Norman Kemp Smith.

A commentary to Kant's 'Critique of pure reason,' online

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teaching, when consistently developed, is bound to lead. For
in insisting that the synthetic character of a judgment need
not render it invalid, and that all the fundamental principles
and most of the derivative judgments of the positive sciences
are of this nature, Kant is really maintaining that the justifica-
tion of a judgment is always to be looked for beyond its own
boundaries in some implied context of coherent experience.
But though the value of his argument lies in clear-sighted
recognition of the synthetic factor in all genuine knowledge,
its cogency is greatly obscured by his continued acceptance
of the possibility of judgments that are purely analytic.
Thus there is little difficulty in detecting the synthetic
character of the proposition : all bodies are heavy. Yet the

1 Leibniz's interpretation of the judgment seems to result in an atomism
which is the conceptual counterpart of his metaphysical monadism (cf. Adamson,
Development of Modern Philosophy, i. p. 77 ff- J an d niy Stiidies in the Cartesian
Philosophy , p. 160 ff. ; also below, p. 603). Each concept is regarded as having
exclusive jurisdiction, so to speak, over a content wholly internal to itself. The
various concepts are like sovereign states with no mediating tribunals capable ol
prescribing to them their mutual dealings. Cf. below, pp. 394-400, 418 ff.


reader has first been required to admit the analytic character
of the proposition : all bodies are extended. The two pro-
positions are really identical in logical character. Neither
can be recognised as true save in terms of a comprehensive
theory of physical existence. If matter must exist in a state
of distribution in order that its parts may acquire through
mutual attraction the property of weight, the size of a body, or
even its possessing any extension whatsoever, may similarly
depend upon specific conditions such as may conceivably not
be universally realised. We find the same difficulty when we
are called upon to decide whether the judgment 7 + 5=12 is
analytic or purely synthetic. Kant speaks as if the concepts
of 7, 5, and 12 were independent entities, each with its own
quite separate connotation. But obviously they can only be
formed in the light of the various connected concepts which go
to constitute our system of numeration. The proposition has
meaning only when interpreted in the light of this conceptual
system. It is not, indeed, a self-evident identical proposition ;
but neither is the connection asserted so entirely synthetic
that intuition will alone account for its possibility. That,
however, brings us to the third main defect in Kant's

When Kant states l that in synthetic judgments we re-
quire, besides the concept of the subject, something else on
which the understanding can rely in knowing that a predicate,
not contained in the concept, nevertheless belongs to it, he
entitles this something x. In the case of empirical judgments,
this x is brute experience. Such judgments, Kant implies,
are merely empirical. No element of necessity is involved,
not even in an indirect manner ; in reference to empirical
judgments there is no problem of a priori synthesis. Now in
formulating the issue in this way, Kant is obscuring the
essential purpose of his whole enquiry. He may, without
essential detriment to his central position, still continue to
preserve a hard-and-fast distinction between analytic and
synthetic judgments. In so doing he is only failing to per-
ceive the ultimate consequences of his final results. But in
viewing empirical judgments as lacking in every element of
necessity, he is destroying the very ground upon which he
professes to base the a priori validity of general principles.
All judgments involve relational factors of an a priori
character. The appeal to experience is the appeal to an
implied system of nature. Only when fitted into the context
yielded by such a system can an empirical proposition have
meaning, and only in the light of such a presupposed system

1 A 9 =B 13.


can its truth be determined. It can be true at all, only if it
can be regarded as necessarily holding, under the same
conditions, for all minds constituted like our own. Assertion
of a contingent relation as in the proposition : this horse
is white is not equivalent to contingency of assertion.
Colour is a variable quality of the genus horse, but in the
individual horse is necessarily determined in some particular
mode. If a horse is naturally white, it is necessarily white.
Though, therefore, in the above proposition, necessity receives
no explicit verbal expression, it is none the less implied.

