinking of the wrong kind of synthesis. For both ordinary language
and that of philosophical discussion imply that synthesis plays some
part in knowledge. Thus we find in ordinary language the phrases
'_putting_ 2 and 2 _together_' and '2 and 2 _make_ 4'. Even in
philosophical discussions we find it said that a complex conception,
e. g. gold, is a _synthesis_ of simple conceptions, e. g. yellowness,
weight, &c.; that in judgement we _relate_ or _refer_ the predicate to
the subject; and that in inference we _construct_ reality, though only
mentally or ideally. Further, in any case it is by thinking or knowing
that the world comes to be _for us_; the more we think, the more of
reality there is for us. Hence at least the world _for us_ or _our_
world is due to our activity of knowing, and so is in some sense made
by us, i. e. by our relating activity.'

This position, however, seems in reality to be based on a simple but
illegitimate transition, viz. the transition to the assertion that in
knowing we relate, or combine, or construct from the assertion that in
knowing we recognize as related, or combined, or constructed--the last
two terms being retained to preserve the parallelism.[41] While the
latter assertion may be said to be true, although the terms 'combined'
and 'constructed' should be rejected as misleading, the former
assertion must be admitted to be wholly false, i. e. true in no sense
whatever. Moreover, the considerations adduced in favour of the
position should, it seems, be met by a flat denial of their truth or,
if not, of their relevance. For when it is said that _our_ world, or
the world _for us_, is due to our activity of thinking, and so is in
some sense _made_ by us, all that should be meant is that our
_apprehending_ the world as whatever we apprehend it to be
_presupposes_ activity on our part. But since the activity is after
all only the activity itself of apprehending or knowing, this
assertion is only a way of saying that apprehending or knowing is not
a condition of mind which can be produced in us _ab extra_, but is
something which we have to do for ourselves. Nothing is implied to be
made. If anything is to be said to be made, it must be not our world
but our activity of apprehending the world; but even we and our
activity of apprehending the world are not related as maker and thing
made. Again, to speak of a complex conception, e. g. gold, and to say
that it involves a synthesis of simple conceptions by the mind is mere
'conceptualism'. If, as we ought to do, we replace the term
'conception' by 'universal', and speak of gold as a synthesis of
universals, any suggestion that the mind performs the synthesis will
vanish, for a 'synthesis of universals' will mean simply a connexion
of universals. All that is mental is our apprehension of their
connexion. Again, in judgement we cannot be said to _relate_ predicate
to subject. Such an assertion would mean either that we relate a
conception to a conception, or a conception to a reality[42], or a
reality to a reality; and, on any of these interpretations, it is
plainly false. To retain the language of 'relation' or of
'combination' at all, we must say that in judgement we recognize real
elements as related or combined. Again, when we infer, we do not
construct, ideally or otherwise. 'Ideal construction'[43] is a
contradiction in terms, unless it refers solely to mental imagining,
in which case it is not inference. Construction which is not 'ideal',
i. e. literal construction, plainly cannot constitute the nature of
inference; for inference would cease to be inference, if by it we
made, and did not apprehend, a necessity of connexion. Again, the
phrase '2 and 2 _make_ 4' does not justify the view that in some sense
we 'make' reality. It of course suggests that 2 and 2 are not 4 until
they are added, i. e. that the addition makes them 4.[44] But the
language is only appropriate when we are literally making a group of 4
by physically placing 2 pairs of bodies in one group. Where we are
counting, we should say merely that 2 and 2 _are_ 4. Lastly, it must
be allowed that the use of the phrase 'putting two and two together',
to describe an inference from facts not quite obviously connected, is
loose and inexact. If we meet a dog with a blood-stained mouth and
shortly afterwards see a dead fowl, we may be said to put two and two
together and to conclude thereby that the dog killed the fowl. But,
strictly speaking, in drawing the inference we do not put anything
together. We certainly do not put together the facts that the mouth of
the dog is blood-stained and that the fowl has just been killed. We do
not even put the premises together, i. e. our apprehensions of these
facts. What takes place should be described by saying simply that
seeing that the fowl is killed, we also remember that the dog's mouth
was stained, and then apprehend a connexion between these facts.

    [41] Cf. Caird, i. 394, where Dr. Caird speaks of 'the
    distinction of the activity of thought from the matter which
    it _combines or recognizes as combined_ in the idea of an
    object'. (The italics are mine.) The context seems to
    indicate that the phrase is meant to express the truth, and
    not merely Kant's view.

    [42] Cf. the account of judgement in Mr. Bradley's _Logic_.


    [43] Cf. the account of inference in Mr. Bradley's _Logic_.

    [44] Cf. Bradley, _Logic_, pp. 370 and 506.

The fact seems to be that the thought of synthesis in no way helps to
elucidate the nature of knowing, and that the mistake in principle
which underlies Kant's view lies in the implicit supposition that it
is possible to elucidate the nature of knowledge by means of something
other than itself. Knowledge is _sui generis_ and therefore a 'theory'
of it is impossible. Knowledge is simply knowledge, and any attempt to
state it in terms of something else must end in describing something
which is not knowledge.[45]

    [45] Cf. p. 124.




CHAPTER X

THE SCHEMATISM OF THE CATEGORIES


As has already been pointed out,[1] the _Analytic_ is divided into
two parts, the _Analytic of Conceptions_, of which the aim is to
discover and vindicate the validity of the categories, and the
_Analytic of Principles_, of which the aim is to determine the use
of the categories in judgement. The latter part, which has now to be
considered, is subdivided into two. It has, according to Kant, firstly
to determine the sensuous conditions under which the categories are
used, and secondly to discover the _a priori_ principles involved in
the categories, as exercised under these sensuous conditions, such,
for instance, as the law that all changes take place according to
the law of cause and effect. The first problem is dealt with in
the chapter on the 'schematism of the pure conceptions of the
understanding', the second in the chapter on the 'system of all
principles of the pure understanding'.

    [1] p. 141.

We naturally feel a preliminary difficulty with respect to the
existence of this second part of the _Analytic_ at all. It seems clear
that if the first part is successful, the second must be unnecessary.
For if Kant is in a position to lay down that the categories must
apply to objects, no special conditions of their application need be
subsequently determined. If, for instance, it can be laid down that
the category of quantity must apply to objects, it is implied either
that there are no special conditions of its application, or that they
have already been discovered and shown to exist. Again, to assert the
applicability of the categories is really to assert the existence of
principles, and in fact of just those principles which it is the aim
of the _System of Principles_ to prove. Thus to assert the
applicability of the categories of quantity and of cause and effect is
to assert respectively the principles that all objects of perception
are extensive quantities, and that all changes take place according
to the law of cause and effect. The _Deduction of the Categories_
therefore, if successful, must have already proved the principles
now to be vindicated; and it is a matter for legitimate surprise
that we find Kant in the _System of Principles_ giving proofs of
these principles which make no appeal to the _Deduction of the
Categories_.[2] On the other hand, for the existence of the account of
the schematism of the categories Kant has a better show of reason. For
the conceptions derived in the _Metaphysical Deduction_ from the
nature of formal judgement are in themselves too abstract to be the
conceptions which are to be shown applicable to the sensible world,
since all the latter involve the thought of time. Thus, the conception
of cause and effect derived from the nature of the hypothetical
judgement includes no thought of time, while the conception of which
he wishes to show the validity is that of necessary succession in
time. Hence the conceptions discovered by analysis of formal judgement
have in some way to be rendered more concrete in respect of time. The
account of the schematism, therefore, is an attempt to get out of the
false position reached by appealing to Formal Logic for the list of
categories. Nevertheless, the mention of a sensuous condition under
which alone the categories can be employed[3] should have suggested to
Kant that the transcendental deduction was defective, and, in fact, in
the second version of the transcendental deduction two paragraphs[4]
are inserted which take account of this sensuous condition.

    [2] The cause of Kant's procedure is, of course, to be found
    in the unreal way in which he isolates conception from
    judgement.

    [3] B. 175, M. 106.

    [4] B. §§ 24 and 26, M. §§ 20 and 22.

The beginning of Kant's account of schematism may be summarized thus:
'Whenever we subsume an individual object of a certain kind, e. g.
a plate, under a conception, e. g. a circle, the object and the
conception must be homogeneous, that is to say, the individual must
possess the characteristic which constitutes the conception, or, in
other words, must be an instance of it. Pure conceptions, however, and
empirical perceptions, i. e. objects of empirical perception, are
quite heterogeneous. We do not, for instance, perceive cases of cause
and effect. Hence the problem arises, 'How is it possible to subsume
objects of empirical perception under pure conceptions?' The
possibility of this subsumption presupposes a _tertium quid_, which is
homogeneous both with the object of empirical perception and with the
conception, and so makes the subsumption mediately possible. This
_tertium quid_ must be, on the one side, intellectual and, on the
other side, sensuous. It is to be found in a 'transcendental
determination of time', i. e. a conception involving time and involved
in experience. For in the first place this is on the one side
intellectual and on the other sensuous, and in the second place it
is so far homogeneous with the category which constitutes its unity
that it is universal and rests on an _a priori_ rule, and so far
homogeneous with the phenomenon that all phenomena are in time[5].
Such transcendental determinations of time are the schemata of the
pure conceptions of the understanding.' Kant continues as follows:

    [5] It may be noted that the argument here really fails. For
    though phenomena as involving temporal relations, might
    possibly be said to be instances of a transcendental
    determination of time, the fact that the latter agrees with
    the corresponding category by being universal and _a priori_
    does not constitute it homogeneous with the category, in the
    sense required for subsumption, viz. that it is an instance
    of or a species of the category.

"The schema is in itself always a mere product of the imagination.
But since the synthesis of the imagination has for its aim no single
perception, but merely unity in the determination of the sensibility,
the schema should be distinguished from the image. Thus, if I place
five points one after another, . . . . . this is an image of the
number five. On the other hand, if I only just think a number in
general--no matter what it may be, five or a hundred--this thinking
is rather the representation of a method of representing in an image
a group (e. g. a thousand), in conformity with a certain conception,
than the image itself, an image which, in the instance given, I should
find difficulty in surveying and comparing with the conception. Now
this representation of a general procedure of the imagination to
supply its image to a conception, I call the schema of this
conception."

"The fact is that it is not images of objects, but schemata, which lie
at the foundation of our pure sensuous conceptions. No image could
ever be adequate to our conception of a triangle in general. For it
would not attain the generality of the conception which makes it valid
for all triangles, whether right-angled, acute-angled, &c., but would
always be limited to one part only of this sphere. The schema of the
triangle can exist nowhere else than in thought, and signifies a rule
of the synthesis of the imagination in regard to pure figures in
space. An object of experience or an image of it always falls short of
the empirical conception to a far greater degree than does the schema;
the empirical conception always relates immediately to the schema of
the imagination as a rule for the determination of our perception in
conformity with a certain general conception. The conception of 'dog'
signifies a rule according to which my imagination can draw the
general outline of the figure of a four-footed animal, without being
limited to any particular single form which experience presents to me,
or indeed to any possible image that I can represent to myself _in
concreto_. This schematism of our understanding in regard to phenomena
and their mere form is an art hidden in the depths of the human soul,
whose true modes of action we are not likely ever to discover from
Nature and unveil. Thus much only can we say: the _image_ is a product
of the empirical faculty of the productive imagination, while the
_schema_ of sensuous conceptions (such as of figures in space) is a
product and, as it were, a monogram of the pure _a priori_
imagination, through which, and according to which, images first
become possible, though the images must be connected with the
conception only by means of the schema which they express, and are in
themselves not fully adequate to it. On the other hand, the schema of
a pure conception of the understanding is something which cannot be
brought to an image; on the contrary, it is only the pure synthesis in
accordance with a rule of unity according to conceptions in general, a
rule of unity which the category expresses, and it is a transcendental
product of the imagination which concerns the determination of the
inner sense in general according to conditions of its form (time)
with reference to all representations, so far as these are to be
connected _a priori_ in one conception according to the unity of
apperception."[6]

    [6] B. 179-81, M. 109-10.

Now, in order to determine whether schemata can constitute the desired
link between the pure conceptions or categories and the manifold of
sense, it is necessary to follow closely this account of a schema.
Kant unquestionably in this passage treats as a mental image related
to a conception what really is, and what on his own theory ought to
have been, an individual object related to a conception, i. e. an
instance of it. In other words, he takes a mental image of an
individual for the individual itself.[7] On the one hand, he treats a
schema of a conception throughout as the thought of a procedure of the
imagination to present to the conception its _image_, and he opposes
schemata not to objects but to _images_; on the other hand, his
problem concerns subsumption under a conception, and what is subsumed
must be an instance of the conception, i. e. an individual object of
the kind in question.[8] Again, in asserting that if I place five
points one after another, . . . . . this is an image of the number
five, he is actually saying that an individual group of five points is
an image of a group of five in general.[9] Further, if the process of
schematizing is to enter--as it must--into knowledge of the phenomenal
world, what Kant here speaks of as the images related to a conception
must be taken to be individual instances of the conception, whatever
his language may be. For, in order to enter into knowledge, the
process referred to must be that by which _objects of experience_ are
constructed. Hence the passage should be interpreted as if throughout
there had been written for 'image' 'individual instance' or more
simply 'instance'. Again, the process of schematizing, although
_introduced_ simply as a process by which an individual is to be
subsumed indirectly under a conception, is assumed in the passage
quoted to be a process of _synthesis_. Hence we may say that the
process of schematizing is a process by which we combine the manifold
of perception into an individual whole in accordance with a
conception, and that the schema of a conception is the thought of the
rule of procedure on our part by which we combine the manifold in
accordance with the conception, and so bring the manifold under the
conception. Thus the schema of the conception of 100 is the thought of
a process of synthesis by which we combine say 10 groups of 10 units
into 100, and the schematizing of the conception of 100 is the process
by which we do so. Here it is essential to notice three points. In the
first place, the schema is a conception which relates not to the
reality apprehended but to us. It is the thought of a rule of
procedure on our part by which an instance of a conception is
constructed, and not the thought of a characteristic of the reality
constructed. For instance, the thought of a rule by which we can
combine points to make 100 is a thought which concerns us and not the
points; it is only the conception corresponding to this schema, viz.
the thought of 100, which concerns the points. In the second place,
although the thought of time is involved in the schema, the succession
in question lies not in the object, but in our act of construction
or apprehension. In the third place, the schema presupposes the
corresponding conception and the process of schematizing directly
brings the manifold of perception under the conception. Thus the
thought of combining 10 groups of 10 units to make 100 presupposes the
thought of 100, and the process of combination brings the units under
the conception of 100.

