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

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judgments among the propositions to be reckoned with by
the Critique ; and yet in B 4 he speaks of the proposition, all
bodies are heavy, as merely empirical. 3

A criterion. 4 Necessity and universality are valid criteria
of the a priori ( = the non- empirical). This follows from
Kant's view 5 of the empirical as synonymous with the con-
tingent (zufaUig). Experience gives only the actual ; the a
priori alone yields that which cannot be otherwise.

" Necessity and strict universality are thus safe criteria of a priori
knowledge, and are inseparable from one another. But since in the
employment of these criteria the empirical limitation of judgments

1 Cf. also above, pp. 2-3. 2 B 3.

3 Cf Metaphysische Anfangsgrunde, Hauptstiick ii. Lehrs. 8, Zus. 2, in which
elasticity and gravity are spoken of as the only universal properties of matter which
can be apprehended a priori.

4 B 3-4. 5 Cf. above, p. 27






KANT'S A PRIORI NOT LEIBNIZIAN 57

is sometimes more easily shown than their contingency, or since, as
frequently happens, their unlimited universality can be more con-
vincingly proved than their necessity, it is advisable to use the" two
criteria separately, each being by itself infallible." l

Now Kant is here, of course, assuming the main point
to be established, namely, that experience is incapable of
accounting for such universality and necessity as are required
for our knowledge, both ordinary and scientific. We have
already considered this assumption, 2 and have also anticipated
misunderstanding by noting the important qualifications to
which, from Kant's new Critical standpoint, the terms
* necessity ' and ' universality ' become subject. 3 The very
specific meaning in which Kant employs the term a priori
must likewise be borne in mind. Though negatively the a
priori is independent of experience, positively it originates in
our human reason. The necessity and universality which
differentiate the a priori distinguish it only from the humanly
accidental. The a priori has no absolute validity. From a
metaphysical standpoint, it is itself contingent. As already
stated, 4 all truth is for Kant merely de facto. The necessary
is not that which cannot be conceived to be otherwise, nor
is it the unconditioned. Our reason legislates only for the
world of appearance. But as yet Kant gives no hint of this
revolutionary reinterpretation of the rationalist criteria. One
of the chief unfortunate consequences of the employment
in this Introduction of the analytic method of the Prolegomena
is that it tends to mislead the reader by seeming to commit
Kant to a logical a priori of the Leibnizian type.

To show that, if experience is to be possible, [pure a priori
propositions] are indispensable, and so to prove their existence a
priori. 5 At first sight Kant would seem to be here referring
to the alternative synthetic method of procedure, i.e. to the
transcendental proof of the a priori. The next sentence shows,
however, that neither in intention nor in fact is that really so.
He argues only that a priori principles, such as the principle
of causality, are necessary in order to give " certainty " to our
experience ; such a principle must be postulated if inductive
inference is to be valid. Experience could have no [scientific]
certainty, "if all rules according to which it proceeds were them-
selves in turn empirical, and therefore contingent. They could
hardly be regarded as first principles." There is no attempt
here to prove that empirical knowledge as such necessarily
involves the a priori. Also the method of argument, though

1 B 4. 2 Cf. above, pp. xxxiii-iv, 27, 599 ff.

3 Cf. above, pp. xxxv-vi, 30; below, pp. 185-6, 257-9.

4 Loc. cit. 5 B 5.



58 INTRODUCTION

it seeks to establish the necessity of the a priori^ is not tran-
scendental or Critical in character. It is merely a repetition of
the kind of argument which both Hume and Leibniz had
already directed against the sensationalist position. 1 Very
strangely, considering that these sentences have been added
in the second edition, and therefore subsequent to the writing of
the objective deduction, Kant gives no indication of the deeper
problem to which he finally penetrated. The explanation is,
probably, that to do so would have involved the recasting of
the entire Introduction. Even on the briefest reference, the
hard-and-fast distinction between the a priori 'and the empirical,
as two distinct and separate classes of judgment, would have
been undermined, and the reader would have been made to feel
the insufficiency of the analysis upon which it is based. 2 The
existence of the deeper view is betrayed only through careless
employment of the familiar phrase " possibility of experience."
For, as here used, it is not really meant. " Certainty of ex-
perience " a very different matter is the meaning that alone
will properly fit the context.

Reason and understanding. 3 They are here distinguished,
having been hitherto, in A 1-2, employed as synonymous. The
former carries us beyond the field of all possible experience ;
the latter is limited to the world of sense. Thus both Reason
and understanding are here used in their narrowest meaning.

