is a merely subjective intuition. Kant, as it would seem,
still maintains that there is a pure manifold of intuition
distinct from the manifold of sense ; and so by the inevit-
able logic of his thought is constrained to view space as
innate in conscious form. This is not, of course, a conclusion
which he could permanently stand by, but its elimination
would have involved a more radical revision of his whole
view of pure intuition and of mathematical science than he
was willing to undertake. Though in the Analytic he has
come to recognise 3 that it is acquired by reflection upon
objects, to the end he would seem to persist in the difficult
contention that such reflection yields a pure manifold distinct
from the manifold of sense. 4 His belief that mathematical
1 Cf. below, p. 291 ff., on Kant's reasons for developing his doctrine of inner
2 As no one passage can be regarded as quite decisively proving Kant's belief
in a pure manifold of intuition, the question can only be decided by a collation of
all the relevant statements in the light of the general tendencies of Kant's thinking.
3 This at least would seem to be implied in the wording of his later positions ;
it is not explicitly avowed. 4 Cf. A 76-7 = B 102.
94 THE TRANSCENDENTAL AESTHETIC
science is based upon pure intuition prevented him from
recognising that though space may be a pure form of in-
tuition, it can never by itself constitute a complete intuition.
Its sole possible content is the manifold of sense. But even
apart from the fact that our apprehension of space is always
empirically conditioned, Kant's view of mathematical pro-
positions as grounded in intuition is, as already observed,
not itself tenable. For though intuitions may perhaps be the
ultimate subject matter of geometry, concepts are its sole
possible instruments. Intuitions yield scientific insight in
exact proportion to our powers of restating their complex
content in the terms of abstract thought. Until the evidence
which they supply has been thus intellectually tested and
defined, they cannot be accepted as justifying even the
simplest proposition. 1
The complicated ambiguities of Kant's treatment of space
may be illustrated and further clarified by discussion of
another difficulty. Is space a totum analyticum or a totum
syntheticum ? Does the whole precondition the parts, or does
it arise through combination of the parts? Or to ask
another but connected question, do we intuit infinitude, or is
it conceptually apprehended only as the presupposition of our
limited intuitions ? To these questions diametrically opposite
answers can be cited from the Critique. As we have above
noted, Kant teaches in the Aesthetic that space is given as a
whole, and that the parts arise only by limitation of it. But
in A 162= B 203 we find him also teaching that a magnitude
is to be entitled extensive
". . . when the representation of the parts makes possible, and
therefore necessarily precedes, the representation of the whole. I
cannot represent to myself a line, however small, without drawing it
in thought, i.e. generating from a point all its parts one after another,
and thus for the first time recording this intuition." 2
He adds in the second edition 3 that extensive magnitude
cannot be apprehended save through a "synthesis of the
manifold," a " combination of the homogeneous."
The note which Kant appends to B 136 is a very strange
combination of both views. It first of all reaffirms the doctrine
of the Aesthetic that space and time are not concepts, but in-
tuitions within which as in a unity a multitude of representa-
tions are contained ; and then proceeds to argue that space
1 Cf. above, pp. xlii, 38-42; below, pp. 118-20, 128-34.
2 The last statement may be more freely translated : "Only in this way can I
get the intuition before me in visible form." Cf. below, pp. 135-6, 347-8, 359.
8 B 202-3.
KANT'S CONFLICTING VIEWS OF SPACE 95
and time, as thus composite^ must presuppose an antecedent
synthesis. In A 505 = 6 533 we find a similar attempt to
combine both assertions.
" The parts of a given appearance are first given through and in
the regress of decomposing synthesis (decomponirenden Synthesis)"
The clash of conflicting tenets which Kant is striving to
reconcile could hardly find more fitting expression than in
this assertion of an analytic synthesis. The same conflict
appears, though in a less violent form, in A 438 = B 466.
" Space should properly be called not compositum but totum, since
its parts are possible only in the whole, not the whole through the
parts. It might, indeed, be said to be a compositum that is ideate,
but not reale. That, however, is a mere subtlety." *
The arguments by which Kant proves space to be an a
priori intuition rest upon the view that space is given as infinite^
and that its parts arise through limitation of this prior-existent
whole. But a principle absolutely fundamental to the entire
Critique is the counter principle, that all analysis rests upon
and presupposes a previously exercised synthesis. Synthesis
or totality as such can never be given. Only in so far as a whole
is synthetically constructed can it be apprehended by the mind.