    [7] Cf. pp. 240-1. The mistake is, of course, facilitated by
    the fact that 'objects in nature', being for Kant only
    'appearances', resemble mental images more closely than they
    do as usually conceived.

    [8] Cf. B. 176, M. 107. That individuals are really referred
    to is also implied in the assertion that 'the synthesis of
    imagination has for its aim no single _perception_, but
    merely unity in the determination of sensibility'. (The
    italics are mine.)

    [9] Two sentences treat individual objects and images as
    if they might be mentioned indifferently. "An object of
    experience or an image of it always falls short of the
    empirical conception to a far greater degree than does
    the schema." "The conception of a 'dog' signifies a rule
    according to which my imagination can draw the general
    outline of the figure of a four-footed animal without being
    limited to any single particular form which experience
    presents to me, or indeed to any possible image that I can
    represent to myself _in concreto_."

If, however, we go on to ask what is required of schemata and of the
process of schematizing, if they are to enable the manifold to be
subsumed under the categories, we see that each of these three
characteristics makes it impossible for them to fulfil this purpose.
For firstly, an individual manifold A has to be brought under a
category B. Since _ex hypothesi_ this cannot be effected directly,
there is needed a mediating conception C. C, therefore, it would seem,
must be at once a species of B and a conception of which A is an
instance. In any case C must be a conception relating to the reality
to be known, and not to any process of knowing on our part, and,
again, it must be more concrete than B. This is borne out by the list
of the schemata of the categories. But, although a schema may be said
to be more concrete than the corresponding conception, in that it
presupposes the conception, it neither is nor involves a more
concrete conception of an _object_ and in fact, as has been pointed
out, relates not to the reality to be known but to the process on our
part by which we construct or apprehend it.[10] In the second place,
the time in respect of which the category B has to be made more
concrete must relate to the object, and not to the successive process
by which we apprehend it, whereas the time involved in a schema
concerns the latter and not the former. In the third place, from the
point of view of the categories, the process of schematizing should be
a process whereby we combine the manifold into a whole A in accordance
with the conception C, and thereby render _possible_ the subsumption
of A under the category B. If it be a process which actually subsumes
the manifold under B, it will _actually_ perform that, the very
impossibility of which has made it necessary to postulate such a
process at all. For, according to Kant, it is just the fact that the
manifold cannot be subsumed directly under the categories that renders
schematism necessary. Yet, on Kant's general account of a schema, the
schematizing must actually bring a manifold under the corresponding
conception. If we present to ourselves an individual triangle by
successively joining three lines according to the conception of a
triangle, i. e. so that they enclose a space, we are directly bringing
the manifold, i. e. the lines, under the conception of a triangle.
Again, if we present to ourselves an instance of a group of 100 by
combining 10 groups of 10 units of any kind, we are directly bringing
the units under the conception of 100. If this consideration be
applied to the schematism of a category, we see that the process said
to be necessary because a certain other process is impossible is the
very process said to be impossible.

    [10] It may be objected that, from Kant's point of view, the
    thought of a rule of construction, and the thought of the
    principle of the whole to be constructed, are the same thing
    from different points of view. But if this be insisted on,
    the schema and its corresponding conception become the same
    thing regarded from different points of view; consequently
    the schema will not be a more concrete conception of an
    object than the corresponding conception, but it will be the
    conception itself.

If, therefore, Kant succeeds in finding schemata of the categories in
detail in the sense in which they are required for the solution of his
problem, i. e. in the sense of more concrete conceptions involving the
thought of time and relating to objects, we should expect either that
he ignores his general account of a schema, or that if he appeals to
it, the appeal is irrelevant. This we find to be the case. His account
of the first two transcendental schemata makes a wholly irrelevant
appeal to the temporal process of synthesis on our part, while his
account of the remaining schemata makes no attempt to appeal to it at
all.

"The pure _schema_ of _quantity_, as a conception of the
understanding, is _number_, a representation which comprises the
successive addition of one to one (homogeneous elements). Accordingly,
number is nothing else than the unity of the synthesis of the manifold
of a homogeneous perception in general, in that I generate time itself
in the apprehension of the perception."[11]

    [11] B. 182, M. 110.

It is clear that this passage, whatever its precise interpretation may
be,[12] involves a confusion between the thought of counting and that
of number. The thought of number relates to objects of apprehension
and does not involve the thought of time. The thought of counting,
which presupposes the thought of number, relates to our apprehension
of objects and involves the thought of time; it is the thought of a
successive process on our part by which we count the number of units
contained in what we already know to consist of units.[13] Now we must
assume that the schema of quantity is really what Kant says it is,
viz. number, or to express it more accurately, the thought of number,
and not the thought of counting, with which he wrongly identifies it.
For his main problem is to find conceptions which at once are more
concrete than the categories and, at the same time, like the
categories, relate to objects, and the thought of counting, though
more concrete than that of number, does not relate to objects. Three
consequences follow. In the first place, although the schema of
quantity, i. e. the thought of number, is more concrete than the
thought of quantity,[14] it is not, as it should be, more concrete in
respect of time; for the thought of number does not include the
thought of time. Secondly, the thought of time is only introduced into
the schema of quantity irrelevantly by reference to the temporal
process of _counting_, by which we come to apprehend the number of a
given group of units. Thirdly, the schema of quantity is only in
appearance connected with the nature of a schema in general, as Kant
describes it, by a false identification of the thought of number with
the thought of the process on our part by which we count groups of
units, i. e. numbers.

    [12] The drift of the passage would seem to be this: 'If we
    are to present to ourselves an instance of a quantity, we
    must successively combine similar units until they form a
    quantity. This process involves the thought of a successive
    process by which we add units according to the conception of
    a quantity. This thought is the thought of number, and since
    by it we present to ourselves an instance of a quantity, it
    is the schema of quantity.' But if this be its drift,
    considerations of sense demand that it should be rewritten,
    at least to the following extent: 'If we are to present to
    ourselves an instance of a _particular_ quantity [which will
    really be a particular number, for it must be regarded as
    discrete, (cf. B. 212, M. 128 fin., 129 init.)] e. g. three,
    we must successively combine units until they form _that_
    quantity. This process involves the thought of a successive
    process, by which we add units according to the conception of
    _that_ quantity. This thought is the thought of a particular
    number, and since by it we present to ourselves an instance
    of _that_ quantity, this thought is the schema of _that_
    quantity.' If this rewriting be admitted to be necessary, it
    must be allowed that Kant has confused (_a_) the thoughts of
    particular quantities and of particular numbers with those of
    quantity and of number in general respectively, (_b_) the
    thought of a particular quantity with that of a particular
    number (for the process referred to presupposes that the
    particular quantity taken is known to consist of a number of
    equal units) and (_c_) the thought of counting with that of
    number.

    [13] This statement is, of course, not meant as a definition
    of counting, but as a means of bringing out the distinction
    between a process of counting and a number.

    [14] For the thought of a number is the thought of a quantity
    of a special kind, viz. of a quantity made up of a number of
    similar units without remainder.

The account of the schema of reality, the second category, runs as
follows: "Reality is in the pure conception of the understanding that
which corresponds to a sensation in general, that therefore of which
the conception in itself indicates a being (in time), while negation
is that of which the conception indicates a not being (in time). Their
opposition, therefore, arises in the distinction between one and the
same time as filled or empty. Since time is only the form of
perception, consequently of objects as phenomena, that which in
objects corresponds to sensation is the transcendental matter of all
objects as things in themselves (thinghood, reality).[15] Now every
sensation has a degree or magnitude by which it can fill the same
time, i. e. the internal sense, in respect of the same representation
of an object, more or less, until it vanishes into nothing ( = 0 =
_negatio_). There is, therefore, a relation and connexion between
reality and negation, or rather a transition from the former to the
latter, which makes every reality representable as a _quantum_; and
the schema of a reality, as the quantity of something so far as it
fills time, is just this continuous and uniform generation of the
reality in time, as we descend in time from the sensation which has a
certain degree, down to the vanishing thereof, or gradually ascend
from negation to the magnitude thereof."[16]

    [15] It is difficult to see how Kant could meet the criticism
    that here, contrary to his intention, he is treating physical
    objects as things in themselves. Cf. p. 265.

    [16] B. 182-3, M. 110-11.

This passage, if it be taken in connexion with the account of the
anticipations of perception,[17] seems to have the following meaning:
'In thinking of something as a reality, we think of it as that which
corresponds to, i. e. produces, a sensation, and therefore as
something which, like the sensation, is in time; and just as every
sensation, which, as such, occupies time, has a certain degree of
intensity, so has the reality which produces it. Now to produce for
ourselves an instance of a reality in this sense, we must add units of
reality till a reality of the required degree is produced, and the
thought of this method on our part of constructing an individual
reality is the schema of reality.' But if this represents Kant's
meaning, the schema of reality relates only to our process of
apprehension, and therefore is not a conception which relates to
objects and is more concrete than the corresponding category in
respect of time. Moreover, it is matter for surprise that in the case
of this category Kant should have thought schematism necessary, for
time is actually included in his own statement of the category.

    [17] B. 207-18, M. 125-32.

The account of the schemata of the remaining categories need not be
considered. It merely _asserts_ that certain conceptions relating
to objects and involving the thought of time are the schemata
corresponding to the remaining categories, without any attempt to
connect them with the nature of a schema. Thus, the schema of
substance is asserted to be the _permanence_ of the real _in time_,
that of cause the _succession_ of the manifold, in so far as that
succession is subjected to a rule, that of interaction the
_coexistence_ of the determinations or accidents of one substance
with those of another according to a universal rule.[18] Again, the
schemata of possibility, of actuality and of necessity are said to be
respectively the accordance of the synthesis of representations with
the conditions of time in general, existence in a determined time, and
existence of an object in all time.

    [18] The italics are mine.

The main confusion pervading the chapter is of course that between
temporal relations which concern the process of apprehension and
temporal relations which concern the realities apprehended. Kant is
continually referring to the former as if they were the latter. The
cause of this confusion lies in Kant's reduction of physical realities
to representations. Since, according to him, these realities are only
our representations, all temporal relations are really relations of
our representations, and these relations have to be treated at one
time as relations of our apprehensions, and at another as relations of
the realities apprehended, as the context requires.




CHAPTER XI

THE MATHEMATICAL PRINCIPLES


As has been pointed out,[1] the aim of the second part of the
_Analytic of Principles_ is to determine the _a priori_ principles
involved in the use of the categories under the necessary sensuous
conditions. These principles Kant divides into four classes,
corresponding to the four groups of categories, and he calls
them respectively 'axioms of perception', 'anticipations of
sense-perception', 'analogies of experience', and 'postulates of
empirical thought'. The first two and the last two classes are grouped
together as 'mathematical' and 'dynamical' respectively, on the ground
that the former group concerns the perception of objects, i. e. their
nature apprehended in perception, while the latter group concerns
their existence, and that consequently, since assertions concerning
the existence of objects presuppose the realization of empirical
conditions which assertions concerning their nature do not, only the
former possesses an absolute necessity and an immediate evidence such
as is found in mathematics.[2]

    [1] p. 246.

    [2] The assertion that all perceptions (i. e. all objects of
    perception) are extensive quantities relates, according to
    Kant, to the nature of objects, while the assertion that an
    event must have a necessary antecedent affirms that such an
    antecedent must exist, but gives no clue to its specific
    nature. Compare "But the existence of phenomena cannot be
    known _a priori_, and although we could be led in this way to
    infer the fact of some existence, we should not know this
    existence determinately, i. e. we could not anticipate the
    respect in which the empirical perception of it differed from
    that of other existences". (B. 221, M. 134). Kant seems to
    think that the fact that the dynamical principles relate to
    the existence of objects is a sufficient justification of
    their name.

    It needs but little reflection to see that the distinctions
    which Kant draws between the mathematical and the dynamical
    principles must break down.

These two groups of principles are not, as their names might suggest,
principles within mathematics and physics, but presuppositions of
mathematics and physics respectively. Kant also claims appropriateness
for the special terms used of each minor group to indicate the kind of
principles in question, viz. 'axioms', 'anticipations', 'analogies',
'postulates'. But it may be noted as an indication of the
artificiality of the scheme that each of the first two groups contains
only one principle, although Kant refers to them in the plural as
axioms and anticipations respectively, and although the existence of
three categories corresponding to each group would suggest the
existence of three principles.

The axiom of perception is that 'All perceptions are extensive
quantities'. The proof of it runs thus:

"An extensive quantity I call that in which the representation of the
parts renders possible the representation of the whole (and therefore
necessarily precedes it). I cannot represent to myself any line,
however small it may be, without drawing it in thought, that is,
without generating from a point all its parts one after another, and
thereby first drawing this perception. Precisely the same is the case
with every, even the smallest, time.... Since the pure perception in
all phenomena is either time or space, every phenomenon as a
perception is an extensive quantity, because it can be known in
apprehension only by a successive synthesis (of part with part). All
phenomena, therefore, are already perceived as aggregates (groups of
previously given parts), which is not the case with quantities of
every kind, but only with those which are represented and apprehended
by us as _extensive_."[3]

    [3] B. 203-4, M. 123.

Kant opposes an extensive quantity to an intensive quantity or a
quantity which has a degree. "That quantity which is apprehended
only as unity and in which plurality can be represented only by
approximation to negation = 0, I call _intensive quantity_."[4] The
aspect of this ultimate distinction which underlies Kant's mode of
stating it is that only an extensive quantity is a whole, i. e.
something made up of parts. Thus a mile can be said to be made up
of two half-miles, but a velocity of one foot per second, though
comparable with a velocity of half a foot per second, cannot be said
to be made up of two such velocities; it is essentially one and
indivisible. Hence, from Kant's point of view, it follows that it is
only an extensive magnitude which can, and indeed must, be apprehended
through a successive synthesis of the parts. The proof of the axiom
seems to be simply this: 'All phenomena as objects of perception are
subject to the forms of perception, space and time. Space and time are
[homogeneous manifolds, and therefore] extensive quantities, only
to be apprehended by a successive synthesis of the parts. Hence
phenomena, or objects of experience, must also be extensive
quantities, to be similarly apprehended.' And Kant goes on to add that
it is for this reason that geometry and pure mathematics generally
apply to objects of experience.

    [4] B. 210, M. 127.

