Norman Kemp Smith.

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

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its parts are possible only in the whole, not the whole through
the parts." 1

As Kant further states, he is speaking only of the simples
of the Leibnizian system. This thesis is " the dialectical
principle of monadology." Again in the Observation on the
antithesis, in commenting on the mathematical proof of the
infinite divisibility of matter, Kant even goes so far as to
declare that the argument of the thesis is based on an illegiti-
mate substitution of things in themselves, conceived by the
pure understanding, for the appearances with which alone the
antinomy is concerned. 2

"... it is quite futile to attempt to overthrow, by sophistical
manipulation of purely discursive concepts, the manifest, demon-
strated truth of mathematics."

Antithesis. No composite thing in the world consists of
simple parts, and there nowhere exists in the world anything

Proof. Let us assume the opposite, namely, that a com-
posite thing (as substance) consists of simple parts. As all
external relation, and therefore all composition of substances,
is only possible in space, space must consist of as many parts
as there are parts of the composite that occupies it. Space,
however, does not consist of simple parts, but of spaces. The
simple must therefore occupy a space. Now as everything
real which occupies a space contains in itself a manifold of
constituents external to one another, and therefore is composite,
and as a real composite is not composed of accidents (for
without substance accidents could not be outside one another),
but of substances, the simple would be a substantial composite,
which is self-contradictory.

Criticism. The Leibnizian standpoint is here completely
deserted. Instead of proceeding to demonstrate the direct
opposite of the thesis, Kant in this argument deals with the
extended bodies of empirical intuition. The proof given
ultimately reduces to an argument from the continuous nature
of space to the continuous nature of the matter which occupies
it. But as the thesis and the antithesis thus refer to different
realities, the former to things in themselves conceived by pure
understanding, and the latter to the sensuous, no antinomy

1 A 438 = B 466. 2 A 439-41 = B 467-9.


is been shown to subsist. Antinomy presupposes that both
the opposing assertions have the same reference. Kant, as
^already noted, argues in the Observation to this antithesis that
% all attempts " made by the monadists " to refute the mathe-
matical proof of the infinite divisibility of matter are quite
futile, and are due to their forgetting that in this discussion
we are concerned only with appearances.

" The monadists have, indeed, been sufficiently acute to seek to
avoid this difficulty by not treating space as a condition of the
possibility of the objects of outer intuition (bodies), but by taking these
and the dynamical relation of substances as the condition of the
possibility of space. But we have a concept of bodies only as
appearances, and as such they necessarily presuppose space as the
condition of the possibility of all outer appearance." l

How Kant, after writing these words, should still have left
standing the proof which he has given of the thesis may
be partially explained as due to the continuing influence of
his earlier view, 2 according to which antinomy represents not
a conflict between opposing views of the world of ordinary
consciousness, but between the demands of pure thought and
the forms of sensuous existence. That older view of antinomy
here gains the upper hand, notwithstanding its lack of agree-
ment with the general scheme of the Dialectic.

There is a further inconsistency in Kant's procedure which
may perhaps be taken as indicating the early origin of this
portion of the Critique. He presents the mathematical proof
of the continuity of matter as conclusive. Yet in the Meta-
physical First Principles of Natural Science (1786) he most
emphatically states that " the infinite divisibility of matter
is very far from being proved through proof of the infinite
divisibility of space." 3

Russell, 4 in discussing the thesis and antithesis on their
merits, from the point of view of certain present-day mathe-
matical theories, makes the following criticism of Kant's

" Here, again, the argument applies to things in space and time,
and to all collections, whether existent or not. . . . And with this
extension 5 the proof of the proposition must, I think, be admitted ;
only that terms or co?icepts should be substituted for substances, and
that, instead of the argument that relations between substances are
accidental (zufdllig\ we should content ourselves with saying that
relations imply terms and complexity implies relations."

1 A 441 = B 469. 2 Developed in the Dissertation (1770).

3 Zweites Hauptstiick, Lehrsatz 4, Anmerkung I. Cf. also Anmerkung 2.

4 Principles of Mathematics, i. p. 460. 5 Cf. above, p. 481 n. 2.


Russell further argues that Kant's assumption in the anti-
thesis, that " space does not consist of simple parts, but of
spaces," cannot be granted. It

"... involves a covert use of the axiom of finitude, i.e. the axiom
that, if a space does consist of points, it must consist of some finite
number of points. When once this is denied, we may admit that no
finite number of divisions of a space will lead to points, while yet
holding every space to be composed of points. A finite space is
a whole consisting of simple parts, but not of any finite number of
simple parts. Exactly the same thing is true of the stretch between
i and 2. Thus the antinomy is not specially spatial, and any
answer which is applicable in Arithmetic is applicable here also.
The thesis, which is an essential postulate of Logic, should be
accepted, while the antithesis should be rejected."