In other words, the distinction between the empirical and
the a priori is not, as Kant inconsistently assumes in this
Introduction, a distinction between two kinds of synthesis or
judgment, but between two elements inseparably involved in
every judgment. Experience is transcendentally conditioned.
Judgment is in all cases the expression of a relation which
implies an organised system of supporting propositions ; and
for the articulation of this system a priori factors are indis-
pensably necessary.

But the most flagrant example of Kant's failure to live up
to his own Critical principles is to be found in his doctrine of
pure intuition. It represents a position which he adopted in
the pre-Critical period. It is prefigured in Ueber die Deut-
lichkeit der Grundsatze ( 1 764),* and in Von dem ersten Grunde
des Unterschiedes der Gegenden im Raume (I768), 2 and is
definitely expounded in the Dissertation (ly/o). 3 That Kant
continued to hold this doctrine, and that he himself regarded
it as an integral part of his system, does not, of course,
suffice to render it genuinely Critical. As a matter of fact,
it is really as completely inconsistent with his Critical stand-
point as is the view of the empirical proposition which we
have just been considering. An appeal to our fingers or to
points 4 is as little capable, in and by itself, of justifying any
a priori judgment as are the sense-contents of grounding an
empirical judgment. Even when Kant is allowed the benefit
of his own more careful statements, 5 and is taken as asserting
that arithmetical propositions are based on a pure a priori
intuition which can find only approximate expression in
sensuous terms, his statements run counter to the main
tendencies of his Critical teaching, as well as to the recognised
methods of the mathematical sciences. Intuition may, as
Poincar and others have maintained, be an indispensable
element in all mathematical concepts ; it cannot afford proof

1 Erste Betrachtung, 2, 3 ; dritte Betrachtung, I.

2 Cf. below, p. 162. 3 12, 15 C. 4 Cf. B 15-16.
5 Cf. below, p. 128 ff., on Kant's views regarding arithmetical science.


of any general theorem. The conceptual system which directs
our methods of decimal counting is what gives meaning to
the judgment 7+5 = 12; it is also what determines that
judgment as true. The appeal to intuition in numerical
judgments must be regarded only as a means of imaginatively
realising in a concrete form the abstract relations of some
such governing system, or else as a means of detecting
relations not previously known. The last thing in the world
which such a method can yield is universal demonstration.
This is equally evident in regard to geometrical propositions.
That a straight line is the shortest distance between two
points, cannot be proved by any mere appeal to intuition.
The judgment will hold if it can be assumed that space
is Euclidean in character ; and to justify that assumption
it must be shown that Euclidean concepts are adequate to
the interpretation of our intuitional data. Should space
possess a curvature, the above proposition might cease to
be universally valid. Space is not a simple, unanalysable
datum. Though intuitionally apprehended, it demands for its
precise determination the whole body of geometrical science. 1
The comparative simplicity of Kant's intuitional theory
of mathematical science, supported as it is by the seemingly
fundamental distinction between abstract concepts of re-
flective thinking and the construction of concepts 2 in
geometry and arithmetic, has made it intelligible even
to those to whom the very complicated argument of the
Analytic makes no appeal. It would also seem to be in-
separably bound up with what from the popular point of
view is the most striking of all Kant's theoretical doctrines,
namely, his view that space and time are given subjective
forms, and that the assertion of their independent reality
must result in those contradictions to which Kant has given
the title antinomy. For these reasons his intuitional theory
of mathematical science has received attention out of all
proportion to its importance. Its pre-Critical character has
been more or less overlooked, and instead of being interpreted
in the light of Critical principles, it has been allowed to
obscure the sounder teaching of the Analytic. In this matter
Schopenhauer is a chief culprit. He not only takes the
views of mathematical science expounded in the Introduction
and Aesthetic as being in line with Kant's main teaching, but
expounds them in an even more unqualified fashion than does
Kant himself.