We need only draw attention to three points. Firstly, no justification
is given of the term 'axiom'. Secondly, the argument does not really
appeal to the doctrine of the categories, but only to the character
of space and time as forms of perception. Thirdly, it need not appeal
to space and time as forms of perception in the proper sense of ways
in which we apprehend objects, but only in the sense of ways in which
objects are related[5]; in other words, it need not appeal to Kant's
theory of knowledge. The conclusion follows simply from the nature of
objects as spatially and temporally related, whether they are
phenomena or not. It may be objected that Kant's thesis is that _all_
objects of perception are extensive quantities, and that unless space
and time are allowed to be ways in which _we must perceive_ objects,
we cannot say that all objects will be spatially and temporally
related, and so extensive quantities. But to this it may be replied
that it is only true that all objects of perception are extensive
quantities if the term 'object of perception' be restricted to parts
of the physical world, i. e. to just those realities which Kant is
thinking of as spatially and temporally related,[6] and that this
restriction is not justified, since a sensation or a pain which has
only intensive quantity is just as much entitled to be called an
object of perception.

    [5] Cf. pp. 37-9.

    [6] The context shows that Kant is thinking only of such
    temporal relations as belong to the physical world, and not
    of those which belong to us as apprehending it. Cf. p. 139.

The anticipation of sense-perception consists in the principle that
'In all phenomena, the real, which is an object of sensation, has
intensive magnitude, i. e. a degree'. The proof is stated thus:

"Apprehension merely by means of sensation fills only one moment
(that is, if I do not take into consideration the succession of many
sensations). Sensation, therefore, as that in the phenomenon the
apprehension of which is not a successive synthesis advancing from
parts to a complete representation, has no extensive quantity; the
lack of sensation in one and the same moment would represent it as
empty, consequently = 0. Now that which in the empirical perception
corresponds to sensation is reality (_realitas phaenomenon_); that
which corresponds to the lack of it is negation = 0. But every
sensation is capable of a diminution, so that it can decrease and thus
gradually vanish. Therefore, between reality in the phenomenon and
negation there exists a continuous connexion of many possible
intermediate sensations, the difference of which from each other is
always smaller than that between the given sensation and zero, or
complete negation. That is to say, the real in the phenomenon has
always a quantity, which, however, is not found in apprehension, since
apprehension takes place by means of mere sensation in one moment and
not by a successive synthesis of many sensations, and therefore does
not proceed from parts to the whole. Consequently, it has a quantity,
but not an extensive quantity."

"Now that quantity which is apprehended only as unity, and in which
plurality can be represented only by approximation to negation = 0,
I call an _intensive quantity_. Every reality, therefore, in a
phenomenon has intensive quantity, that is, a degree."[7]

    [7] B. 209-10, M. 127.

In other words, 'We can lay down _a priori_ that all sensations have a
certain degree of intensity, and that between a sensation of a given
intensity and the total absence of sensation there is possible an
infinite number of sensations varying in intensity from nothing to
that degree of intensity. Therefore the real, which corresponds to
sensation, can also be said _a priori_ to admit of an infinite variety
of degree.'

Though the principle established is of little intrinsic importance,
the account of it is noticeable for two reasons. In the first place,
although Kant clearly means by the 'real corresponding to sensation' a
body in space, and regards it as a phenomenon, it is impossible to see
how he can avoid the charge that he in fact treats it as a thing in
itself.[8] For the correspondence must consist in the fact that the
real causes or excites sensation in us, and therefore the real, i. e.
a body in space, is implied to be a thing in itself. In fact, Kant
himself speaks of considering the real in the phenomenon as the cause
of sensation,[9] and, in a passage added in the second edition, after
proving that sensation must have an intensive quantity, he says that,
corresponding to the intensive quantity of sensation, an intensive
quantity, i. e. _a degree of influence on sense_, must be attributed
to all objects of sense-perception.[10] The difficulty of consistently
maintaining that the real, which corresponds to sensation, is a
phenomenon is, of course, due to the impossibility of distinguishing
between reality and appearance within phenomena.[11]

    [8] Cf. p. 257 note.

    [9] B. 210, M. 128.

    [10] B. 208, M. 126. The italics are mine. Cf. from the same
    passage, "Phenomena contain, over and above perception, the
    materials for some object (through which is represented
    something existing in space and time), i. e. they contain the
    real of sensation as a merely subjective representation of
    which we can only become conscious that _the subject is
    affected_, and which we relate _to an object in general_."
    (The italics are mine.)

    [11] Cf. pp. 94-100.

In the second place, Kant expressly allows that in this anticipation
we succeed in discovering _a priori_ a characteristic of sensation,
although sensation constitutes that empirical element in phenomena,
which on Kant's general view cannot be apprehended _a priori_.

"Nevertheless, this anticipation of sense-perception must always be
somewhat surprising to an inquirer who is used to transcendental
reflection, and is thereby rendered cautious. It leads us to feel some
misgiving as to whether the understanding can anticipate such a
synthetic proposition as that respecting the degree of all that is
real in phenomena, and consequently respecting the possibility of the
internal distinction of sensation itself, if we abstract from its
empirical quality. There remains, therefore, a problem not unworthy of
solution, viz. 'How can the understanding pronounce synthetically and
_a priori_ upon phenomena in this respect, and thus anticipate
phenomena even in that which is specially and merely empirical, viz.
that which concerns sensations?'"[12] But although Kant recognizes
that the anticipation is surprising, he is not led to revise his
general theory, as being inconsistent with the existence of the
anticipation. He indeed makes an attempt[13] to deal with the
difficulty; but his solution consists not in showing that the
anticipation is consistent with his general theory--as he should have
done, if the theory was to be retained--but in showing that, in the
case of the degree of sensation, we do apprehend the nature of
sensation _a priori_.

    [12] B. 217, M. 131; cf. B. 209, M. 127.

    [13] B. 217-18, M. 132.

Strangely enough, Hume finds himself face to face with what is in
principle the same difficulty, and treats it in a not dissimilar way.
"There is, however, one contradictory phenomenon, which may prove,
that 'tis not absolutely impossible for ideas to go before their
correspondent impressions. I believe it will readily be allow'd, that
the several distinct ideas of colours, which enter by the eyes, or
those of sounds, which are convey'd by the hearing, are really
different from each other, tho' at the same time resembling. Now if
this be true of different colours, it must be no less so of the
different shades of the same colour, that each of them produces a
distinct idea, independent of the rest. For if this shou'd be deny'd,
'tis possible, by the continual gradation of shades, to run a colour
insensibly into what is most remote from it; and if you will not allow
any of the means to be different, you cannot without absurdity deny
the extremes to be the same. Suppose therefore a person to have
enjoyed his sight for thirty years, and to have become perfectly well
acquainted with colours of all kinds, excepting one particular shade
of blue, for instance, which it never has been his fortune to meet
with. Let all the different shades of that colour, except that single
one, be plac'd before him, descending gradually from the deepest to
the lightest; 'tis plain that he will perceive a blank, where that
shade is wanting, and will be sensible, that there is a greater
distance in that place betwixt the contiguous colours, than in any
other. Now I ask, whether 'tis possible for him, from his own
imagination, to supply this deficiency, and raise up to himself the
idea of that particular shade, tho' it had never been conveyed to him
by his senses? I believe there are few but will be of opinion that he
can; and this may serve as a proof, that the simple ideas are not
always derived from the correspondent impressions; tho' the instance
is so particular and singular, that 'tis scarce worth our observing,
and does not merit that for it alone we should alter our general
maxim."[14]

    [14] Hume, _Treatise_, Bk. I, Part 1, § 1.




CHAPTER XII

THE ANALOGIES OF EXPERIENCE


Each of the three categories of relation, i. e. those of substance and
accident, of cause and effect, and of interaction between agent and
patient involves, according to Kant, a special principle, and these
special principles he calls 'analogies of experience'. They are stated
thus:[1] (1) In all changes of phenomena the substance is permanent,
and its quantity in nature is neither increased nor diminished. (2)
All changes take place according to the law of the connexion of cause
and effect. (3) All substances, so far as they can be perceived in
space as coexistent, are in complete interaction. The justification of
the term _analogy_ of experience is as follows. In mathematics an
analogy is a formula which asserts the equality of two _quantitative_
relations, and is such that, if three of the terms are given, we can
discover the fourth, e. g. if we know that _a_ : _b_ = _c_ : _d_, and
that _a_ = 2, _b_ = 4, _c_ = 6 we can discover that _d_ = 12. But in
philosophy an analogy is the assertion of the equality of two
_qualitative_ relations and is such that, if three of the terms are
given, we can discover, not the fourth, but only the relation of the
third to the fourth, though at the same time we are furnished with a
clue whereby to search for the fourth in experience. In this
philosophical sense, the principles involved in the categories of
relation are analogies. For instance, the principles of causality can
be stated in the form 'Any known event _X_ is to _some other_ event
_Y_, whatever it be, as effect to cause'; so stated, it clearly
informs us not of the character of _Y_ but only of the fact that there
must be a _Y_, i. e. a necessary antecedent, though at the same time
this knowledge enables us to search in experience for the special
character of _Y_.

    [1] The formulation of them in the first edition is slightly
    different.

The principles to be established relate to the two kinds of temporal
relation apprehended in the world of nature, viz. coexistence and
succession. The _method_ of proof, which is to be gathered from the
proofs themselves rather than from Kant's general remarks[2] on the
subject, is the same in each case. Kant expressly rejects any proof
which is 'dogmatical' or 'from conceptions', e. g. any attempt to show
that the very conception of change presupposes the thought of an
identical subject of change.[3] The proof is transcendental in
character, i. e. it argues that the principle to be established is a
condition of the possibility of _apprehending_ the temporal relation
in question, e. g. that the existence of a permanent subject of change
is presupposed in any _apprehension_ of change. It assumes that we
become aware of sequences and coexistences in the world of nature by a
process which begins with a succession of mere perceptions, i. e.
perceptions which are so far not the perceptions of a sequence or of a
coexistence or indeed of anything;[4] and it seeks to show that this
process involves an appeal to one of the principles in question--the
particular principle involved depending on the temporal relation
apprehended--and consequently, that since we do apprehend this
temporal relation, which, as belonging to the world of nature, must be
distinct from any temporal relation of our perceptions, the principle
appealed to is valid.

    [2] B. 218-24, M. 132-6; and B. 262-5, M. 159-61.

    [3] B. 263-4, M. 160-1; B. 289, M. 174-5.

    [4] This assumption is of course analogous to the assumption
    which underlies the _Transcendental Deduction of the
    Categories_, that knowledge begins with the successive
    origination in us of isolated data of sense.

The proof of the first analogy is given somewhat differently in the
first edition, and in a passage added in the second. The earlier
version, which is a better expression of the attitude underlying
Kant's general remarks on the analogy, is as follows:

"Our _apprehension_ of the manifold of a phenomenon is always
successive, and is therefore always changing. By it alone, therefore,
we can never determine whether this manifold, as an object of
experience, is coexistent or successive, unless there lies at the base
of it something that exists _always_, that is, something _enduring_
and _permanent_, of which all succession and coexistence are nothing
but so many ways (_modi_ of time) in which the permanent exists. Only
in the permanent, then, are time relations possible (for simultaneity
and succession are the only relations in time); i. e. the permanent is
the _substratum_ of the empirical representation of time itself, in
which alone all time-determination is possible. Permanence expresses
in general time, as the persisting correlate of all existence of
phenomena, of all change, and of all concomitance.... Only through the
permanent does _existence_ in different parts of the successive series
of time gain a _quantity_ which we call _duration_. For, in mere
succession, existence is always vanishing and beginning, and never
has the least quantity. Without this permanent, then, no time
relation is possible. Now, time in itself cannot be perceived[5];
consequently this permanent in phenomena is the substratum of all
time-determination, and therefore also the condition of the
possibility of all synthetic unity of sense-perceptions, that is, of
experience, and in this permanent all existence and all change in time
can only be regarded as a mode of the existence of that which endures
and is permanent. Therefore in all phenomena the permanent is the
object itself, i. e. the substance (_phenomenon_); but all that
changes or can change belongs only to the way in which this substance
or substances exist, consequently to their determinations."[6]
"Accordingly since substance cannot change in existence, its quantity
in nature can neither be increased nor diminished."[7] The argument
becomes plainer if it be realized that in the interval between the two
editions, Kant came to think that the permanent in question was matter
or bodies in space.[8] "We find that in order to give something
_permanent_ in perception corresponding to the conception of
_substance_ (and thereby to exhibit the objective reality of this
conception), we need a perception _in space_ (of matter), because
space alone has permanent determinations, while time, and consequently
everything which is in the internal sense, is continually flowing."[9]

    [5] _Wahrgenommen._

    [6] A. 182-4 and B. 225-7, M. 137-8. This formulation of the
    conclusion is adapted only to the form in which the first
    analogy is stated in the first edition, viz. "All phenomena
    contain the permanent (_substance_) as the object itself and
    the changeable as its mere determination, i. e. as a way
    in which the object exists." Hence a sentence from the
    conclusion of the proof added in the second edition is quoted
    to elucidate Kant's meaning; its doctrine is as legitimate a
    conclusion of the argument given in the first edition as of
    that peculiar to the second.

    [7] B. 225, M. 137.

    [8] Cf. Caird, i. 541-2.

    [9] B. 291, M. 176 (in 2nd ed. only). Cf. B. 277 fin.-278
    init., M. 168 (in 2nd ed. only).

Kant's thought appears to be as follows: 'Our apprehension of the
manifold consists of a series of successive acts in which we apprehend
its elements one by one and in isolation. This apprehension,
therefore, does not enable us to determine that its elements are
temporally related either as successive or as coexistent.[10] In order
to determine this, we must apprehend the elements of the manifold as
related to something permanent. For a succession proper, i. e. a
change, is a succession of states or determinations of something
permanent or unchanging. A mere succession which is not a succession
of states of something which remains identical is an unconnected
series of endings and beginnings, and with respect to it, 'duration',
which has meaning with regard to changes, i. e. successions proper,
has no meaning at all. Similarly, coexistence is a coexistence of
states of two permanents. Hence, to apprehend elements of the manifold
as successive or coexistent, we must apprehend them in relation to a
permanent or permanents. Therefore, to apprehend a coexistence or a
succession, we must perceive something permanent. But this permanent
something cannot be time, for time cannot be perceived. It must
therefore be a permanent in phenomena; and this must be the object
itself or the substance of a phenomenon, i. e. the substratum of the
changes which it undergoes, or that of which the elements of the
manifold are states or modifications.[11] Consequently, there must be
a permanent substance of a phenomenon, and the quantity of substances
taken together must be constant.'