These inevitable problems of pure Reason itself are God, freedom,
and immortality. The science which, with all its methods, is
in its final intention directed solely to the solution of these prob-
lems, is called metaphysics. 4 These sentences are character-
istic of the second edition with its increased emphasis upon
the positive results of the Critique on the one hand, and with
its attitude of increased favour towards transcendent meta-
physics on the other. The one change would seem to be
occasioned by the nature of the criticisms passed upon the
first edition, as, for instance, by Moses Mendelssohn who
describes Kant as " the all-destroyer " (der alles zermalmende}.
The other is due to Kant's preoccupation with the problems
of ethics and of teleology. The above statements are repeated
with even greater emphasis in B 395 n. 5 The definition here
given of metaphysics is not strictly kept to by Kant. As
above noted, 6 Kant really distinguishes within it two forms,
immanent and transcendent. In so doing, however, he still 7
regards transcendent metaphysics as the more important.

1 Cf. above, pp. xxx, 599 ff. 2 Cf. above, pp. 39, 54.

3 A2 = B6. 4 67.

5 Cf. Kritik der Urtheilskraft , 91, W. v. p. 473. Fortschritte, Werke
(Hartenstein), viii. pp. 572-3. 6 Cf. above, pp. 22, 49-50, 52.

7 Cf. Prolegomena, 40 ; Fortschritte, pp. 577-8.



FAILURE OF PHILOSOPHICAL THINKING 59

Immanent metaphysics is chiefly of value as contributing to
the solution of the " inevitable problems of pure Reason."

A 3-4 = B 7-8. The reasons, here cited by Kant, for the
failure of philosophical thinking to recognise the difference
between immanent and transcendent judgments are : (i) the
misunderstood character, and consequent misleading influence,
of a priori mathematical judgments ; (2) the fact that once we
are beyond the sensible sphere, experience can never contradict
us ; (3) natural delight in the apparent enlargement of our
knowledge ; (4) the ease with which logical contradictions
can be avoided ; (5) neglect of the distinction between analytic
and synthetic a priori judgments. Vaihinger points out l that
in the Fortschritte 2 Kant adds a sixth reason confusion of the
concepts of understanding with the Ideas of Reason. Upon
the first of the above reasons the best comment is that of the
Methodology? But the reader must likewise bear in mind that
in B xvi Kant develops his new philosophical method on the
analogy of the mathematical method. The latter is, he claims,
mutatis mutandis, the true method of legitimate speculation,
i.e. of immanent metaphysics. The one essential difference
(as noted by Kant 4 ), which has been overlooked by the dog-
matists, is that philosophy gains its knowledge from concepts,
mathematics from the construction of concepts.

Remain investigations only. 6 Cf. Prolegomena, 35.

The analysis of our concepts of objects. 6 Vaihinger's inter-
pretation, that the concepts here referred to are those which
we " form a priori of things," 7 seems correct. 8 The rationalists
sought to deduce the whole body of rational psychology from
the a priori conception of the soul as a simple substance, and
of rational theology from the a priori conception of God as the
all-perfect Being.

Analytic and synthetic judgments. 9 "All analytic judgments
depend wholly on the law of contradiction, and are in their nature
a priori cognitions, whether the concepts that supply them with
matter be empirical or not For the predicate of an affirmative
analytic judgment is already contained in the concept of the subject,
of which it cannot be denied without contradiction. In the same
way its opposite is necessarily denied of the subject in an analytic,
but negative, judgment by the same law of contradiction. . . . For
this very reason all analytic judgments are a priori even when the
concepts are empirical, as, for example, gold is a yellow metal ; for to
know this I require no experience beyond my concept of gold as a

1 i- P- 238. 2 P. 579.