1 Cf. below, p. 117 ff., on Kant and modern geometry, and p. 128 ff., on
Kant's views regarding arithmetical science.

2 Cf. below, pp. 131-3, 338-9, 418 ff.


There are thus four main defects in the argument of this
Introduction, regarded as representative of Critical teaching,
(l) Its problems are formulated exclusively in terms of the
attributive judgment ; the other forms of relational judgment
are ignored. (2) It maintains that judgments are either
merely analytic or completely synthetic. (3) It proceeds in
terms of a further division of judgments into those that are
purely empirical and those that are a priori. (4) It seems to
assert that the justification for mathematical judgments is in-
tuitional. All these four positions are in some degree retained
throughout the Critique, but not in the unqualified manner of
this Introduction. In the Analytic, judgment in all its possible
forms is shown to be a synthetic combination of a given
manifold in terms of relational categories. This leads to a
fourfold conclusion. In the first place, judgment must be
regarded as essentially relational. Secondly, the a priori and
the empirical must not be taken as two separate kinds of
knowledge, but as two elements involved in all knowledge.
Thirdly, analysis and synthesis must not be viewed as
co-ordinate processes ; synthesis is the more fundamental ;
it conditions all analysis. And lastly, it must be recog-
nised that nothing is merely given ; intuitional experience,
whether sensuous or a priori, is conditioned by processes
of conceptual interpretation. Though the consequences
which follow from these conclusions, if fully developed,
would carry us far beyond any point which Kant himself
reached in the progressive maturing of his views, the next
immediate steps would still be on the strict lines of the
Critical principles, and would involve the sacrifice only of
such pre-Critical doctrines as that of the intuitive character of
mathematical proof. Such correction of Kant's earlier posi-
tions is the necessary complement of his own final discovery
that sense-intuition is incapable of grounding even the so-
called empirical judgment.

The Introduction to the first edition bears all the signs of
having been written previous to the central portions of the
Analytic^ That it was not, however , written prior to the
Aesthetic seems probable. The opening sections of the
Aesthetic represent what is virtually an independent intro-
duction which takes no account of the preceding argument,
and which redefines terms and distinctions that have already

1 That certain parts of the Introduction were written at different dates is
shown below, pp. 71-2. That other parts may be of similarly composite origin
is always possible. There is, however, no sufficient evidence to establish this
conclusion. Adickes' attempt to do so (K. pp. 35-7 n.} is not convincing.


been dwelt upon. The extensive additions which Kant made
in recasting the Introduction for the second edition are in
many respects a great improvement. In the first edition
Kant had not, except when speaking of the possibility of con-
structing the concepts of mathematical science, referred to the
synthetic character of mathematical judgments. This is now
dwelt upon in adequate detail. Kant's reason for not making
the revision more radical was doubtless his unwillingness to
undertake the still more extensive alterations which this would
have involved. Had he expanded the opening, statement of the
second edition Introduction, that even our empirical knowledge
is a compound of the sensuous and the a priori^ an entirely
new Introduction would have become necessary. The additions
made are therefore only such as will not markedly conflict
with the main tenor of the argument of the first edition.


Treatment of detailed points will be simplified if we now
consider in systematic fashion the many difficulties that
present themselves in connection with Kant's mode of
formulating his central problem : How are synthetic a priori
judgments possible ? This formula is less definite and precise
than would at first sight appear. The central phrase ' syn-
thetic a priori* is sufficiently exact (the meaning to be
attached to the a priori has already been considered 1 ), but
ambiguities of the most various kinds lurk in the seemingly
innocent and simple terms with which the formula begins
and ends :

A. ' How ' has two very different meanings :

(a) How possible = in what manner possible = wie.
(b} How possible = in how far possible, i.e. whether
possible = ob.

In connection with these two meanings of the term ' how,'
we shall have to consider the distinction between the synthetic
method employed in the Critique and the analytic method
employed in the Prolegomena.

B. ' Possible ' has a still wider range of application.
Vaihinger 2 distinguishes within it no less than three pairs
of alternative meanings :

(a) Psychological and logical possibility.

(b) Possibility of explanation and possibility of existence.

(c) Real and ideal possibility.