    [10] The account of the first analogy as a whole makes it
    necessary to think that Kant in the first two sentences of
    the proof quoted does not mean exactly what he says, what he
    says being due to a desire to secure conformity with his
    treatment of the second and third analogies. What he _says_
    suggests (1) that he is about to discuss the implications,
    not of the process by which we come to apprehend the manifold
    as temporally related in one of the two ways possible, i. e.
    either as successive or as coexistent, but of the process by
    which we decide whether the relation of the manifold which we
    already know to be temporal is that of succession or that of
    coexistence, and (2) that the necessity for this process is
    due to the fact that our _apprehension_ of the manifold is
    always successive. The context, however, refutes both
    suggestions, and in any case it is the special function of
    the processes which involve the second and third analogies to
    determine the relations of the manifold as that of succession
    and that of coexistence respectively.

    [11] Cf. B. 225, M. 137 (first half).

Now, if Kant's thought has been here represented fairly, it is open to
the following comments. In the first place, even if his position be
right in the main, Kant should not introduce the thought of the
_quantity_ of substance, and speak of the quantity as constant. For he
thereby implies that in a plurality of substances--if such a plurality
can in the end be admitted--there may be total extinction of, or
partial loss in, some, if only there be a corresponding compensation
in others; whereas such extinction and creation would be inconsistent
with the nature of a substance.[12] Even Kant himself speaks of having
established the impossibility of the origin and extinction of
substance.[13]

    [12] I owe this comment to Professor Cook Wilson.

    [13] B. 232-3, M. 141 fin.

In the second place, it is impossible to see how it can be legitimate
for Kant to speak of a permanent substratum of change at all.[14] For
phenomena or appearances neither are nor imply the substratum of which
Kant is thinking. They might be held to imply ourselves as the
identical substratum of which they are successive states, but this
view would be irrelevant to, if not inconsistent with, Kant's
doctrine. It is all very well to _say_ that the substratum is to be
found in matter, i. e. in bodies in space,[15] but the assertion is
incompatible with the phenomenal character of the world; for the
sensations or appearances produced in us by the thing in itself cannot
be successive states of bodies in space. In the third place, in spite
of Kant's protests against any proof which is 'dogmatical' or 'from
conceptions', such a proof really forms the basis of his thought. For
if the argument is to proceed not from the nature of change as such
but from the possibility of perceiving change, it must not take into
account any implications of the possibility of perceiving change which
rest upon implications of the nature of change as such. Yet this is
what the argument does. For the reason really given for the view that
the apprehension of change involves the apprehension of the manifold
as related to a permanent substratum is that a change, as such,
implies a permanent substratum. It is only because change is held to
imply a substratum that we are said to be able to apprehend a change
only in relation to a substratum. Moreover, shortly afterwards, Kant,
apparently without realizing what he is doing, actually uses what is,
on the very face of it, the dogmatic method, and in accordance with it
develops the implications of the perception of change. "Upon this
permanence is based the justification of the conception of _change_.
Coming into being and perishing are not changes of that which comes to
be or perishes. Change is but a mode of existence, which follows on
another mode of existence of the same object. Hence everything which
changes _endures_ and only its _condition changes_.... Change,
therefore, can be perceived only in substances, and absolute coming to
be or perishing, which does not concern merely a determination of the
permanent, cannot be a possible perception."[16] Surely the fact that
Kant is constrained in spite of himself to use the dogmatic method is
some indication that it is the right method. It is in reality
impossible to make any discoveries about change, or indeed about
anything, except by consideration of the nature of the thing itself;
no study of the conditions under which it can be apprehended can throw
any light upon its nature.[17] Lastly, although the supposition is not
so explicit as the corresponding supposition made in the case of the
other analogies, Kant's argument really assumes, and assumes wrongly,
the existence of a process by which, starting with the successive
apprehension of elements of the manifold in isolation, we come to
apprehend them as temporally related.

    [14] The term 'permanent' is retained to conform to Kant's
    language. Strictly speaking, only a state of that which
    changes can be said to persist or to be permanent; for the
    substratum of change is not susceptible of any temporal
    predicates. Cf. p. 306.

    [15] B. 291, M. 176.

    [16] B. 230-1, M. 176.

    [17] Cf. pp. 300-1.

The deduction of the second and third analogies argues that the
principles of causality and reciprocal action are involved
respectively in the processes by which we become aware of successions
and of coexistences in the world of nature. From this point of view it
would seem that the first analogy is a presupposition of the others,
and that the process which involves the first is presupposed by the
process which involves the others. It would seem that it is only upon
the conclusion of a process by which, beginning with the successive
apprehension of elements of the manifold in isolation, we come to
apprehend them as _either_ successive or coexistent elements in the
world of nature, that there can arise a process by which we come to
decide _whether_ the specific relation is that of succession or of
coexistence. For if the latter process can take place independently of
the former, i. e. if it can start from the successive apprehension of
the manifold, the former process will be unnecessary, and in that
case the vindication of the first analogy will be invalid. It is
necessary, however, to distinguish between Kant's nominal and his
actual procedure. Though he nominally regards the first analogy as the
presupposition of the others,[18] he really does not. For he does not
in fact treat the process which involves the validity of the first
analogy as an antecedent condition of the processes which involve the
validity of the others. On the contrary, the latter processes begin
_ab initio_ with the mere successive apprehension of the manifold,
i. e. they begin at a stage where we are not aware of any relation in
the physical world at all; and Kant, in his account of them, nowhere
urges that they involve the first analogy.[19]

    [18] Cf. B. 229, M. 140; B. 232-3, M. 141-2; and Caird, i.
    545 and ff.

    [19] This is not disproved by B. 247-51, M. 150-2, which
    involves a different conception of cause and effect.

Moreover, just because Kant does not face the difficulties involved in
the thought of a process which begins in this way until he comes to
vindicate causality, it is only when we come to this vindication that
we realize the real nature of his deduction of the analogies, and, in
particular, of that of the first.

Kant, prompted no doubt by his desire to answer Hume, treats the
principle of causality very fully. The length of the discussion,
however, is due not so much to the complication of the argument as to
Kant's desire to make his meaning unmistakable; his account consists
mainly in a repetition of what is substantially the same argument no
less than five times. Hence it will suffice to consider those passages
which best express Kant's meaning. At the same time, the prominence of
the principle of causality in Kant's theory, and in the history of
philosophy generally, and also the way in which Kant's treatment of
it reveals the true nature of his general position, makes it necessary
to consider these passages in some detail.

Hume had denied that we are justified in asserting any causal
connexion, i. e. any necessity of succession in the various events
which we perceive, but even this denial presupposed that we do
apprehend particular sequences in the world of nature, and therefore
that we succeed in distinguishing between a sequence of events in
nature and a mere sequence of perceptions, such as is also to be found
when we apprehend a coexistence of bodies in space. Kant urges, in
effect, that this denial renders it impossible to explain, as we
should be able to do, the possibility of making the distinction in
question, which even the denial itself presupposes that we make.
Holding, with Hume, that in all cases of perception what we are
directly aware of is a succession of perceptions, he contends that it
is necessary to explain how in certain cases we succeed in passing
from the knowledge of our successive perceptions to the knowledge of a
succession in what we perceive. How is it that we know, when, as we
say, we see a boat going down stream, that there is a succession in
what we perceive, and not merely a succession in our perception of it,
as is the case when, as we say, we see the parts of a house? Hume,
according to Kant, cannot answer this question; he has only the right
to say that in all cases we have a succession of perceptions; for in
reality an answer to the question will show that the acquisition of
this knowledge involves an appeal to the principle of causality.
Since, then, we do in fact, as even Hume implicitly allowed, succeed
in distinguishing between a succession in objects in nature and a
succession in our apprehension of them, the law of causality must be
true. "It is only under this presupposition (i. e. of causality) that
even the experience of an event is possible."[20]

    [20] B. 240, M. 146. For the general view, cf. Caird, i.
    556-61.

Kant begins[21] his proof as follows: "Our apprehension of the
manifold of a phenomenon is always successive. The representations of
the parts succeed one another. Whether they succeed one another in the
object also is a second point for reflection which is not contained in
the first."[22] But, before he can continue, the very nature of these
opening sentences compels him to consider a general problem which they
raise. The distinction referred to between a succession in our
apprehensions or representations and a succession in the object
implies an object distinct from the apprehensions or representations.
What, then, can be meant by such an object? For prima facie, if we
ignore the thing in itself as unknowable, there is no object; there
are only representations. But, in that case, what can be meant by a
succession in the object? Kant is therefore once more[23] forced to
consider the question 'What is meant by object of representations?'
although on this occasion with special reference to the meaning of a
succession in the object; and the vindication of causality is bound up
with the answer. The answer is stated thus:

    [21] The preceding paragraph is an addition of the second
    edition.

    [22] B. 234, M. 142.

    [23] Cf. A. 104-5, Mah. 198-9, and pp. 178-86 and 230-3.

"Now we may certainly give the name of object to everything, and even
to every representation, so far as we are conscious thereof; but what
this word may mean in the case of phenomena, not in so far as they (as
representations) are objects, but in so far as they only indicate an
object, is a question requiring deeper consideration. So far as they,
as representations only, are at the same time objects of
consciousness, they are not to be distinguished from apprehension,
i. e. reception into the synthesis of imagination, and we must
therefore say, 'The manifold of phenomena is always produced
successively in the mind'. If phenomena were things in themselves, no
man would be able to infer from the succession of the representations
of their manifold how this manifold is connected in the object. For
after all we have to do only with our representations; how things may
be in themselves, without regard to the representations through which
they affect us, is wholly outside the sphere of our knowledge. Now,
although phenomena are not things in themselves, and are nevertheless
the only thing which can be given to us as data for knowledge, it is
my business to show what kind of connexion in time belongs to the
manifold in phenomena themselves, while the representation of this
manifold in apprehension is always successive. Thus, for example, the
apprehension of the manifold in the phenomenon of a house which stands
before me is successive. Now arises the question, whether the manifold
of this house itself is in itself also successive, which of course no
one will grant. But, so soon as I raise my conceptions of an object to
the transcendental meaning thereof, the house is not a thing in
itself, but only a phenomenon, i. e. a representation, the
transcendental object of which is unknown. What, then, am I to
understand by the question, 'How may the manifold be connected in the
phenomenon itself (which is nevertheless nothing in itself)?' Here
that which lies in the successive apprehension is regarded as
representation, while the phenomenon which is given me, although it
is nothing more than a complex of these representations, is regarded
as the object thereof, with which my conception, drawn from the
representations of apprehension, is to agree. It is soon seen that,
since agreement of knowledge with the object is truth, we can ask here
only for the formal conditions of empirical truth, and that the
phenomenon, in opposition to the representations of apprehension, can
only be represented as the object of the same, distinct therefrom, if
it stands under a rule, which distinguishes it from every other
apprehension, and which renders necessary a mode of conjunction of the
manifold. That in the phenomenon which contains the condition of this
necessary rule of apprehension is the object."[24]

    [24] B. 234-6, M. 143-4. Cf. B. 242, M. 147.

This passage is only intelligible if we realize the _impasse_ into
which Kant has been led by his doctrine that objects, i. e. realities
in the physical world, are only representations or ideas. As has
already been pointed out,[25] an apprehension is essentially
inseparable from a reality of which it is the apprehension. In other
words, an apprehension is always the apprehension of a reality, and a
reality apprehended, i. e. an object of apprehension, cannot be stated
in terms of the apprehension of it. We never confuse an apprehension
and its object; nor do we take the temporal relations which belong to
the one for the temporal relations which belong to the other, for
these relations involve different terms which are never confused, viz.
apprehensions and the objects apprehended. Now Kant, by his doctrine
of the unknowability of the thing in itself, has really deprived
himself of an object of apprehension or, in his language, of an
object of representations. For it is the thing in itself which is,
properly speaking, the object of the representations of which he is
thinking, i. e. representations of a reality in nature; and yet the
thing in itself, being on his view inapprehensible, can never be for
him an object in the proper sense, i. e. a reality apprehended. Hence
he is only able to state the fact of knowledge in terms of mere
apprehensions, or ideas, or representations--the particular name is a
matter of indifference--and consequently his efforts to recover an
object of apprehension are fruitless. As a matter of fact, these
efforts only result in the assertion that the object of
representations consists in the representations themselves related in
a certain necessary way. But this view is open to two fatal
objections. In the first place, a complex of representations is just
not an object in the proper sense, i. e. a reality apprehended. It
essentially falls on the subject side of the distinction between an
apprehension and the reality apprehended. The _complexity_ of a
complex of representations in no way divests it of the character which
it has as a complex of _representations_. In the second place, on this
view the same terms have to enter at once into two incompatible
relations. Representations have to be related successively as our
representations or apprehensions--as in fact they are related--and, at
the same time, successively or otherwise, as the case may be, as parts
of the object apprehended, viz. a reality in nature. In other words,
the same terms have to enter into both a subjective and an objective
relation, i. e. both a relation concerning us, the knowing subjects,
and a relation concerning the object which we know.[26] "A phenomenon
in opposition to the representations of apprehension can only be
represented as the object of the same, distinct therefrom, if it
stands under a rule which distinguishes it from _every other_
apprehension, and renders necessary a mode of conjunction of the
manifold."[27] A representation, however, cannot be so related by a
rule to another representation, for the rule meant relates to
realities in nature, and, however much Kant may try to maintain the
contrary, two representations, not being realities in nature, cannot
be so related. Kant is in fact only driven to treat rules of nature as
relating to representations, because there is nothing else to which he
can regard them as relating. The result is that he is unable to
justify the very distinction, the implications of which it is his aim
to discover, and he is unable to do so for the very reason which would
have rendered Hume unable to justify it. Like Hume, he is committed to
a philosophical vocabulary which makes it meaningless to speak of
relations of objects at all in distinction from relations of
apprehensions. It has been said that for Kant the road to objectivity
lay through necessity.[28] But whatever Kant may have thought, in
point of fact there is no road to objectivity, and, in particular, no
road through necessity. No necessity in the relation between two
representations can render the relation objective, i. e. a relation
between objects. No doubt the successive acts in which we come to
apprehend the world are necessarily related; we certainly do not
suppose their order to be fortuitous. Nevertheless, their relations
are not in consequence a relation of realities apprehended.