3 A 712 ff. =B 740 ff. ; cf. also Fortschritte \ p. 522.

4 A 4 = B 8 ; cf. below, p. 563 ff. 6 A 4 = 6 8. 6 A 5 = B 9.

7 Cf. B 18. 8 Cf. above, p. 29. 9 A 6 ff. =B 10 ff.



60 INTRODUCTION

yellow metal : it is, in fact, the very concept, and I need only analyse
it, without looking beyond it elsewhere. . . . [Synthetic judgments,
a posteriori and a priori] agree in this, that they cannot possibly
spring solely from the principle of analysis, the law of contradiction.
They require a quite different principle. From whatever they may be
deduced, the deduction must, it is true, always be in accordance
with the principle of contradiction. For that principle must never
be violated. But at the same time everything cannot be deduced
from it." 1

In A 594 = B 622 analytic judgments are also spoken of
as identical ; but in the Fortschritte 2 this use of terms is
criticised :

"Judgments are analytic if their predicate only represents clearly
(explirite) what was thought obscurely (implicite) in the concept of
the subject, e.g. all bodies are extended. Were we to call such
judgments identical only confusion would result. For identical
judgments contribute nothing to the clearness of the concept, and
that must be the purpose of all judging. Identical judgments are
therefore empty, e.g. all bodies are bodily (or to use another term
material) beings. Analytic judgments do, indeed, ground themselves
upon identity and can be resolved into it; but they are not
identical. For they demand analysis and serve for the explanation
of the concept. In identical judgments, on the other hand, idem
is defined /^r idem, and nothing at all is explained."

Vaihinger 3 cites the following contrasted examples of
analytic and synthetic judgments :

Analytic. (a) Substance is* that which exists only as
subject in which qualities inhere. 4 (&) Every effect has a
cause. 5 (c} Everything conditioned presupposes a condition.

Synthetic. (a) Substance is permanent, (b) Every event
has a cause. 5 (c) Everything conditioned presupposes an
unconditioned.

B 11-12. The first half of this paragraph is transcribed
practically word for word from the Prolegomena? The second
half is a close restatement of an omitted paragraph of the first
edition. The chief addition lies in the concluding statement,
that " experience is itself a synthetic connection of intuitions."
This is in keeping with statements made in the deduction
of the categories in the second edition, 7 and in the paragraph
inserted in the proof of the second analogy in the second
edition. 8 The x has strangely been omitted in the second

1 Prolegomena, 2, , c ; Eng. trans, pp. 15-16. On the connection of mathe-
matical reasoning with the principle of contradiction, cf. below, pp. 64-5.

2 P. 582 ; cf. Logik, 37. 3 ii. p. 257.
4 Prolegomena, 4. 5 Cf. B 290. 6 % 2, c.

7 B 161. 8 B 218.



KANT'S RELATION TO HUME 61

edition in reference to empirical judgments, though retained
in reference to synthetic a priori judgments.

The proposition : everything which happens has its cause. 1
As we have already observed, 2 Hume influenced Kant at two
distinct periods in his philosophical development in 1756-
1763, and again at some time (not quite definitely datable) after
February 1772. The first influence concerned the character
of concrete causal judgments ; the second related to the
causal axiom. Though there are few distinctions which are
more important for understanding the Critique than that of
the difference between these two questions, it has nowhere
been properly emphasised by Kant, and in several of the
references to Hume, which occur in the Critique and in the
Prolegomena, the two problems are confounded in a most un-
fortunate manner. The passages in the Introduction 3 are clear
and unambiguous ; the influence exercised by Hume subse-
quent to February 1772 is quite adequately stated. The causal
axiom claims to be a priori, and is, as Hume asserts, likewise
synthetic. Consequently there are only two alternatives, each
decisive and far-reaching. Either valid a priori synthesis must,
contrary to all previous philosophical belief, be possible, or
" everything which we call metaphysics must turn out to be
a mere delusion of reason." The solution of this problem is
" a question of life and death to metaphysics." To this
appreciation of Hume, Kant adds criticism. Hume did not
sufficiently universalise his problem. Had he done so, he
would have recognised that pure mathematics involves a
priori synthesis no less necessarily than do the metaphysical
disciplines. From denying the possibility of mathematical
science "his good sense would probably have saved him."
Hume's problem, thus viewed, finds its final and complete
expression in the formula : How are synthetic a priori
judgments possible?

In A 760 = B 788 the account differs in two respects :
first, it discusses the metaphysical validity of the causal axiom
as well as its intrinsic possibility as a judgment ; and
secondly, reference is made to the conception of causality as
well as to the axiom. The implied criticism of Hume is
correspondingly modified. Otherwise, it entirely harmonises
with the passages in the Introduction.