But, as above observed, 1 those mathematicians who adopt
this view so alter the meaning of the term point that it would
perhaps be equally true to say that the thesis, as thus inter-
preted by Russell, coincides with what Kant believes himself
to be asserting in the antithesis.


Thesis. Causality according to the laws of nature is not
the only causality from which the appearances of the world
can be deduced. There is also required for their explanation
another, that of freedom.

Proof. Let us assume the opposite. In that case every-
thing that happens presupposes a previous state upon which
it follows according to a rule. That previous state is itself
caused in similar fashion, and so on in infinitum. But if every-
thing thus happens according to the mere laws of nature,
there can never be a first beginning, and therefore no com-
pleteness of the series on the side of the derivative causes.
But the law of nature is that nothing happens without a
cause sufficiently determined a priori. If, therefore, all causality
is possible only according to the laws of nature, the principle
contradicts itself when taken in unlimited universality. Such
causality cannot therefore be the sole causality possible. We
must admit an absolute spontaneity, whereby a series of
appearances, that proceed according to laws of nature, begins
by itself.

Criticism. The vital point of this argument lies in the
assertion that the principle of causality calls for a sufficient
cause for each event, and that such sufficiency is not to be

1 P. 489 n.


found in natural causes which are themselves derivative or
conditioned. As the antecedent series of causes for an event
can never be traced back to a first cause, it can never be
completed, and can never, therefore, be sufficient to account
for the event under consideration. Either, therefore, the
principle of causality contradicts itself, or some form of free
self-originative causality must be postulated. This argument
cannot be accepted as valid. Each natural cause is sufficient
to account for its effect. That is to say, the causation is
sufficient at each stage. That the series of antecedent causes
cannot be completed is due to its actual infinitude, not to any
insufficiency in the causality which it embodies. 1 To prove
his point, Kant would have to show that the conception of
the actual infinite is inherently self-contradictory ; and that,
as we have already noted, he does not mean to assert. His
argument here lies open to the same criticism as we have
already passed upon his argument in proof of the thesis of the
first antinomy.

Antithesis. There is no freedom ; everything in the world
proceeds solely in accordance with laws of nature.

Proof. Let us assume the opposite. Free causality, i.e.
the power of absolute origination, presupposes the possibility
of a state of the cause which has no causal connection with
its preceding state, and which does not follow from it. But
this is opposed to the law of causality, and would render unity
of experience impossible. Freedom is therefore an empty
thought-entity (Gedank ending] > and is not to be met with in
any experience.

1 Cf. Schopenhauer, World as Will and Idea ( Werke, Frauenstadt, ii. p. 590 ;
Eng. trans, ii. pp. 111-12). "The argument for the third thesis is a very fine
sophism, and is really Kant's pretended principle of pure reason itself entirely
unadulterated and unchanged. It tries to prove the finiteness of the series of
causes by saying that, in order to be sufficient, a cause must contain the complete
sum of the conditions from which the succeeding state, the effect, proceeds. For
the completeness of the determinations present together in the state which is the
cause, the argument now substitutes the completeness of the series of causes by
which that state itself was brought to actuality ; and because completeness pre-
supposes the condition of being rounded off or closed in, and . this again pre-
supposes finiteness, the argument infers from this a first cause, closing the series
and therefore unconditioned. But the juggling is obvious. In order to conceive
the state A as the sufficient cause of the state B, I assume that it contains the sum
of the necessary determinations from the coexistence of which the state B
inevitably follows. Now by this my demand upon it as a sufficient cause is
entirely satisfied, and has no direct connection with the question how the state
A itself came to be ; this rather belongs to an entirely different consideration, in
which I regard the said state A no more as cause, but as itself an effect ; in which
case another state again must be related to it, just as it was related to B. The
assumption of the finiteness of the series of causes and effects, and accordingly of
a first beginning, appears nowhere in this as necessary, any more than the
presentness of the present moment requires us to assume a beginning of time


Criticism. We may first observe the strange relation in
which the proof of the thesis stands to that of the antithesis.
According to the former, freedom must be postulated because
otherwise the principle of causality would contradict itself.
According to the latter, freedom is impossible, and for the
same reason. Now, as Erhardt has pointed out, 1 a principle
cannot be reconciled with itself through the making of an
assumption which contradicts it. That would only be the
institution of a second contradiction, not the removal of the
previous conflict. If the proof of the thesis be correct, that
of the antithesis must be false ; if the proof of the antithesis
be correct, that of the thesis must be invalid. For though
the thesis and the antithesis may themselves contradict one
another, such conflict must not exist between the grounds
upon which they establish themselves. If the reasons cited
in their support are contradictory of one another, the total
argument is rendered null and void. The supporting proofs
being contradictory of one another, nothing whatsoever has
been established. There will remain as a pressing and im-
mediate problem the task of distinguishing the truth from
among the competing alternatives ; and until this has been
done, the argument cannot proceed. The assumption of
freedom either does or does not contradict the principle of
causality. Antinomy is not the simple assertion that both A
and not-A are true, but that A and not-A, though contradictory
of one another, can both be established by arguments in which
such contradiction does not occur. 2