    [25] pp. 133-4; cf. pp. 180 and 230-1.

    [26] Cf. p. 209, note 3, and p. 233.

    [27] The italics are mine.

    [28] Caird, i. 557.

Kant only renders his own view plausible by treating an apprehension
or representation as if it consisted in a sensation or an appearance.
A sensation or an appearance, so far from being the apprehension of
anything, is in fact a reality which can be apprehended, of the kind
called mental. Hence it can be treated as an object, i. e. something
apprehended or presented, though not really as an object in nature. On
the other hand, from the point of view of the thing in itself it can
be treated as only an apprehension, even though it is an unsuccessful
apprehension. Thus, for Kant, there is something which can with some
plausibility be treated as an object as well as an apprehension, and
therefore as capable of standing in both a subjective and an objective
relation to other realities of the same kind.[29]

    [29] Cf. pp. 137 and 231.

If we now turn to the passage under discussion, we find it easy to
vindicate the justice of the criticism that Kant, inconsistently with
the distinction which he desires to elucidate, treats the same thing
as at once the representation of an object and the object represented.
He is trying to give such an account of 'object of representations' as
will explain what is meant by a succession in an object in nature,
i. e. a phenomenon, in distinction from the succession in our
apprehension of it. In order to state this distinction at all, he has
to speak of what enters into the two successions as different. "It is
my business to show what sort of connexion in time belongs to the
_manifold_ in phenomena themselves, while the _representation_ of this
manifold in apprehension is always successive."[30] Here an element of
the manifold is distinguished from the representation of it. Yet Kant,
though he thus distinguishes them, repeatedly identifies them; in
other words, he identifies a representation with that of which it is a
representation, viz. an element in or part of the object itself. "_Our
apprehension_ of the manifold of the phenomenon is always successive.
_The representations_ of the parts succeed one another. Whether _they_
[i. e. _the representations_[31]] succeed one another _in the object_
also, is a second point for reflection.... So far as they [i. e.
phenomena], as representations only, are at the same time objects of
consciousness, they are not to be distinguished from apprehension,
i. e. reception into the synthesis of imagination, and we must
therefore say, _'The manifold of phenomena_ is always produced
successively in the mind'. If phenomena were things in themselves, no
man would be able to infer from the succession of the representations
how _this manifold_ is connected _in the object_.... The phenomenon,
in opposition to the representations of apprehension, can only be
represented as the object of the same, distinct therefrom, if it
stands under a rule, which distinguishes _it_ from every _other_
representation and which renders necessary a mode of conjunction of
the manifold."[32]

    [30] The italics are mine.

    [31] This is implied both by the use of 'also' and by the
    context.

    [32] The italics are mine.

Since Kant in introducing his vindication of causality thus identifies
elements in the object apprehended (i. e. the manifold of phenomena)
with the apprehensions of them, we approach the vindication itself
with the expectation that he will identify a causal rule, which
consists in a necessity in the succession of objects, viz. of events
in nature, with the necessity in the succession of our apprehensions
of them. This expectation turns out justified. The following passage
adequately expresses the vindication:

"Let us now proceed to our task. That something happens, i. e. that
something or some state comes to be which before was not, cannot be
empirically perceived, unless a phenomenon precedes, which does not
contain in itself this state; for a reality which follows upon an
empty time, and therefore a coming into existence preceded by no state
of things, can just as little be apprehended as empty time itself.
Every apprehension of an event is therefore a perception which follows
upon another perception. But because this is the case with all
synthesis of apprehension, as I have shown above[33] in the phenomenon
of a house, the apprehension of an event is thereby not yet
distinguished from other apprehensions. But I notice also, that if in
a phenomenon which contains an event, I call the preceding state of my
perception A, and the following state B, B can only follow A in
apprehension, while the perception A cannot follow B but can only
precede it. For example, I see a ship float down a stream. My
perception of its place lower down follows upon my perception of its
place higher up the course of the river, and it is impossible that in
the apprehension of this phenomenon the vessel should be perceived
first below and afterwards higher up the stream. Here, therefore, the
order in the sequence of perceptions in apprehension is determined,
and apprehension is bound to this order. In the former example of a
house, my perceptions in apprehension could begin at the roof and end
at the foundation, or begin below and end above; in the same way they
could apprehend the manifold of the empirical perception from left to
right, or from right to left. Accordingly, in the series of these
perceptions, there was no determined order, which necessitated my
beginning at a certain point, in order to combine the manifold
empirically. But this rule is always to be found in the perception of
that which happens, and it makes the order of the successive
perceptions (in the apprehension of this phenomenon) _necessary_."

    [33] B. 235-6, M. 143 (quoted p. 279).

"In the present case, therefore, I shall have to derive the
_subjective sequence_ of apprehension from the _objective sequence_ of
phenomena, for otherwise the former is wholly undetermined, and does
not distinguish one phenomenon from another. The former alone proves
nothing as to the connexion of the manifold in the object, for it is
wholly arbitrary. The latter, therefore [i. e. the objective sequence
of phenomena[34]], will consist in that order of the manifold of the
phenomenon, according to which the apprehension of the one (that which
happens) follows that of the other (that which precedes) _according to
a rule_. In this way alone can I be justified in saying of the
phenomenon itself, and not merely of my apprehension, that a sequence
is to be found therein, which is the same as to say that I cannot
arrange my apprehension otherwise than in just this sequence."

    [34] The sense is not affected if 'the latter' be understood
    to refer to the connexion of the manifold in the object.

"In conformity with such a rule, therefore, there must exist in that
which in general precedes an event the condition of a rule, according
to which this event follows always and necessarily, but I cannot
conversely go back from the event, and determine (by apprehension)
that which precedes it. For no phenomenon goes back from the
succeeding point of time to the preceding point, although it does
certainly relate to _some preceding point of time_; on the other hand,
the advance from a given time to the determinate succeeding time is
necessary. Therefore, because there certainly is something which
follows, I must relate it necessarily to something else in general,
which precedes, and upon which it follows in conformity with a rule,
that is necessarily, so that the event, as the conditioned, affords
certain indication of some condition, while this condition determines
the event."

"If we suppose that nothing precedes an event, upon which this event
must follow in conformity with a rule, all sequence of perception
would exist only in apprehension, i. e. would be merely subjective,
but it would not thereby be objectively determined which of the
perceptions must in fact be the preceding and which the succeeding
one. We should in this manner have only a play of representations,
which would not be related to any object, i. e. no phenomenon would be
distinguished through our perception in respect of time relations from
any other, because the succession in apprehension is always of the
same kind, and so there is nothing in the phenomenon to determine the
succession, so as to render a certain sequence objectively necessary.
I could therefore not say that in the phenomenon two states follow
each other, but only that one apprehension follows on another, a fact
which is merely _subjective_ and does not determine any object, and
cannot therefore be considered as knowledge of an object (not even in
the phenomenon)."

"If therefore we experience that something happens, we always thereby
presuppose that something precedes, on which it follows according to a
rule. For otherwise, I should not say of the object, that it follows,
because the mere sequence in my apprehension, if it is not determined
by a rule in relation to something preceding, does not justify the
assumption of a sequence in the object. It is therefore always in
reference to a rule, according to which phenomena are determined in
their sequence (i. e. as they happen) by the preceding state, that I
make my subjective synthesis (of apprehension) objective, and it is
solely upon this presupposition that even the experience of something
which happens is possible."[35]

    [35] B. 236-41, M. 144-6.

The meaning of the first paragraph is plain. Kant is saying that when
we reflect upon the process by which we come to apprehend the world of
nature, we can lay down two propositions. The first is that the
process is equally successive whether the object apprehended be a
succession in nature or a coexistence of bodies in space, so that the
knowledge that we have a succession of apprehensions would not by
itself enable us to decide whether the object of the apprehensions is
a sequence or not. The second proposition is that, nevertheless, there
is this difference between the succession of our apprehensions where
we apprehend a succession and where we apprehend a coexistence, that
in the former case, and in that only, the succession of our
apprehensions is irreversible or, in other words, is the expression of
a rule of order which makes it a necessary succession. So far we find
no mention of causality, i. e. of a necessity of succession in
objects, but only a necessity of succession in our apprehension of
them. So far, again, we find no contribution to the problem of
explaining how we distinguish between successive perceptions which are
the perceptions of an event and those which are not. For it is
reasonable to object that it is only possible to say that the order of
our perceptions is irreversible, if and because we already know that
what we have been perceiving is an event, and that therefore any
attempt to argue from the irreversibility of our perceptions to the
existence of a sequence in the object must involve a [Greek: hysteron
proteron]. And it is clear that, if irreversibility in our perceptions
were the only irreversibility to which appeal could be made, even Kant
would not have supposed that the apprehension of a succession was
reached through belief in an irreversibility.

The next paragraph, of which the interpretation is difficult, appears
to introduce a causal rule, i. e. an irreversibility in objects, by
identifying it with the irreversibility in our perceptions of which
Kant has been speaking. The first step to this identification is taken
by the assertion: "In the present case, therefore, I shall have to
derive the subjective sequence of perceptions from the objective
sequence of phenomena.... The latter will consist in the order of the
_manifold of the phenomenon_, according to which _the apprehension_ of
the one (that which happens) follows that of the other (that which
precedes) according to a rule."[36] Here Kant definitely implies that
an objective sequence, i. e. an order or sequence of the _manifold_ of
a phenomenon, consists in a sequence of _perceptions or apprehensions_
of which the order is necessary or according to a rule; in other
words, that a succession of perceptions in the special case where the
succession is necessary is a succession of events perceived.[37] This
implication enables us to understand the meaning of the assertion that
'we must therefore derive the subjective sequence of perceptions from
the objective sequence of phenomena', and to see its connexion with
the preceding paragraph. It means, 'in view of the fact that in all
apprehensions of a succession, and in them alone, the sequence of
perceptions is irreversible, we are justified in saying that a given
sequence of perceptions is the apprehension of a succession, if we
know that the sequence is irreversible; in that case we must be
apprehending a real succession, for an irreversible sequence of
perceptions _is_ a sequence of events perceived.' Having thus implied
that irreversibility of perceptions constitutes them events perceived,
he is naturally enough able to go on to speak of the irreversibility
of perceptions as if it were the same thing as an irreversibility of
events perceived, and thus to bring in a causal rule. "In this way
alone [i. e. only by deriving the subjective from the objective
sequence] can I be justified in saying of the phenomenon itself, and
not merely of my apprehension, that a sequence is to be found therein,
_which is the same as to say_ that I cannot _arrange_ my apprehension
otherwise than in just this sequence. In conformity with _such a
rule_, therefore, there must exist in that which in general precedes
_an event_ the condition of a rule, according to which _this event
follows always and necessarily_."[38] Here the use of the word
'arrange'[39] and the statement about the rule in the next sentence
imply that Kant has now come to think of the rule of succession as a
causal rule relating to the objective succession. Moreover, if any
doubt remains as to whether Kant really confuses the two
irreversibilities or necessities of succession, it is removed by the
last paragraph of the passage quoted. "If therefore we experience that
something happens, we always thereby presuppose that something
precedes on which _it_ follows according to a rule. For otherwise I
should not say of the object that _it_ follows; because the mere
succession of my apprehension, if _it_ is not determined by a rule in
relation to something preceding, does not justify the assumption of a
succession in the object. It is therefore always in reference to a
rule, according to which _phenomena_ are determined in their sequence
(i. e. as they happen) by the preceding state, that I make my
subjective sequence (of apprehension) objective."[40] The fact is
simply that Kant _must_ identify the two irreversibilities, because,
as has been pointed out, he has only one set of terms to be related as
irreversible, viz. the elements of the manifold, which have to be,
from one point of view, elements of an object and, from another,
representations or apprehensions of it.

    [36] The italics are mine. 'According to which' does not
    appear to indicate that the two orders referred to are
    different.

    [37] Cf. B. 242 fin., M. 147 fin.

    [38] The italics are mine

    [39] _Anstellen._

    [40] The italics are mine.

As soon, therefore, as the real nature of Kant's vindication of
causality has been laid bare, it is difficult to describe it as an
argument at all. He is anxious to show that in apprehending A B as a
real or objective succession we presuppose that they are elements in a
causal order of succession. Yet in support of his contention he points
only to the quite different fact that where we apprehend a succession
A B, we think of the _perception_ of A and the _perception_ of B as
elements in a necessary but subjective succession.

Before we attempt to consider the facts with which Kant is dealing, we
must refer to a feature in Kant's account to which no allusion has
been made. We should on the whole expect from the passage quoted that,
in the case where we regard two perceptions A B as necessarily
successive and therefore as constituting an objective succession, the
necessity of succession consists in the fact that A is the cause of B.
This, however, is apparently not Kant's view; on the contrary, he
seems to hold that, in thinking of A B as an objective succession, we
presuppose not that A causes B, but only that the state of affairs
which precedes B, and which therefore includes A, contains a cause of
B, the coexistence or identity of this cause with A rendering the
particular succession A B necessary. "Thus [if I perceive that
something happens] it arises that there comes to be an order among our
representations in which the present (so far as it has taken place)
points to some preceding state as a correlate, _though a still
undetermined correlate_,[41] of this event which is given, and this
correlate relates to the event by determining the event as its
consequence, and connects the event with itself necessarily in the
series of time."[42]

    [41] The italics are mine.

    [42] B. 244, M. 148. Cf. B. 243, M. 148 (first half) and B.
    239, M. 145 (second paragraph). The same implication is to
    be found in his formulation of the rule involved in the
    perception of an event, e. g. "In conformity with such a
    rule, there must exist in that which in general precedes an
    event, the condition of a rule, according to which this event
    follows always and necessarily." Here the condition of a rule
    is the necessary antecedent of the event, whatever it may be.

The fact is that Kant is in a difficulty which he feels obscurely
himself. He seems driven to this view for two reasons. If he were to
maintain that A was necessarily the cause of B, he would be
maintaining that all observed sequences are causal, i. e. that in them
the antecedent and consequent are always cause and effect, which is
palpably contrary to fact. Again, his aim is to show that we become
aware of a succession by presupposing the law of causality. This law,
however, is quite general, and only asserts that _something_ must
precede an event upon which it follows always and necessarily. Hence
by itself it palpably gives no means of determining whether this
something is A rather than anything else.[43] Therefore if he were
to maintain that the antecedent member of an apprehended objective
succession must be thought of as its cause, the analogy would
obviously provide no means of determining the antecedent member, and
therefore the succession itself, for the succession must be the
sequence of B upon some definite antecedent. On the other hand, the
view that the cause of B need not be A only incurs the same difficulty
in a rather less obvious form. For, even on this view, the argument
implies that in order to apprehend two individual perceptions A B as
an objective succession, we must know that A _must_ precede B, and the
presupposition that B implies a cause in the state of affairs
preceding B in no way enables us to say either that A coexists with
the cause, or that it is identical with it, and therefore that it must
precede B.