Representation of the parts precedes and renders possible repre-
sentation of the whole.
The solution of the dilemma arising out of these diverse
views demands the drawing of two distinctions. First,
between a synthesised totality and a principle of synthesis ;
the former may involve a prior synthesis ; the latter does
not depend upon synthesis, but expresses the predetermined
nature of some special form of synthesis. Secondly, it
demands a distinction between the a priori manifolds of
space and time and the empirical manifold which is appre-
hended in and through them. This, as we have already
noted, is a distinction difficult to take quite seriously, and
is entirely unsupported by psychological evidence. But it
would seem to be insisted upon by Kant, and to have been
a determining factor in the formulation of several of his
In terms of the first distinction we are compelled to
recognise that the view of space which underlies the Aesthetic
is out of harmony with the teaching of the Analytic. In the
Aesthetic Kant interprets space not merely as a form of
intuition but also as a formal intuition, which is given com-
1 Cf. Reflexionen, ii. 393, 409, 465, 630, 649.
96 THE TRANSCENDENTAL AESTHETIC
plete in its totality, and which is capable of being apprehended
independently of its empirical contents, and even prior to
them. That would seem to be the view of space which is
presupposed in Kant's explanation of pure mathematical
science. The passages from the Analytic, quoted above, are,
however, its express recantation. Space, as the intuition of
a manifold, is a totum syntheticum, not a totum analyticum.
It is constructed, not given. The divergence of views
between the Aesthetic and the Analytic springs out of the
difficulty of meeting at once the logical demands of a world
which Kant conceives objectively, and the psychological
demands which arise when this same world is conceived as
subjectively conditioned. In principle, the whole precedes
the parts ; in the process of being brought into existence as
an intuition, the parts precede the whole. The principle
which determines our apprehension of any space, however
small or however large, is that it exists in and through
universal space. This is the principle which underlies both
the synthetic construction of space and also its apprehension
once it is constructed. In principle, therefore, i.e. in the
order of logical thought, the whole precedes the parts. 1 The
process, however, which this principle governs and directs,
cannot start with space as a whole, but must advance to
it through synthesis of smaller parts.
But Kant does not himself recognise any conflict between
this teaching and the doctrine of the Aesthetic. He seems to
himself merely to be making more definite a position which
he has consistently held all along ; and this was possible
owing to his retention and more efficient formulation of the
second of the two distinctions mentioned above, viz. that
between the manifold of sense and the manifold of intuition.
This distinction enables him to graft the new view upon the
old, and so in the very act of insisting upon the indispens-
ableness of the conceptual syntheses of understanding, none
the less to maintain his view of geometry as an intuitive
" Space and time contain a manifold of pure a priori intuition,
but at the same time are conditions of the receptivity of our mind
conditions under which alone it can receive representations of
1 This, indeed, is Kant's reason for describing space as an Idea of reason. Cf.
below, pp. 97-8.
2 Geometry is for Kant the fundamental and chief mathematical science (cf.
A 39 = B 56 and Dissertation^ 15 c). In this respect he is a disciple of Newton,
not a follower of Leibniz. His neglect to take adequate account of arithmetic and
algebra is due to this cause. Just as in speaking of the manifold of sense he almost
invariably has sight alone in view, so in speaking of mathematical science he
usually refers only to geometry and the kindred discipline of pure mechanics.
KANT'S CONFLICTING VIEWS OF SPACE 97
objects, and which therefore must also affect the concept of them.
But if this manifold is to be known, the spontaneity of our thinking
requires that it be gone through in a certain way, taken up, and
connected. This action I name synthesis. . . . Such a synthesis is
pure, if the manifold is not empirical, but is given a priori, as is that
of space and of time." l
Thus Kant recognises that space, as apprehended by us,
is constructed, not given, and so by implication that the infini-
tude of space is a principle of apprehension, not a given in-
tuition. But he also holds to the view that it contains a pure,
and presumably infinite, manifold, given as such. 2 In what
this pure manifold consists, and how the description of it as a
manifold, demanding synthesis for its apprehension, is to be
reconciled with its continuity, Kant nowhere even attempts to
explain. Nor does he show what the simple elements are
from which the synthesis of apprehension and reproduction
in pure intuition might start. The unity and multiplicity
of space are, indeed, as he himself recognises, 8 inseparably
involved in one another ; and recognition of this fact must
render it extremely difficult to assign them to separate faculties.