The proof given of the thesis would seem, as already
noted, to be untenable. The principle of natural causality is
not self-contradictory. What now is to be said regarding the
proof of the antithesis? If the principle of natural causality
be formulated as asserting that every event has an antecedent
cause determining it to exist, then certainly free, spontaneous,
or self-originating causality is excluded. Here, as in Kant's
proof of the antithesis of the first antinomy, everything
depends upon definition of the terms employed. It must be
borne in mind that the antinomies are asserted to exist only
on the dogmatic level. Critical considerations must not,
therefore, be allowed to intervene. Now for ordinary con-
sciousness the concept of causality has a very indefinite mean-
ing, and a very wide application. Causation may be spon-
taneous as well as mechanical, spiritual as well as material.
All possibilities lie open, and no mere reference to the concept
of causal dependence suffices to decide between them. Free

1 Op. cit. p. 24.
2 For comment upon Kant's defence of his procedure cf. below, p. 496.


causality, so far as dogmatic analysis of the causal postulate
can show to the contrary, may or may not be possible. 1
Kant has failed to establish the antithesis save by the sur-
reptitious introduction of conclusions which presuppose the
truth of his Critical teaching. This is especially shown in
the emphasis laid upon 'unity of experience.' The further
statement 2 that freedom means lawlessness is only true if
Kant's teaching is mutilated by reduction merely to its as-
sertion of the objective validity of the mechanistic principles
of natural science. Kant is both running with the hare and
hunting with the hounds.

Though this antinomy is chiefly concerned with the
problem of freedom, i.e. of spontaneous origination within
the world, the proof of the thesis refers only to the cosmo-
logical problem of a first cause. 3 The reasons of this oscillation
we shall have occasion to consider in dealing with the fourth
antinomy. The terms world and nature play the same
ambiguous part as in the antithesis of the first antinomy ;
they tend to be employed in the narrower, mechanistic sense
of Kant's own Critical teaching.


As the proofs of the thesis and antithesis proceed on lines
identical with those of the third antinomy, I shall omit
detailed statement of them. 4 Kant again argues from the
fact that every change has a condition which precedes it in
time. There is no difference in the proofs themselves, but
only in the nature of the inference which they are made to
support. In the third antinomy they lead to the assertion
and denial of free causality ; in the fourth antinomy they lead
to the assertion and denial of an absolutely necessary being.
The assertion is required in order to save the principle of
causality from self-contradiction ; the denial is also necessary,
and for the same reason. The illegitimacy of this procedure
has already been pointed out. 5 Though the thesis and the
antithesis will, if antinomy be assumed to represent an actual

1 Cf. Kant's Observation on the thesis.

2 A 451 = 6479. 3 Cf. also A 451 = 6479.

4 Cf. Schopenhauer, op. cit. p. 591 ; Eng. trans, p. 113. "The fourth con-
flict is ... really tautological with the third ; and the proof of the thesis is also
essentially the same as that of the preceding one. Kant's assertion that every
conditioned presupposes a complete series of conditions, and therefore a series
which ends with an unconditioned, is a petitio principii which must simply be
denied. Everything conditioned presupposes nothing but its condition ; that this
is again conditioned raises a new consideration which is not directly contained in
the first." s Above, p. 494.


conflict, contradict one another, no such conflict is allowable
in the grounds which profess to establish them. We must
not assert, as argument, that both A and not-A are true.

In the Observation on the antithesis 1 Kant has himself
taken notice of this " strange " situation.

" From the same ground on which, in the thesis, the existence
of an original being was inferred, its non-existence is inferred, and
that with equal stringency."

A necessary being is inferred to exist, because the past
series of events cannot contain all the conditions of an event,
unless the unconditioned is to be found among them. A
necessary being is denied to exist, because the series of merely
conditioned events contains all the conditions that there are.
Kant's defence of this procedure is as follows :

" Nevertheless, the method of argument in both cases is entirely
in conformity even with ordinary human reason, which frequently
falls into conflict with itself from considering its object from two
different points of view. M. de Mairan 2 regarded the controversy
between two famous astronomers, which arose from a similar difficulty
in regard to choice of standpoint, as a sufficiently remarkable pheno-
menon to justify his writing a special treatise upon it. The one had
argued that the moon revolves on its own axis, because it always turns
the same side towards the earth. The other drew the opposite con-
clusion that the moon does not revolve on its own axis, because it
always turns the same side towards the earth. Both inferences were
correct, according to the point of view which each chose in observing
the moon's motion."