    [43] Cf. B. 165, M. 101, where Kant points out that the
    determination of particular laws of nature requires
    experience.

Nevertheless, it cannot be regarded as certain that Kant did not think
of A, the apprehended antecedent of B, as necessarily the cause of B,
for his language is both ambiguous and inconsistent. When he considers
the apprehension of a succession from the side of the successive
perceptions, he at least tends to think of A B as cause and
effect;[44] and it may well be that in discussing the problem from
the side of the law of causality, he means the cause of B to be A,
although the generality of the law compels him to refer to it as
_something_ upon which B follows according to a rule.

    [44] He definitely implies this, B. 234, M. 142.

Further, it should be noticed that to allow as Kant, in effect, does
elsewhere[45], that experience is needed to determine the cause of B is
really to concede that the apprehension of objective successions is
_prior to_, and _presupposed by_, any process which appeals to the
principle of causality; for if the principle of causality does not by
itself enable us to determine the cause of B, it cannot do more than
enable us to pick out the cause of B among events known to precede B
independently of the principle. Hence, from this point of view, there
can be no process such as Kant is trying to describe, and therefore
its precise nature is a matter of indifference.

    [45] Cf. B. 165, M. 101, where Kant points out that the
    determination of particular laws of nature requires
    experience.

We may now turn to the facts. There is, it seems, no such thing as a
process by which, beginning with the knowledge of successive
apprehensions or representations, of the object of which we are
unaware, we come to be aware of their object. Still less is there a
process--and it is really this which Kant is trying to describe--by
which, so beginning, we come to apprehend these successive
representations as objects, i. e. as parts of the physical world,
through the thought of them as necessarily related. We may take Kant's
instance of our apprehension of a boat going down stream. We do not
first apprehend two perceptions of which the object is undetermined
and then decide that their object is a succession rather than a
coexistence. Still less do we first apprehend two perceptions or
representations and then decide that they are related as successive
events in the physical world. From the beginning we apprehend a real
sequence, viz. the fact that the boat having left one place is
arriving at another; there is no process _to_ this apprehension. In
other words, from the beginning we are aware of real elements, viz. of
events in nature, and we are aware of them as really related, viz. as
successive in nature. This must be so. For if we begin with the
awareness of two mere perceptions, we could never thence reach the
knowledge that their object was a succession, or even the knowledge
that they had an object; nor, so beginning, could we become aware of
the perceptions themselves as successive events in the physical world.
For suppose, _per impossibile_, the existence of a process by which we
come to be aware of two elements A and B as standing in a relation of
sequence in the physical world. In the first place, A and B, with the
awareness of which we begin, must be, and be known to be, real or
objective, and not perceptions or apprehensions; otherwise we could
never come to apprehend them as related in the physical world. In the
second place, A and B must be, and be known to be, real with the
reality of a physical event, otherwise we could never come to
apprehend them as related by way of succession in the physical world.
If A and B were bodies, as they are when we apprehend the parts of a
house, they could never be apprehended as successive. In other words,
the process by which, on Kant's view, A and B become, and become known
to be, events presupposes that they already are, and are known to be,
events. Again, even if it be granted that A and B are real events, it
is clear that there can be no process by which we come to apprehend
them as successive. For if we apprehended events A and B separately,
we could never thence advance to the apprehension of their relation,
or, in other words, we could never discover which came first. Kant
himself saw clearly that the perception of A followed by the
perception of B does not by itself yield the perception that B follows
A. In fact it was this insight which formed the starting-point of his
discussion.[46] Unfortunately, instead of concluding that the
apprehension of a succession is ultimate and underivable from a more
primitive apprehension, he tried to formulate the nature of the
process by which, starting from such a succession of perceptions, we
reach the apprehension of a succession. The truth is simply that there
is and can be no _process to_ the apprehension of a succession; in
other words, that we do and must apprehend a real succession
immediately or not at all. The same considerations can of course be
supplied _mutatis mutandis_ to the apprehension of the coexistence of
bodies in space, e. g. of the parts of a house.

    [46] Cf. B. 237, M. 144.

It may be objected that this denial of the existence of the process
which Kant is trying to describe must at least be an overstatement.
For the assertion that the apprehension of a succession or of a
coexistence is immediate may seem to imply that the apprehension of
the course of a boat or of the shape of a house involves no process at
all; yet either apprehension clearly takes time and so must involve a
process. But though a process is obviously involved, it is not a
process from the apprehension of what is not a succession to the
apprehension of a succession, but a process from the apprehension of
one succession to that of another. It is the process by which we pass
from the apprehension of one part of a succession which may have, and
which it is known may have, other parts to the apprehension of what
is, and what is known to be, another part of the same succession.
Moreover, the assertion that the apprehension of a succession must be
immediate does not imply that it may not be reached by a process. It
is not inconsistent with the obvious fact that to apprehend that the
boat is now turning a corner is really to apprehend that what before
was going straight is now changing its course, and therefore
presupposes a previous apprehension of the boat's course as straight.
It only implies that the apprehension of a succession, if reached by a
process at all, is not reached by a process of which the
starting-point is not itself the apprehension of a succession.

Nevertheless, a plausible defence of Kant's treatment of causality can
be found, which may be formulated thus: 'Time, just as much as space,
is a sphere within which we have to distinguish between appearance and
reality. For instance, when moving in a lift, we see, as we say, the
walls moving, while the lift remains stationary. When sitting in a
train which is beginning to move out of a station, we see, as we say,
another train beginning to move, although it is in fact standing
still. When looking at distant trees from a fast train, we see, as we
say, the buildings in the intermediate space moving backwards. In
these cases the events seen are not real, and we only succeed in
determining what is really happening, by a process which presupposes
the law of causality. Thus, in the last case we only believe that the
intermediate buildings do not move, by realizing that, given the
uniformity of nature, belief in their motion is incompatible with what
we believe on the strength of experience of these buildings on other
occasions and of the rest of the world. These cases prove the
existence of a process which enables us, and is required to enable us,
to decide whether a given change is objective or subjective, i. e.
whether it lies in the reality apprehended or in our apprehension of
it; and this process involves an appeal to causality. Kant's mistake
lay in his choice of illustrations. His illustrations implied that the
process which involves causality is one by which we distinguish a
succession in the object apprehended from another relation in the
object, viz. a coexistence of bodies. But he ought to have taken
illustrations which implied that the process is one by which we
distinguish a succession in the object from a succession in our
perception of it. In other words, the illustrations should, like those
just given, have illustrated the process by which we distinguish an
objective from a subjective change, and not a process by which we
distinguish an objective change from something else also objective.
Consequently, Kant's conclusion and his _general_ method of treatment
are right, even if, misled by his instances, he supports his position
by arguments which are wrong.'

This defence is, however, open to the following reply: 'At first sight
the cases taken undoubtedly seem to illustrate a process in which we
seek to discover whether a certain change belongs to objects or only
to our apprehension of them, and in which we appeal to causality in
arriving at a decision. But this is only because we ignore the
relativity of motion. To take the third case: our first statement of
the facts is that we saw the intermediate buildings moving, but that
subsequent reflection on the results of other experience forced us to
conclude that the change perceived was after all only in our
apprehension and not in the things apprehended. The statement,
however, that we saw the buildings moving really assumes that we, the
observers, were stationary; and it states too much. What we really
perceived was a relative changing of position between us, the near
buildings, and the distant trees. This is a fact, and the apprehension
of it, therefore, does not afterwards prove mistaken. It is equally
compatible with motion on the part of the trees, or of the buildings,
or of the observers, or of a combination of them; and that for which
an appeal to causality is needed is the problem of deciding which of
these alternatives is correct. Moreover, the perceived relative change
of position is objective; it concerns the things apprehended. Hence,
in this case too, it can be said that we perceive an objective
succession from the beginning, and that the appeal to causality is
only needed to determine something further about it. It is useless to
urge that to be aware of an event is to be aware of it in all its
definiteness, and that this awareness admittedly involves an appeal to
causality; for it is easy to see that unless our awareness of the
relative motion formed the starting-point of any subsequent process in
which we appealed to the law of causality, we could never use the law
to determine which body really moved.'

Two remarks may be made in conclusion. In the first place, the basis
of Kant's account, viz. the view that in our apprehension of the world
we advance from the apprehension of a succession of perceptions to
the apprehension of objects perceived, involves a [Greek: hysteron
proteron]. As Kant himself in effect urges in the _Refutation of
Idealism_,[47] self-consciousness, in the sense of the consciousness
of the successive process in which we apprehend the world, is plainly
only attained by reflecting upon our apprehension of the world. We
first apprehend the world and only by subsequent reflection become
aware of our activity in apprehending it. Even if consciousness of
the world must lead to, and so is in a sense inseparable from,
self-consciousness, it is none the less its presupposition.

    [47] Cf. p. 320.

In the second place, it seems that the true vindication of causality,
like that of the first analogy, lies in the dogmatic method which Kant
rejects. It consists in insight into the fact that it is of the very
nature of a physical event to be an element in a process of change
undergone by a system of substances in space, this process being
through and through necessary in the sense that any event (i. e. the
attainment of any state by a substance) is the outcome of certain
preceding events (i. e. the previous attainment of certain states by
it and other substances), and is similarly the condition of certain
subsequent events.[48] To attain this insight, we have only to reflect
upon what we really mean by a 'physical event'. The vindication can
also be expressed in the form that the very _thought_ of a physical
event presupposes the _thought_ of it as an element in a necessary
process of change--provided, however, that no distinction is implied
between the nature of a thing and what we think its nature to be. But
to vindicate causality in this way is to pursue the dogmatic method;
it is to argue from the nature, or, to use Kant's phrase, from the
conception, of a physical event. On the other hand, it seems that the
method of arguing transcendentally, or from the possibility of
perceiving events, must be doomed to failure in principle. For if, as
has been argued to be the case,[49] apprehension is essentially the
apprehension of a reality as it exists independently of the
apprehension of it, only those characteristics can be attributed to
it, as characteristics which it must have if it is to be apprehended,
which belong to it in its own nature or in virtue of its being what it
is. It can only be because we think that a thing has some
characteristic in virtue of its own nature, and so think
'dogmatically', that we can think that in apprehending it we must
apprehend it as having that characteristic.[50]

    [48] This statement of course includes the third analogy.

    [49] Cf. Chh. IV and VI.

    [50] Cf. p. 275.

There remains to be considered Kant's proof of the third analogy,
i. e. the principle that all substances, so far as they can be
perceived in space as coexistent, are in thorough-going interaction.
The account is extremely confused, and it is difficult to extract from
it a consistent view. We shall consider here the version added in the
second edition, as being the fuller and the less unintelligible.

"Things are _coexistent_, when in empirical intuition[51] the
perception[52] of the one can follow upon the perception of the other,
and vice versa (which cannot occur in the temporal succession of
phenomena, as we have shown in the second principle). Thus I can
direct my perception first to the moon and afterwards to the earth, or
conversely, first to the earth and then to the moon, and because the
perceptions of these objects can reciprocally follow each other, I say
that they coexist. Now coexistence is the existence of the manifold in
the same time. But we cannot perceive time itself, so as to conclude
from the fact that things are placed in the same time that the
perceptions of them can follow each other reciprocally. The synthesis
of the imagination in apprehension, therefore, would only give us each
of these perceptions as existing in the subject when the other is
absent and vice versa; but it would not give us that the objects are
coexistent, i. e. that, if the one exists, the other also exists in
the same time, and that this is necessary in order that the
perceptions can follow each other reciprocally. Hence there is needed
a conception-of-the-understanding[53] of the reciprocal sequence of
the determinations of these things coexisting externally to one
another, in order to say that the reciprocal succession of perceptions
is grounded in the object, and thereby to represent the coexistence as
objective. But the relation of substances in which the one contains
determinations the ground of which is contained in the other is the
relation of influence, and if, reciprocally, the former contains the
ground of the determinations in the latter, it is the relation of
community or interaction. Consequently, the coexistence of substances
in space cannot be known in experience otherwise than under the
presupposition of their interaction; this is therefore also the
condition of the possibility of things themselves as objects of
experience."[54]

    [51] _Anschauung._

    [52] _Wahrnehmung._

    [53] _Verstandesbegriff._

    [54] B. 257-8, M. 156-7.

The proof begins, as we should expect, in a way parallel to that of
causality. Just as Kant had apparently argued that we learn that a
succession of perceptions is the perception of a sequence when we find
the order of the perceptions to be irreversible, so he now definitely
asserts that we learn that certain perceptions are the perceptions of
a coexistence of bodies in space when we find that the order of the
perceptions is reversible, or, to use Kant's language, that there can
be a reciprocal sequence of the perceptions. This beginning, if read
by itself, seems as though it should also be the end. There seems
nothing more which need be said. Just as we should have expected Kant
to have completed his account of the apprehension of a succession when
he pointed out that it is distinguished by the irreversibility of the
perceptions, so here we should expect him to have said enough when he
points out that the earth and the moon are said to be coexistent
because our perceptions of them can follow one another reciprocally.