For the same reason it is impossible to distinguish temporally,
as Kant so frequently does, the processes of synthesis and of
analysis, making the former in all cases precede the latter in
time. The very nature of space and time, and, as he came to
recognise, the very nature of all Ideas of reason, in so far as
they involve the notion of the unconditioned, conflict with
such a view.
Even when Kant is dealing with space as a principle of
synthesis, he speaks with no very certain voice. In the
Analytic it is ascribed to the co-operation of sensibility and
understanding. In the Dialectic it is, by implication, ascribed
to Reason ; and in the Metaphysical First Principles it is
explicitly so ascribed.
" Absolute space cannot be object of experience ; for space without
matter is no object of perception, and yet it is a necessary conception
of Reason, and therefore nothing but a mere Idea." 4 "Absolute space
is not necessary as a conception of an actual object, but as an Idea
which can serve as rule. . . ." 5
Kant's teaching in the Critique of Judgment is a further
development of this position.
"The mind listens to the voice of Reason which, for every given
1 A 76-7 = 6 102. Cf. B 1 60- 1 n.
2 Cf. above, pp. 90, 92 ff. ; below, pp. 171, 226-9, 267-70, 337.
8 Cf. B 160. 4 Metaphysical First Principles, W. iv. p. 559, cf. p. 481.
5 Op. cit. p. 560.
98 THE TRANSCENDENTAL AESTHETIC
magnitude even for those that can never be entirely apprehended,
although (in sensible representation) they are judged as entirely
gi ven requires totality. ... It does not even except the infinite
(space and past time) from this requirement; on the contrary, it
renders it unavoidable to think the infinite (in the judgment of
common reason) as entirely given (in its totality). But the infinite is
absolutely (not merely comparatively) great. Compared with it
everything else (of the same kind of magnitudes) is small. But what
is most important is that the mere ability to think it as a whole indi-
cates a faculty of mind which surpasses every standard of sense. . . .
The bare capability of thinking the given infinite without contradiction
requires in the human mind a faculty itself supersensible. For it is
only by means of this faculty and its Idea of a noumenon . . . that
the infinite of the world of sense, in the pure intellectual estimation
of magnitude, can be completely comprehended under one concept.
. . . Nature is, therefore, sublime in those of its phenomena, whose
intuition brings with it the Idea of its infinity. . . . For just as
imagination and understanding, in judging of the beautiful, generate a
subjective purposiveness of the mental powers by means of their
harmony, so imagination and Reason do so by means of their
Kant has here departed very far indeed from the position
of the Aesthetic?
1 Critique of Judgment, 26-7, Eng. trans, pp. 115-16 and 121.
2 Cf. below, pp. 102 ., 165-6, 390-1.
THE TRANSCENDENTAL AESTHETIC
METAPHYSICAL EXPOSITION OF THE CONCEPTION
OF SPACE 1
Space: First Argument. "Space is not an empirical concept
(Begriff) which has been abstracted from outer experiences. For in
order that certain sensations be related to something outside me (i.e.
to something in another region of space from that in which I find
myself), and similarly in order that I may be able to represent them
as outside [and alongside] 2 one another, and accordingly as not only
[qualitatively] different but as in different places, the representation
of space must be presupposed (muss schon zum Grunde liegen). The
representation of space cannot, therefore, be empirically obtained at
second-hand from the relations of outer appearance. This outer
experience is itself possible at all only through that representation." 3
The first sentence states the thesis of the argument : space is
not an empirical concept abstracted from outer experiences. The
use of the term Begriff in the title of the section, and also in
this sentence, is an instance of the looseness with which Kant
employs his terms. It is here synonymous with the term
representation ( Vorstellung\ which covers intuitions as well as
general or discursive concepts. Consequently, the contradic-
tion is only verbal, not real, when Kant proceeds to prove
that the concept of space is an intuition, not a concept. But
this double employment of the term is none the less misleading.