1 Cf. above, pp. xxxiii ff., 1-2, 26 ff. 2 i. pp. 317 and 450 ff.


A. Kant personally believed that the possibility of valid
a priori synthetic judgment is proved by the existing sciences
of mathematics and physics. And that being so, there were
for Kant two very different methods which could be employed
in accounting for their possibility, the synthetic or progressive,
and the analytic or regressive. The synthetic method would
start from given, ordinary experience (in its simplest form, as
consciousness of time), to discover its conditions, and from
them to prove the validity of knowledge that is a priori. The
analytic method would start " from the sought as if it were
given," that is, from the existence of a priori synthetic judg-
ments, and, assuming them as valid, would determine the con-
ditions under which alone such validity can be possible. The
precise formulation of these two methods, the determination of
their interrelations, of their value and comparative scope, is a
matter of great importance, and must therefore be considered
at some length.

The synthetic method may easily be confounded with the
analytic method. For in the process of its argument it makes
use of analysis. By analysing ordinary experience in the
form in which it is given, it determines (in the Aesthetic and
in the Analytic of Concepts) the fundamental elements of
which knowledge is composed, and the generating conditions
from which it results. From these the validity of the a priori
principles that underlie mathematics and physics can (in the
Analytic of Principles] be directly deduced. The funda-
mental differentiating feature, therefore, of the so-called
synthetic method is not its synthetic procedure, since in great
part, in the solution of the most difficult portion of its task,
it employs an analytic method, but only its attitude towards
the one question of the validity of a priori synthetic know-
ledge. It does not postulate this validity as a premiss, but
proves it as a consequence of conditions which are inde-
pendently established. By a preliminary regress upon the
conditions of our de facto consciousness it acquires data from
which it is enabled to advance by a synthetic, progressive
or deductive procedure to the establishment of the validity
of synthetic a priori judgments. The analytic method, on
the other hand, makes no attempt to prove the validity of
a priori knowledge. It seeks only to discover the condi-
tions under which such knowledge, if granted to exist, can
possess validity, and in the light of which its paradoxical
and apparently contradictory features can be viewed as comple-
mentary to one another. The conditions, thus revealed, will
render the validity of knowledge conceivable, will account
for it once it has been assumed ; but they do not prove it.


The validity is a premiss ; the whole argument rests upon the
assumption of its truth. The conditions are only postulated
as conditions ; and their reality becomes uncertain, if the
validity, which presupposes them, is itself called in question.
Immediately we attempt to reverse the procedure, and to prove
validity from these conditions, our argument must necessarily
adopt the synthetic form ; and that, as has been indicated,
involves the prior application of a very different and much
more thorough process of analysis. The distinction between
the two methods may therefore be stated as follows. In
the synthetic method the grounds which are employed to
explain a priori knowledge are such as also at the same time
suffice to prove its validity. In the analytic method they are
grounds of explanation, but not of proof. They are them-
selves proved only in so far as the assumption of validity is
previously granted.

The analytic procedure which is involved in the complete
synthetic method ought, however, for the sake of clearness,
to be classed as a separate, third, method. And as such I
shall henceforth regard it. It establishes by an independent line
of argument the existence of a priori factors, and also their
objective validity as conditions necessary to the very possi-
bility of experience. So viewed, it is the most important and
the most fundamental of the three methods. The argument
which it embodies constitutes the very heart of the Critique.
It is, indeed, Kant's new transcendental method ; and in the
future, in order to avoid confusion with the analytic method
of the Prolegomena, I shall refer to it always by this title. It
is because the transcendental method is an integral part of the
complete, synthetic method, but cannot be consistently made
a part of the analytic method, that the synthetic method alone
serves as an adequate expression of the Kantian standpoint.
This new transcendental method is proof by reference to the
possibility of experience. Experience is given as psycho-
logical fact. The conditions which can alone account for it,
as psychological fact, also suffice to prove its objective validity ;
but at the same time they limit that validity to the phenomenal