The analogy, however, has in some way to be brought in, and to this
the rest of the proof is devoted. In order to consider how this is
done, we must first consider the nature of the analogy itself. Kant
speaks of 'a conception-of-the-understanding of the reciprocal
sequence of the determinations of things which coexist externally to
one another'; and he says that 'that relation of substances in which
the one contains determinations, the ground of which is contained in
the other substance, is the relation of influence'. His meaning can be
illustrated thus. Suppose two bodies, A, a lump of ice, and B, a fire,
close together, yet at such a distance that they can be observed in
succession. Suppose that A passes through changes of temperature a_{1}
a_{2} a_{3} ... in certain times, the changes ending in states
[alpha]_{1} [alpha]_{2} [alpha]_{3} ..., and that B passes through
changes of temperature b_{1} b_{2} b_{3} ... in the same times, the
changes ending in states [beta]_{1} [beta]_{2} [beta]_{3}. Suppose
also, as we must, that A and B interact, i. e. that A in passing
through its changes conditions the changes through which B passes, and
therefore also the states in which B ends, and vice versa, so that
a_{2} and [alpha]_{2} will be the outcome not of a_{1} and [alpha]_{1}
alone, but of a_{1} and [alpha]_{1}, and b_{1} and [beta]_{1} jointly.
Then we can say (1) that A and B are in the relation of influence, and
also of interaction or reciprocal influence, in the sense that they
_mutually_ (not alternately) determine one another's states. Again, if
we first perceive A in the state [alpha]_1 by a perception A_{1}, then
B in the state [beta]_{2} by a perception B_{2}, then A in the state
[alpha]_{3} by a perception A_{3} and so on, we can speak (2) of a
reciprocal sequence of perceptions, in the sense of a sequence of
perceptions in which alternately a perception of B follows a
perception of A and a perception of A follows a perception of B; for
first a perception of B, viz. B_{2}, follows a perception of A, viz.
A_{1}, and then a perception of A, viz. A_{3}, follows a perception of
B, viz. B_{2}. We can also speak (3) of a reciprocal sequence of the
determinations of two things in the sense of a necessary succession of
states which _alternately_ are states of A and of B; for [alpha]_{1},
which is perceived first, can be said to contribute to determine
[beta]_{2}, which is perceived next, and [beta]_{2} can be said to
contribute to determine [alpha]_{3}, which is perceived next, and so
on; and this reciprocal sequence can be said to be involved in the
very nature of interaction. Further, it can be said (4) that if we
perceive A and B alternately, and so only in the states [alpha]_{1}
[alpha]_{3} ... [beta]_{2} [beta]_{4} ... respectively, we can
only fill in the blanks, i. e. discover the states [alpha]_{2}
[alpha]_{4} ... [beta]_{1} [beta]_{3} ... _coexistent_ with [beta]_{2}
[beta]_{4} ... and [alpha]_{1} [alpha]_{3} ... respectively, if we
presuppose the thought of interaction. For it is only possible to use
the observed states as a clue to the unobserved states, if we
presuppose that the observed states are members of a necessary
succession of which the unobserved states are also members and
therefore have partially determined and been determined by the
observed states. Hence it may be said that the determination of the
unobserved states coexistent with the observed states presupposes the
thought of interaction.

How then does Kant advance from the assertion that the apprehension of
a coexistence requires the knowledge that our _perceptions_ can be
reciprocally sequent to the assertion that it presupposes the thought
that the _determinations of phenomena_ are reciprocally sequent? The
passage in which the transition is effected is obscure and confused,
but it is capable of interpretation as soon as we see that it is
intended to run parallel to the proof of the second analogy which is
added in the second edition.[55] Kant apparently puts to himself the
question, 'How are we to know when we have a reciprocal sequence of
perceptions from which we can infer a coexistence in what we
perceived?' and apparently answers it thus: 'Since we cannot perceive
time, and therefore cannot perceive objects as dated in time with
respect to one another, we cannot begin with the apprehension of the
coexistence of two objects, and thence infer the possibility of
reciprocal sequence in our perceptions. This being so, the synthesis
of imagination in apprehension can indeed combine these perceptions
[these now being really considered as determinations or states of an
object perceived] in a reciprocal sequence, but there is so far no
guarantee that the sequence produced by the synthesis is not an
arbitrary product of the imagination, and therefore we cannot think of
it as a reciprocal sequence in objects. In order to think of such a
reciprocal sequence as not arbitrary but as constituting a real
sequence in objects [ = 'as grounded in the object'], we must think of
the states reciprocally sequent [as necessarily related and therefore]
as successive states of two coexisting substances which interact or
mutually determine one another's successive states. Only then shall we
be able to think of the coexistence of objects involved in the
reciprocal sequence as an objective fact, and not merely as an
arbitrary product of the imagination.' But, if this fairly expresses
Kant's meaning, his argument is clearly vitiated by two confusions. In
the first place, it confuses a subjective sequence of perceptions
which are alternately perceptions of A and of B, two bodies in space,
with an objective sequence of perceived states of bodies, [alpha]_{1}
[beta]_{2} [alpha]_{3} [beta]_{4}, which are alternately states of two
bodies A and B, the same thing being regarded at once as a perception
and as a state of a physical object. In the second place, mainly in
consequence of the first confusion, it confuses the necessity that the
perceptions of A and of B can follow one another alternately with the
necessity of succession in the alternately perceived states of A and B
as interacting. Moreover, there is really a change in the cases under
consideration. The case with which he begins, i. e. when he is
considering merely the reciprocal sequence of perceptions, is the
successive perceptions of two _bodies in space_ alternately, e. g. of
the moon and the earth, the nature of their states at the time of
perception not being in question. But the case with which he ends is
the successive perception of the _states of two bodies_ alternately,
e. g. of the states of the fire and of the lump of ice. Moreover, it
is only in the latter case that the objective relation apprehended is
that of coexistence in the proper sense, and in the sense which Kant
intends throughout, viz. that of being contemporaneous in distinction
from being successive. For when we say that two bodies, e. g. the moon
and the earth, coexist, we should only mean that both exist, and not,
as Kant means, that they are contemporaneous. For to a substance,
being as it is the substratum of changes, we can ascribe no temporal
predicates. That which changes cannot be said either to begin, or to
end, or to exist at a certain moment of time, or, therefore, to exist
contemporaneously with, or after, or before anything else; it cannot
even be said to persist through a portion of time or, to use the
phrase of the first analogy, to be permanent. It will be objected
that, though the cases are different, yet the transition from the one
to the other is justified, for it is precisely Kant's point that the
existence together of two substances in space can only be discovered
by consideration of their successive states under the presupposition
that they mutually determine one another's states. "Besides the mere
fact of existence there must be something by which A determines the
place in time for B, and conversely B the place for A, because only
under this condition can these substances be empirically represented
as coexistent."[56] The objection, however, should be met by two
considerations, each of which is of some intrinsic importance. In the
first place, the apprehension of a body in space in itself involves
the apprehension that it exists together with all other bodies in
space, for the apprehension of something as spatial involves the
apprehension of it as spatially related to, and therefore as existing
together with, everything else which is spatial. No process,
therefore, such as Kant describes is required in order that we may
learn that it exists along with some other body. In the second place,
that for which the principle of interaction is really required is not,
as Kant supposes, the determination of the coexistence of an
unperceived body with a perceived body, but the determination of that
unperceived state of a body already known to exist which is coexistent
with a perceived state of a perceived body. As has been pointed out,
if we perceive A and B alternately in the states [alpha]_{1}
[beta]_{2} [alpha]_{3} [beta]_{4} ... we need the thought of
interaction to determine the nature of [beta]_{1} [alpha]_{2}
[beta]_{3} [alpha]_{4} ... Thus it appears that Kant in his
vindication of the third analogy omits altogether to notice the one
process which really presupposes it.

    [55] B. 233-4, M. 142.

    [56] B. 259, M. 157.




CHAPTER XIII

THE POSTULATES OF EMPIRICAL THOUGHT


The postulates of empirical thought, which correspond to the
categories of modality, are stated as follows:

"1. That which agrees with the formal conditions of experience
(according to perception and conceptions) is _possible_.

2. That which is connected with the material conditions of experience
(sensation) is _actual_.

3. That of which the connexion with the actual is determined according
to universal conditions of experience is _necessary_ (exists
necessarily)."[1]

    [1] B. 265-6, M. 161.

These principles, described as only 'explanations of the conceptions
of possibility, actuality, and necessity as employed in experience',
are really treated as principles by which we decide what is possible,
what is actual, and what is necessary. The three conceptions involved
do not, according to Kant, enlarge our knowledge of the nature of
objects, but only 'express their relation to the faculty of
knowledge'[2]; i. e. they only concern our ability to apprehend an
object whose nature is already determined for us otherwise as at least
possible, or as real, or as even necessary. Moreover, it is because
these principles do not enlarge our knowledge of the nature of objects
that they are called postulates; for a postulate in geometry, from
which science the term is borrowed (e. g. that it is possible with a
given line to describe a circle from a given point), does not augment
the conception of the figure to which it relates, but only asserts the
possibility of the conception itself.[3] The discussion of these
principles is described, contrary to the terminology adopted in the
case of the preceding principles, as 'explanation' and not as 'proof'.
The discussion, however, certainly includes a proof of them, for it is
Kant's main object to _prove_ that these principles constitute the
general character of what can be asserted to be possible, actual, or
necessary respectively. Again, as before, the basis of proof lies in a
theory of knowledge, and in particular in Kant's theory of knowledge;
for it consists in the principle that everything knowable must conform
to the conditions involved in its being an object of possible
experience.

    [2] B. 266, M. 161. Cf. B. 286-7, M. 173-4.

    [3] B. 286-7, M. 173-4.

To understand these principles and the proof of them, we must notice
certain preliminary considerations. In the _first_ place, the very
problem of distinguishing the possible, the actual, and the necessary
presupposes the existence of distinctions which may prove open to
question. It presupposes that something may be possible without being
actual, and again that something may be actual without being
necessary. In the _second_ place, Kant's mode of approaching the
problem assumes that we can begin with a conception of an object,
e. g. of a man with six toes, and then ask whether the object of it is
possible, whether, if possible, it is also actual, and whether, if
actual, it is also necessary. In other words, it assumes the
possibility of separating what is conceived from what is possible, and
therefore _a fortiori_ from what is actual,[4] and from what is
necessary. _Thirdly_, in this context, as in most others, Kant in
speaking of a conception is thinking, to use Locke's phraseology, not
of a 'simple' conception, such as that of equality or of redness, but
of a 'complex' conception, such as that of a centaur, or of a triangle
in the sense of a three-sided three-angled figure. It is the
apprehension of a 'complex' of elements.[5] _Fourthly_, what is said
to be possible, real, or necessary is not the conception but the
corresponding object. The question is not, for instance, whether the
conception of a triangle or of a centaur is possible, actual, or
necessary, but whether a triangle or a centaur is possible, actual, or
necessary. Kant sometimes speaks loosely of conceptions as
possible,[6] but the terms which he normally and, from the point of
view of his theory, rightly applies to conceptions are 'objectively
real' and 'fictitious'.[7] _Lastly_, Kant distinguishes 'objectively
real' and 'fictitious' conceptions in two ways. He speaks of
establishing the objective reality of a conception as consisting in
establishing the possibility of a corresponding object,[8] implying
therefore that a fictitious conception is a conception of which the
corresponding object is not known to be possible. Again, he describes
as fictitious new conceptions of substances, powers, and interactions,
which we might form from the material offered to us by perception
without borrowing from experience itself the example of their
connexions, e. g. the conception of a power of the mind to perceive
the future; and he says that the possibility of these conceptions
(i. e. the possibility of corresponding objects) cannot, like that of
the categories, be acquired _a priori_ through their being conditions
on which all experience depends, but must be discovered empirically or
not at all. Of such conceptions he says that, without being based upon
experience and its known laws, they are arbitrary syntheses which,
although they contain no contradiction, have no claim to objective
reality, and therefore to the possibility of corresponding objects.[9]
He implies, therefore, that the object of a conception can be said to
be possible only when the conception is the apprehension of a complex
of elements together with the apprehension--which, if not _a priori_,
must be based upon experience--that they are connected. Hence a
conception may be regarded as 'objectively real', or as 'fictitious'
according as it is the apprehension of a complex of elements
accompanied by the apprehension that they are connected, or the
apprehension of a complex of elements not so accompanied.

    [4] The view that 'in the mere conception of a thing no sign
    of its existence is to be found' (B. 272, M. 165) forms, of
    course, the basis of Kant's criticism of the ontological
    argument for the existence of God. Cf. _Dialectic_, Bk. II,
    Ch. III, § 4.

    [5] Cf. 'a conception which includes in itself a synthesis'
    (B. 267 med., M. 162 med.).

    [6] E. g. B. 269 fin., M. 163 fin.; B. 270 med., M. 164 init.
    The formulation which really expresses Kant's thought is to
    be found B. 266 med., M. 161 fin.; B. 268 init., M. 162 fin.;
    B. 268 med., M. 163 init.; and B. 270 med., M. 164 init.

    [7] _Gedichtete._

    [8] B. 268 init., M. 162 fin.

    [9] B. 269-70, M. 163-4.

It is now possible to state Kant's problem more precisely. With regard
to a given complex conception he wishes to determine the way in which
we can answer the questions (1) 'Has the conception a possible object
to correspond to it', or, in other words, 'Is the conception
'objectively real' or 'fictitious'?' (2) 'Given that a corresponding
object is possible, is it also real?' (3) 'Given that it is real, is
it also necessary?'

The substance of Kant's answer to this problem may be stated thus:
'The most obvious guarantee of the objective reality of a conception,
i. e. of the possibility of a corresponding object, is the experience
of such an object. For instance, our experience of water guarantees
the objective reality of the conception of a liquid which expands as
it solidifies. This appeal to experience, however, takes us beyond the
possibility of the object to its reality, for the experience
vindicates the possibility of the object only through its reality.
Moreover, here the basis of our assertion of possibility is only
empirical, whereas our aim is to discover the conceptions of which the
objects can be determined _a priori_ to be possible. What then is the
answer to this, the real problem? To take the case of cause and
effect, we cannot reach any conclusion by the mere study of the
conception of cause and effect. For although the conception of a
necessary succession contains no contradiction, the necessary
succession of events is a mere arbitrary synthesis as far as our
thought of it is concerned; we have no direct insight into the
necessity. Therefore we cannot argue from this conception to the
possibility of a corresponding object, viz. a necessarily successive
series of events in nature. We can, however, say that that synthesis
is not arbitrary but necessary to which any object must conform, if it
is to be an object of experience. From this point of view we can say
that there must be a possible object corresponding to the conception
of cause and effect, because only as subjected to this synthesis are
there objects of experience at all. Hence, if we take this point of
view, we can say generally that all spatial and temporal conceptions,
as constituting the conditions of perceiving in experience, and all
the categories, as constituting the conditions of conceiving in
experience, must have possible objects. In other words, 'that which
agrees with the formal conditions of experience (according to
perception and conceptions) is _possible_'. Again, if we know that
the object of a conception is possible, how are we to determine
whether it is also actual? It is clear that, since we cannot advance
from the mere conception, objectively real though it may be, to the
reality of the corresponding object, we need perception. The case,
however, where the corresponding object is directly perceived may be
ignored, for it involves no inference or process of thought; the
appeal is to experience alone. Therefore the question to be considered
is, 'How do we determine the actuality of the object of a conception
comparatively _a priori_, i. e. without direct experience of it[10]?'
The answer must be that we do so by finding it to be 'connected
with an actual perception in accordance with the analogies of
experience'[11]. For instance, we must establish the actuality of an
object corresponding to the conception of a volcanic eruption by
showing it to be involved, in accordance with the analogies (and with
particular empirical laws), in the state of a place which we are now
perceiving. In other words, we can say that 'that which is connected
with the material conditions of existence (sensation) is _actual_'.
Finally, since we cannot learn the existence of any object of
experience wholly _a priori_, but only relatively to another existence
already given, the necessity of the existence of an object can never
be known from conceptions, but only from its connexion with what is
perceived; this necessity, however, is not the necessity of the
existence of a substance, but only the necessity of connexion of an
unobserved state of a substance with some observed state of a
substance. Therefore we can (and indeed must) say of an unobserved
object corresponding to a conception, not only that it is real, but
also that it is necessary, when we know it to be connected with a
perceived reality 'according to universal conditions of experience';
but the necessity can be attributed only to states of substances and
not to substances themselves.'