When Kant employs it in a strict sense, it signifies solely the
general class concept. 4 All true concepts are for Kant of that
single type. He has not re-defined the term concept in any
1 The title of this section, and the points raised in the opening paragraph, are
commented upon below. Cf. pp. no, 114-15, 134 ff. I pass at once to the first
2 Added in second edition.
3 This argument is an almost verbal repetition of the first argument on space
in the Dissertation, 15.
4 Cf. below, pp. 106-7, 126, 132-3, 177-84, 338-9.
ioo THE TRANSCENDENTAL AESTHETIC
manner which would render it applicable to the relational
categories. For unfortunately, and very strangely, he never
seems to have raised the question whether categories are not
also concepts. The application to the forms of understanding
of the separate title categories seems to have contented him.
Much that is obscure and even contradictory in his teaching
might have been prevented had he recognised that the term
concept is a generic title which includes, as its sub-species,
both general notions and relational categories.
.Kant's limitation of the term concept to the merely generic, 1
and his consequent equating of the categorical proposition
with the assertion of the substance-attribute relation, 2 would
seem in large part to be traceable to his desire to preserve
for himself, in the pioneer labours of his Critical enquiries,
the guiding clues of the distinctions drawn in the traditional
logic. Kant insists on holding to them, at least in outward
appearance, at whatever sacrifice of strict consistency. Critical
doctrine is made to conform to the exigencies of an artificial
framework, with which its own tenets are only in very imperfect
harmony. Appreciation of the ramifying influence, and, as
regards the detail of exposition, of the far-reaching conse-
quences, of this desire to conform to the time-honoured
rubrics, is indeed an indispensable preliminary to any adequate
estimate whether of the strength or of the defects of the
Critical doctrines. As a separate and ever-present influence
in the determining of Kant's teaching, this factor may con-
veniently and compendiously be entitled Kant's logical archi-
tectonic? We shall have frequent occasion to observe its
The second sentence gives expression to the fact through
which Kant proves his thesis. Certain sensations, those of
the special senses as distinguished from the organic sensations, 5
are related to something which stands in a different region of
space from the em bodied self, and consequently are apprehended
as differing from one another not only in quality but also in
spatial position. As is proved later in the Analytic, thought
plays an indispensable part in constituting this reference of
sensations to objects. Kant here, however, makes no mention
of this further complication. He postulates, as he may
legitimately do at this stage, the fact that our sensations are
1 Cf. above, p. 37 ff. ; below, p. 178 ff.
2 That is particularly obvious in Kant's formulation of his problem in the
Introduction. For that is the assumption which underlies his mode of distinguish-
ing between analytic and synthetic judgments. Cf. above, p. 37.
3 Cf. above, p. xxii. 4 Cf. especially, pp. 184, 332-6, 419, 474, 479.
8 I here use the more modern terms. Kant, in Anthropologie, 14, distinguishes
between them as Organencmpfindungen and Vttalemfifindungen.
FIRST ARGUMENT ON SPACE 10
thus objectively interpreted, and limits his enquiry to the
spatial factor. Now the argument, as Vaihinger justly points
out, 1 hinges upon the assumption which Kant has already
embodied 2 in his definition of the " form " of sense, viz. that
sensations are non-spatial, purely qualitative. Though this
is an assumption of which Kant nowhere attempts to give
proof, it serves none the less as an unquestioned premiss from
which he draws all-important conclusions. This first argu-
ment on space derives its force entirely from it.
The proof that the representation of space is non-empirical
may therefore be explicitly stated as follows. As sensations^
are non-spatial and differ only qualitatively, the representa-i
tion of space must have been added to them. And not )
being supplied by the given sensations, it must, as the only (
alternative, have been. contributed by the mind. The repre- j
sentation of space, so far from being derived from external
experience, is what first renders it possible. As a subjective
form that lies ready in the mind, it precedes experience
and co-operates in generating it. This proof of the apriority
of space is thus proof of the priority of the representation of
space to every empirical perception.