"Hume dwelt especially upon the principle of causality, and
quite rightly observed that its truth, and even the objective validity
of the concept of efficient cause in general, is based on no insight,

1 A 9 =Bi 3 .

2 Cf. above, pp. xxv ff., 26 ; below, p. 593 ff. ; cf. Vaihinger, i. p. 340 ff.
3 AQ = B 13, B 11, B 19.



62 INTRODUCTION

i.e. on no a priori knowledge, and that its authority cannot therefore
be ascribed to its necessity, but merely to its general utility in the
course of experience and to a certain subjective necessity which
it thereby acquires, and which he entitles custom. From the
incapacity of our reason to make use of this principle in any
manner that transcends experience he inferred the nullity of all
pretensions of reason to advance beyond the empirical."

Now so far, in these references to Hume, Kant has had
in view only the problems of mathematical and physical
science and of metaphysics. The problems involved in the
possibility of empirical knowledge are left entirely aside.
His account of Hume's position and of his relation to Hume
suffers change immediately these latter problems are raised.
And unfortunately it is a change for the worse. The various
problems treated by Hume are then confounded together,
and the issues are somewhat blurred. Let us take the chief
passages in which this occurs. In A 764 = B 792 ff. Kant gives
the following account of Hume's argument. Hume, recognis-
ing the impossibility of predicting an effect by analysis of
the concept of the cause, or of discovering a cause from the
concept of the effect, viewed all concrete causal judgments
as merely contingent, and therefrom inferred the contingency
of the causal axiom. In so doing Hume, Kant argues,
confuses the legitimate and purely a priori inference from a
given event to some antecedent with the very different infer-
ence, possible only through special experience, to a specific
cause. Now this is an entire misrepresentation of Hume's
real achievement, and may perhaps be explained, at least in
part, as being due to the fact that Kant was acquainted with
Hume's Treatise only through the indirect medium of Beattie's
quotations. Hume committed no such blunder. He clearly
recognised the distinction between the problem of the validity
of the causal axiom and the problem of the validity of concrete
causal judgments. He does not argue from the contingency
of concrete causal laws to the contingency of the universal
principle, but shows, as Kant himself recognises, 1 that the
principle is neither self-evident nor demonstrable a priori.
And as necessity cannot be revealed by experience, neither
is the principle derivable from that source. Consequently,
Hume concludes, it cannot be regarded as objectively valid.
It must be due to a subjective instinct or natural belief.
(The two problems are similarly confounded by Kant in
A 217 = B 264.)

In the Introduction to the Prolegomena there is no such



In AQ = B 13, B ii, B 19.






KANT'S RELATION TO HUME 63

confusion of the two problems, but matters are made even
worse by the omission of all reference to Hume's analysis of
the causal axiom. Only Hume's treatment of the concept of
causality is dwelt upon. This is the more unfortunate, and
has proved the more misleading, in that it is here that Kant
makes his most explicit acknowledgment of his indebtedness to
Hume. In 27 ff. of the Prolegomena both problems reappear,
but are again confounded. The section is preceded by
sentences in which the problem of experience is emphasised ;
and in keeping with these prefatory remarks, Kant represents
" Hume's cruxmetaphysicorum " as concerning only the concept
of causality (viewed as a synthetic, and professedly a priori,
connection between concrete existences). Yet in 30 the
causal axiom is also referred to, and together they are taken
as constituting " Hume's problem."

Now if we bear in mind that Hume awakened Kant to
both problems how a priori knowledge is possible, and how
experience is possible this confusion can easily be under-
stood. Kant had already in the early 'sixties studied Hume
with profound admiration and respect. 1 In the period sub-
sequent to 1772 this admiration had only deepened; and
constantly, as we may believe, Kant had returned with fresh
relish to Hume's masterly analyses of causality and of in-
ductive inference. It is not, therefore, surprising that as the
years passed, and as the other elements in Hume's teaching
revealed to him, through the inner growth of his own views,
their full worth and significance, he should allow the con-
tribution that had more specifically awakened him to fall into
the background, and should, in vague fashion, ascribe to
Hume's teaching as a whole the specific influence which was
really due to one particular part. By 1783, the date of the
Prolegomena, Kant's first enthusiasm over the discovery of
the fundamental problem of a priori synthesis had somewhat
abated, and the problem of experience had more or less taken
its place. This would seem to be the reason why in the Pro-
legomena he thus deals with both aspects of Hume's problem,
and why in so doing he gives a subordinate place to Hume's
treatment of the causal axiom. But though the misunder-
standing may be thus accounted for, it must none the less be
deplored. For the reader is seriously misled, and much that
is central to the Critical philosophy is rendered obscure. The
influence which Kant in the Prolegomena thus ascribes to

1 Cf. Borowski's Darstdlung des Lebens und Charakters Int. Kants
(Hoffmann's edition, 1902), p. 252. The German translation of Hume's Enquiry
concerning the Human Understanding appeared in 1755, an ^ Kant probably made
his first acquaintance with Hume through it. Cf. above, p. xxviii ; below, p. 156.