    [10] Cf. B. 279, M. 169 and p. 4, note 1.

    [11] B. 273, M. 165.

Throughout this account there runs one fatal mistake, that of
supposing that we can separate our knowledge of things as possible, as
actual, and as necessary. Even if this supposition be tenable in
certain cases,[12] it is not tenable in respect of the objects of a
complex conception, with which Kant is dealing. If we know the object
of a complex conception to be possible, we already know it to be
actual, and if we know it to be actual, we already know it to be
necessary. A complex conception in the proper sense is the
apprehension of a complex of elements together with the apprehension
of, or insight into, their connexion.[13] Thus, in the case of the
conception of a triangle we see that the possession of three sides
necessitates the possession of three angles. From such a conception
must be distinguished Kant's 'fictitious' conception, i. e. the
apprehension of a complex of elements without the apprehension of
connexion between them. Thus, in the case of the conception of a man
with six toes, there is no apprehension of connexion between the
possession of the characteristics indicated by the term 'man' and the
possession of six toes. In such a case, since we do not apprehend any
connexion between the elements, we do not really 'conceive' or 'think'
the object in question, e. g. a man with six toes. Now in the case of
a complex conception proper, it is impossible to think of a
corresponding individual as only possible. The question 'Is a
triangle, in the sense of a figure with three sides and three angles,
possible?' really means 'Is it possible for a three-sided figure to
have three angles?' To this question we can only answer that we see
that a three-sided figure can have three angles, because we see that
it must have, and therefore has, and can have, three angles; in other
words, that we see a triangle in the sense in question to be possible,
because we see it to be necessary, and, therefore, actual, and
possible. It cannot be argued that our insight is limited to the fact
that if there are three-sided figures they must be three-angled, and
that therefore we only know a triangle in the sense in question to be
possible. Our apprehension of the fact that the possession of three
sides necessitates the possession of three angles presupposes
knowledge of the existence of three-sided figures, for it is only in
an actual three-sided figure that we can apprehend the necessity. It
may, however, be objected that the question ought to mean simply 'Is a
three-sided figure possible?' and that, understood in this sense, it
cannot be answered in a similar way. Nevertheless, a similar answer is
the right answer. For the question 'Is a three-sided figure possible?'
really means 'Is it possible for three straight lines to form a
figure, i. e. to enclose a space?' and we can only answer it for
ourselves by seeing that a group of three straight lines or
directions, no two of which are parallel, must, as such, enclose a
space, this insight presupposing the apprehension of an actual group
of three straight lines. It may be said, therefore, that we can only
determine the possibility of the object of a complex conception in
the proper sense, through an act in which we apprehend its necessity
and its actuality at once. It is only where conceptions are
'fictitious', and so not properly conceptions, that appeal to
experience is necessary. The question 'Is an object corresponding to
the conception of a man with six toes possible?' presupposes the
reality of man and asks whether any man can have six toes. If we
understood the nature of man and could thereby apprehend either that
the possession of six toes was, or that it was not, involved in one of
the possible differentiations of man, we could decide the question of
possibility _a priori_, i. e. through our conceiving alone without an
appeal to experience; but we could do so only because we apprehended
either that a certain kind of man with six toes was necessary and
actual, or that such a man was impossible and not actual. If, however,
as is the case, we do not understand the nature of man, we can only
decide the question of possibility by an appeal to experience, i. e.
to the experience of a corresponding object, or of an object from
which the existence of such an object could be inferred. Here,
therefore--assuming the required experience to be forthcoming--we
can appeal to Kant's formula and say that we know that such a man,
i. e. an object corresponding to the conception, is actual, as
being connected with the material conditions of experience. But the
perception which constitutes the material conditions of experience
in the case in question is only of use because it carries us beyond
possibility to actuality, and appeal to it is only necessary because
the object is not really conceived or, in other words, because the
so-called conception is not really a conception.

    [12] For instance, it might at least be _argued_ that we know
    space to be actual without knowing it to be necessary.

    [13] _Not_ 'together with the apprehension _that_ the
    elements are connected'. Cf. p. 311.

Kant really treats his 'objectively real' conceptions as if they were
'fictitious', even though he speaks of them as complete. Consequently,
his conceptions not being conceptions proper, he is necessarily led to
hold that an appeal to experience is needed in order to establish the
reality of a corresponding object. Yet, this being so, he should have
asked himself whether, without an appeal to perception, we could even
say that a corresponding object was possible. That he did not ask this
question is partly due to the fact that he attributes the form and the
matter of knowledge to different sources, viz. to the mind and to
things in themselves. While the conceptions involved in the forms of
perception, space, and time, and also the categories are the
manifestations of the mind's own nature, sensations, which form the
matter of knowledge, are due to the action of things in themselves on
our sensibility, and of this activity we can say nothing. Hence, from
the point of view of our mind--and since we do not know things in
themselves, this is the only point of view we can take--the existence
of sensations, and therefore of objects, which must be given in
perception, is wholly contingent and only to be discovered through
experience. On the other hand, since the forms of perception and
conception necessarily determine in certain ways the nature of
objects, _if_ there prove to be any objects, the conceptions involved
may be thought to determine what objects are possible, even though the
very existence of the objects is uncertain. Nevertheless, on his own
principles, Kant should have allowed that, apart from perception, we
could discover _a priori_ at least the reality, even if not the
necessity, of the objects of these conceptions. For his general view
is that the forms of perception and the categories are only actualized
on the occasion of the stimulus afforded by the action of things in
themselves on the sensibility. Hence the fact that the categories and
forms of perception are actualized--a fact implied in the very
existence of the _Critique_--involves the existence of objects
corresponding to the categories and to the conceptions involved in the
forms of perception. On Kant's own principles, therefore, we could say
_a priori_ that there must be objects corresponding to these
conceptions, even though their nature in detail could only be filled
in by experience.[14]

    [14] Cf. Caird, i. 604-5.




NOTE ON THE REFUTATION OF IDEALISM


This well-known passage[1] practically replaces a long section,[2]
contained only in the first edition, on the fourth paralogism of
pure reason. Its aim is to vindicate against 'idealism' the reality
of objects in space, and it is for this reason inserted after the
discussion of the second postulate. The interest which it has excited
is due to Kant's use of language which at least seems to imply that
bodies in space are things in themselves, and therefore that here he
really abandons his main thesis.

    [1] B. 274-9, M. 167-9. Cf. B. xxxix (note), M. xl (note).

    [2] A. 367-80, Mah. 241-53.

Idealism is the general name which Kant gives to any view which
questions or denies the reality of the physical world; and, as has
been pointed out before,[3] he repeatedly tries to defend himself
against the charge of being an idealist in this general sense. This
passage is the expression of his final attempt. Kant begins by
distinguishing two forms which idealism can take according as it
regards the existence of objects in space as false and _impossible_,
or as doubtful and _indemonstrable_. His own view, which regards their
existence as certain and demonstrable, and which he elsewhere[4]
calls transcendental idealism, constitutes a third form. The first
form is the dogmatic idealism of Berkeley. This view, Kant says,
is unavoidable, if space be regarded as a property of things in
themselves, and the basis of it has been destroyed in the _Aesthetic_.
The second form is the problematic idealism of Descartes, according to
which we are immediately aware only of our own existence, and belief
in the existence of bodies in space can be only an inference, and an
uncertain inference, from the immediate apprehension of our own
existence. This view, according to Kant, is the outcome of a
philosophical attitude of mind, in that it demands that a belief
should be proved, and apparently--to judge from what Kant says of
Berkeley--it does not commit Descartes to the view that bodies in
space, if their reality can be vindicated, are things in themselves.

    [3] Cf. p. 76.

    [4] A. 369, Mah. 243; cf. B. 44, M. 27.

The assertion that the _Aesthetic_ has destroyed the basis of
Berkeley's view, taken together with the drift of the _Refutation_
as a whole, and especially of Remark I, renders it clear that the
_Refutation_ is directed against Descartes and not Berkeley. Kant
regards himself as having already refuted Berkeley's view, as he
here states it, viz. that the existence of objects in space is
_impossible_, on the ground that it arose from the mistake of
supposing that space, if real at all, must be a property of things in
themselves, whereas the _Aesthetic_ has as he thinks, shown that space
can be, and in point of fact is, a property of phenomena. He now wants
to prove--compatibly with their character as phenomena--that the
existence of bodies in space is not even, as Descartes contends,
_doubtful_. To prove this he seeks to show that Descartes is wrong in
supposing that we have no immediate experience of these objects. His
method is to argue that reflection shows that internal experience
presupposes external experience, i. e. that unless we were directly
aware of spatial objects, we could not be aware of the succession of
our own states, and consequently that it is an inversion to hold that
we must reach the knowledge of objects in space, if at all, by an
inference from the immediate apprehension of our own states.

An examination of the proof itself, however, forces us to allow that
Kant, without realizing what he is doing, really abandons the view
that objects in space are phenomena, and uses an argument the very
nature of which implies that these objects are things in themselves.
The proof runs thus:

_Theorem._ "The mere but empirically determined consciousness of my
own existence proves the existence of objects in space external to
me."

"_Proof._ I am conscious of my own existence as determined in
time. All time-determination presupposes something permanent in
perception.[5] This permanent, however, cannot be an intuition[6]
in me. For all grounds of determination of my own existence, which
can be found in me, are representations, and as such themselves need
a permanent different from them, in relation to which their change
and consequently my existence in the time in which they change can
be determined.[7] The perception of this permanent, therefore, is
possible only through a _thing_ external to me, and not through the
mere _representation_ of a thing external to me. Consequently, the
determination of my existence in time is possible only through the
existence of actual things, which I perceive external to me. Now
consciousness in time is necessarily connected with the consciousness
of the possibility of this time-determination; hence it is necessarily
connected also with the existence of things external to me, as the
condition of time-determination, i. e. the consciousness of my own
existence, is at the same time an immediate consciousness of the
existence of other things external to me."[8]

    [5] _Wahrnehmung._

    [6] _Anschauung._

    [7] The text has been corrected in accordance with Kant's
    note in the preface to the second edition, B. xxxix, M. xl.

    [8] B. 275-6, M. 167.

The nature of the argument is clear. 'In order to be conscious, as
I am, of a determinate succession of my states, I must perceive
something permanent as that in relation to which alone I can perceive
my states as having a definite order.[9] But this permanent cannot be
a perception in me, for in that case it would only be a representation
of mine, which, as such, could only be apprehended in relation to
another permanent. Consequently, this permanent must be a thing
external to me and not a representation of a thing external to me.
Consequently, the consciousness of my own existence, which is
necessarily a consciousness of my successive states, involves the
immediate consciousness of things external to me.'

    [9] Cf. Kant's proof of the first analogy.

Here there is no way of avoiding the conclusion that Kant is deceived
by the ambiguity of the phrase 'a thing external to me' into thinking
that he has given a proof of the existence of bodies in space which is
compatible with the view that they are only phenomena, although in
reality the proof presupposes that they are things in themselves. In
the 'proof', the phrase 'a thing external to me' must have a double
meaning. It must mean a thing external to my body, i. e. any body
which is not my body; in other words, it must be a loose expression
for a body in space. For, though the 'proof' makes us appeal to the
spatial character of things external to me, the _Refutation_ as a
whole, and especially Remark II, shows that it is of bodies in space
that he is thinking throughout. The phrase must also, and primarily,
mean a thing external to, in the sense of independent of, my mind,
i. e. a thing in itself. For the nerve of the argument consists in the
contention that the permanent the perception of which is required for
the consciousness of my successive states must be a _thing_ external
to me in opposition to the representation of a thing external to me,
and a thing external to me in opposition to a thing external to me can
only be a thing in itself. On the other hand, in Kant's conclusion,
'a thing external to me' can only mean a body in space, this being
supposed to be a phenomenon; for his aim is to establish the reality
of bodies in space compatibly with his general view that they are only
phenomena. The proof therefore requires that things external to me, in
order that they may render possible the consciousness of my successive
states, should have the very character which is withheld from them in
the conclusion, viz. that of existing independently of me; in other
words, if Kant establishes the existence of bodies in space at all,
he does so only at the cost of allowing that they are things in
themselves.[10]

    [10] The ambiguity of the phrase 'external to me' is pointed
    out in the suppressed account of the fourth paralogism,
    where it is expressly declared that objects in space are
    only representations. (A. 372-3, Mah. 247). Possibly the
    introduction of an argument which turns on the view that they
    are not representations may have had something to do with the
    suppression.

Nevertheless, the _Refutation_ may be considered to suggest the proper
refutation of Descartes. It is possible to ignore Kant's demand for a
permanent as a condition of the apprehension of our successive states,
and to confine attention to his remark that he has shown that external
experience is really immediate, and that only by means of it is the
consciousness of our existence as determined in time possible.[11] If
we do so, we may consider the _Refutation_ as suggesting the view that
Descartes' position is precisely an inversion of the truth; in other
words, that our consciousness of the world, so far from being an
uncertain inference from the consciousness of our successive states,
is in reality a presupposition of the latter consciousness, in that
this latter consciousness only arises through reflection upon the
former, and that therefore Descartes' admission of the validity of
self-consciousness implicitly involves the admission _a fortiori_ of
the validity of our consciousness of the world.[12]

    [11] B. 277, M. 167 fin.

    [12] Cf. Caird, i. 632 and ff.


      Oxford: Printed at the Clarendon Press by HORACE HART, M.A.