In thus interpreting Kant's argument as proving more
than the thesis of the first sentence claims, we are certainly
reading into the proof more than Kant has himself given full
expression to. But, as is clearly shown by the argument of
the next section, we are only stating what Kant actually takes
the argument as having proved, namely, that the representa-
tion of space is not only non- empirical but is likewise of
subjective origin and precedes experience in temporal fashion.
The point of view which underlies and inspires the argu-
ment can be defined even more precisely. Kant's con-
clusion may be interpreted in either of two ways. The form
of space may precede experience only as a potentiality.
Existing as a power of co-ordination, 3 it will come to con-
sciousness only indirectly through the addition which it
makes to the given sensations. Though subjective in origin,
it will be revealed to the mind only in and through experi-
ence. This view may indeed be reconciled with the terms of
the proof. But a strictly literal interpretation of its actual
wording is more in keeping with what, as we shall find, is
1 ii. p. 165. 2 Cf. above, pp. 85-8.
3 Cf. Dissertation, 15 D : " Space is not anything objective and real. It is
neither substance, nor accident, nor relation, but is subjective and ideal, proceed-
ing by a fixed law from the nature of the mind, and being, as it were, a schema for
co-ordinating, in the manner which it prescribes, all external sensations whatso-
ever." And 15, corollary at end: "Action of the mind co-ordinating its
sensations in accordance with abiding laws."
102 THE TRANSCENDENTAL AESTHETIC
the general trend of the Aesthetic as a whole. We are then
confronted by a very different and extremely paradoxical view^
which may well seem too naive to be accepted by the modern
reader, but which we seem forced, 1 none the less, to regard as
the view actually presented in the text before us. Kant here
asserts, in the most explicit manner, that the mind, in order
to construe sensations in spatial terms, must already be in
possession of a representation of space, and that it is in the
light of this representation that it apprehends sensations.
The conscious representation of space precedes in time ex-
ternal experience. Such, then, would seem to be Kant's first
argument on space. It seeks to establish a negative con-
clusion, viz. that space is not derived from experience. But,
in so doing, it also yields a positive psychological explana-
tion of its origin.
Those commentators 2 who refuse to recognise that Kant's
problem is in any degree psychological, or that Kant himself
so regards it, and who consequently seek to interpret the
Aesthetic from the point of view of certain portions of the
Analytic, give a very different statement of this first argument.
They state it in purely logical terms. 8 Its problem, they
claim, is not that of determining the origin of our representa-
tion of space, but only its logical relation to our specific
sense-experiences. The notion of space in general precedes,
as an indispensable logical presupposition, all particular
specification of the space relation. Consciousness of space as
a whole is not constructed from consciousness of partial
spaces ; on the contrary, the latter is only possible in and
through the former.
Such an argument does of course represent a valuable truth ;
and it alone harmonises with much in Kant's maturer teach-
ing ; 4 but we must not therefore conclude that it is also the
teaching of the Aesthetic. The Critique contains too great
a variety of tendencies, too rich a complexity of issues, to
allow of such simplification. It loses more than it gains by
such rigorous pruning of the luxuriant secondary tendencies
of its exposition and thought. And above all, this procedure
involves the adoption by the commentator of impossible
responsibilities, those of deciding what is essential and valu-
able in Kant's thought and what is irrelevant. The value
1 Especially in view of the third and fourth arguments on space, and of Kant's
teaching in the transcendental exposition.
2 E.g. Cohen, Riehl, Caird, Watson.
3 Cf. Watson, The Philosophy of Kant explained, p. 83: "Kant, therefore,
concludes from the logical priority of space that it is a priori."
4 Upon it Kant bases the assertion that space is an Idea of reason ; cf. above,
pp. 96-8, and below, pp. 165-6, 390-1.
SECOND ARGUMENT ON SPACE 103
and suggestiveness of Kant's philosophy largely consist in his
sincere appreciation of conflicting tendencies, and in his
persistent attempt to reduce them to unity with the least
possible sacrifice. But in any case the logical interpretation
misrepresents this particular argument. Kant is not here dis-
tinguishing between space in general and its specific modifica-
tions. He is maintaining that no space relation can be revealed
in sensation. It is not only that the apprehension of any