64 INTRODUCTION

Hume was not that which really awakened him from his
dogmatic slumber, but is in part that which he had assimilated
at least as early as 1763, and in part that which acted upon
him with renewed force when he was struggling (probably
between 1778 and 1780) with the problems involved in the
deduction of the categories. It was Hume's treatment of the
causal axiom, and that alone, which, at some time subsequent
to February 1772, was the really effective influence in pro-
ducing the Copernican change. 1

Purely a priori and out of mere concepts. 2 Vaihinger's
comment seems correct : Kant means only that neither
actual experience nor pure intuition can be resorted to. This
does not contradict the complementary assertion, 3 that the
principle, everything which happens has its cause, can be
known a priori, not immediately from the concepts involved
in it, but only indirectly 4 through the relation of these
concepts to possible experience. " Possible experience," even
though it stands for " something purely contingent," is itself
a concept. Vaihinger 5 quotes Apelt upon this " mysterious "
type of judgment.

"Metaphysics is synthetic knowledge from mere concepts, not
like mathematics from their construction in intuition, and yet these
synthetic propositions cannot be known from bare concepts, i.e.
not analytically. The necessity of the connection in those proposi-
tions is to be apprehended through thought alone, and yet is not
to rest upon the form of thought, the principle of contradiction.
The conception of a kind of knowledge which arises from bare
concepts, and yet is synthetic, eludes our grasp. The problem is :
How can one concept be necessarily connected with another,
without also at the same time being contained in it ? "

The paragraphs in B 14 to B 17 are almost verbal tran-
scripts from Prolegomena^ 2 c y 2 ff.

Mathematical judgments are one and all (insgesammt) syn-
thetic. 6 This assertion is carelessly made, and does not
represent Kant's real view. In B 16 he himself recognises the
existence of analytic mathematical judgments, but unduly
minimises their number and importance.

All mathematical conclusions proceed according to the principle
of contradiction. 7 To the objection made by Paulsen that
Kant, in admitting that mathematical judgments can be
deduced from others by means of the principle of contra-

1 Cf. below, Appendix B, p. 593 ff. 2 A 9 = B 13.

A 733 = 8761. 4 A 7 37-B 7 6 4 .

5 i. p. 291. 6 B 14.
7 B 14. Cf. above, pp. 59-60.



MATHEMATICAL REASONING 65

diction, ought consistently to have recognised as synthetic
only axioms and principles, Vaihinger replies as follows : 1

" The proposition the angles of a triangle are together equal to
two right angles Kant regards as synthetic. It is indeed deduced
from the axiom of parallels (with the aid of auxiliary lines), and to
that extent is understood in accordance with the principle of contra-
diction. . . . The angles in the triangle constitute a special case of
the angles in the parallel lines which are intersected by other lines.
The principle of contradiction thus serves as vehicle in the deduction,
because once the identity of A and A' is recognised, the predicate
b, which belongs to A, must also be ascribed to A". But the pro-
position is not for that reason itself analytic in the Kantian sense.
In the analytic proposition the predicate is derived from the analysis
of the subject concept. But that does not happen in this case.
The synthetic proposition can never be derived in and by itself from
the principle of contradiction ; . . . but only with the aid of that
principle from other propositions. Besides, in this deduction intuition
must always be resorted to ; and that makes an essential difference.
Without it the identity of A and A' cannot become known."

Pure mathematics. 2 " Pure," as thus currently used, is
opposed only to applied, not to empirical. Kant here
arbitrarily reads the latter opposition into it. Under this
guise he begs the point in dispute.

7 + 5 = 12. 3 Though 7 + 5 = 12 expresses an identity or
equality, it is an equality of the objects or magnitudes, 7 + 5
and 12, not of the concepts through which we think them. 4
Analysis of the concepts can never reveal this equality. Only
by constructing the concepts in intuition can it be recognised
by the mind. This example has been already cited in the
first edition. 5 It is further elaborated in the Prolegomena, 2 c,



Online LibraryNorman Kemp SmithA commentary to Kant's 'Critique of pure reason,' → online text (page 12 of 72)