We have next to enquire to what extent these methods
are consistently employed in the Critique. This is a
problem over which there has been much controversy, but
which seems to have been answered in a quite final manner
by Vaihinger. It is universally recognised that the Critique
professes to follow the synthetic method, and that the
Prolegomena, for the sake of a simpler and more popular
form of exposition, adopts the analytic method. How far


these two works live up to their professions, especially the
Critique in its two editions, is the only point really in question.
Vaihinger found two diametrically opposed views dividing
the field. Paulsen, Riehl, and Windelband maintain the view
that Kant starts from the fact that mathematics, pure natural
science, and metaphysics contain synthetic a priori judgments
claiming to be valid. Kant's problem is to test these claims ;
and his answer is that they are valid in mathematics and pure
natural science, but not in metaphysics. Paulsen, and those
who follow him, further contend that in the first edition
this method is in the main consistently held to, but that
in the second edition, owing to the occasional employment
(especially in the Introduction] of the analytic method of the
Prolegomena, the argument is perverted and confused : Kant
assumes what he ought first to have proved. Fischer, on
the other hand, and in a kindred manner also B. Erdmann,
maintain that Kant never actually doubted the validity of
synthetic a priori judgments ; starting from their validity,
in order to explain it, Kant discovers the conditions upon
which it rests, and in so doing is able to show that these
conditions are not of such a character as to justify the
professed judgments of metaphysics.

Vaihinger * combines portions of both views, while com-
pletely accepting neither. Hume's profound influence upon
the development and formulation of Kant's Critical problem
can hardly be exaggerated, but it ought not to prevent us
from realising that this problem, in its first form , was quite in-
dependently discovered. As the letter of 1772 to Herz clearly
shows, 2 Kant was brought to the problem, how an idea in us
can relate to an object, by the inner development of his own
views, through reflection upon the view of thought which he
had developed in the Dissertation of 1770. The conformity
between thought and things is in that letter presented, not as
a sceptical objection, but as an actual fact calling for explana-
tion. He does not ask whether there is such conformity, but
only how it should be possible. Even after the further
complication, that thought is synthetic as well as a priori,
came into view through the influence of Hume, the problem
still continued to present itself to Kant in this non-sceptical
light. And this largely determines the wording of his exposi-
tion, even in passages in which the demands of the synthetic
method are being quite amply fulfilled. Kant, as it would
seem, never himself doubted the validity of the mathematical
sciences. But since their validity is not beyond possible
impeachment, and since metaphysical knowledge, which is

1 i. p. 412 ff. ; cf. p. 388 ff. 2 Cf. below, pp. 219-20.


decidedly questionable, would appear to be of somewhat
similar type, Kant was constrained to recognise that, from
the point of view of strict proof, such assumption of validity
is not really legitimate. Though, therefore, the analytic
method would have resolved Kant's own original difficulty,
only the synthetic method is fully adequate to the situation.

Kant accordingly sets himself to prove that whether or not
we are ready (as he himself is) to recognise the validity of
scientific judgments, the correctness of this assumption can be
firmly established. And being thus able to prove its correct-
ness, he for that very reason does not hesitate to employ it
in his introductory statement. The problem, he says, is that
of ' understanding ' how synthetic a priori judgments can be
valid. A 'difficulty,' a 'mystery,' a 'secret,' lies concealed
in them. How can a predicate be ascribed to a subject
term which does not contain it ? And even more strangely
(if that be possible), how can a priori judgments legislate
for objects which are independent existences? Such judg-
ments, even if valid beyond all disputing, would still call for
explanation. This is, indeed, Kant's original and ground
problem. As already indicated, no one, save only Hume, had
hitherto perceived its significance. Plato, Malebranche, and
Crusius may have dwelt upon it, but only to suggest explana-
tions still stranger and more mystical than the mysterious
fact itself. 1

Paulsen is justified in maintaining that Kant, in both editions
of the Critique, recognises the validity of mathematics and
pure natural science. The fact of their validity is less explicitly
dwelt upon in the first edition, but is none the less taken for
granted. The sections transferred from the Prolegomena to

Online LibraryNorman Kemp SmithA commentary to Kant's 'Critique of pure reason,' → online text (page 10 of 72)