This example is not really relevant. In spite of Kant's
assertion to the contrary, the point of view is one and the
same in thesis and in antithesis. In both cases the absolutely
necessary being is viewed as the first of the changes in the
world of sense. To maintain that when thus viewed it both
is and is not demanded by the law of causality, is as impossible
as to assert that in one and the same meaning of our terms
the moon both does and does not revolve on its own axis.

That the proofs of the fourth antinomy are identical with
those of the third is due to the fact that Kant, under the
stress of his architectonic, 3 is striving to construct four
antinomies while only three are really distinguishable. The
third and fourth antinomies coincide as formulations of
the problem whether or not the conditioned implies, and

1 A 459 =B 487.

2 Jean Jacques Dortous de Mairan (1678-1771), physicist and mathematician.
In 1740 he succeeded Fontenelle as perpetual Secretary of the French Academy of
Sciences. 3 Cf. above, pp. 435, 495 n. 4.


originates in, the unconditioned. The precise determination
of this unconditioned, whether as free causality or as a
necessary being, or in any other way, is a further problem,
and does not properly fall within the scope of the cosmological
inquiries, which are alone in place in this division of the

The manner in which Kant, in treating of freedom,
makes the transition J from the cosmological (or theological)
unconditioned to the psychological is significant. The
cosmological unconditioned is proved to exist by the argu-
ment of the thesis, and its existence is at once interpreted as
establishing at least in this one case the actuality of free
spontaneous causality. Kant remarks that this

"... transcendental Idea of freedom does not by any means
constitute the entire content of the psychological concept of that
name, which is mainly empirical, but only that of absolute spontaneity
of action. . . . The necessity of a first beginning, due to freedom,
of a series of appearances we have demonstrated only in so far as
it is required for the conceivability of an origin of the world. . . .
But as, after all, the power of spontaneously originating a series in
time has thus been proved (though not understood), it is now per-
missible for us to admit within the course of the world different
series as capable in their causality of beginning of themselves, and
so to attribute to their substances a power of acting from freedom."

That each such successive series in the world can only
have a relatively primary beginning, and must always be
preceded by some other state of things, is no sufficient
objection to such causality.

" For we are here speaking of an absolutely first beginning not
in time, but in causality. If, for instance, I at this moment arise
from my chair in complete freedom, without being necessarily
determined thereto by the influence of natural causes, a new series,
with all its natural consequences in infinitum, has its absolute
beginning in this event, although the event itself is only, with regard
to time, the continuation of a preceding series."

Thus Kant's proof of freedom in the thesis of the third
antinomy is merely a corollary from his proof of the existence
of a cosmological or theological unconditioned ; and further,
this freedom is not, like the cosmological unconditioned, proved
to exist, but only to be " admissible " as a possibility. Similarly
in the antithesis, the only disproof of freedom is the disproof
of unconditioned causality in general. The antinomy deals
with the general opposition and relation between the con-
tingent and the unconditioned.

1 A 448-50 = B 476-8.

2 K


It is this same opposition exactly which constitutes the
subject-matter of the fourth antinomy. The terms used are
different, but their meanings are one and the same. For
though Kant substitutes * absolutely necessary being ' . for
' unconditioned causality,' the former is still conceived as
belonging to the world of sense, as the unconditioned origin
of its changes. And as Kant is careful to add, only the
causal, cosmological argument can be employed to establish
the existence of an absolutely necessary being ; nothing can
legitimately be inferred from the mere Idea. The verbal
change is consequently verbal only ; the argument of the
fourth antinomy coincides in result no less than in method
of proof with the argument of the third. It is impossible to
define the unconditioned in any more specific fashion save
by an enquiry which entirely transcends the scope of the
argument that Kant is here presenting. Kant's procedure
also lies open to the further objection that the conception
of an absolutely necessary being, which he here introduces
without preliminary analysis or explanation, is later shown
by him l to be devoid of significance. He employs it,
but precludes himself from either investigating it or from
drawing any serviceable consequences from it. The situa-
tion is not without the elements of comedy. In order to
seem to mark a real distinction between the fourth and the
third antinomies, Kant has perforce to trespass upon the
domain of theology ; but as he is aware that the trespass is
forbidden, he seeks to mitigate the offence by returning from
the foray empty-handed. To such unhappy straits is he
again reduced by his over-fond devotion to architectonic.



This section, though extremely important, requires no
lengthy comment. It is lucid and straightforward. It may
be summarised as follows. The theses and the antitheses
rest upon diverse and conflicting interests. The theses,
though expressed in dry formulas, divested of the empirical
features through which alone their true grandeur can be dis-
played, represent the proud pretensions of dogmatic Reason.
The antitheses give expression to principles of pure empiricism.
The former are supported by interests of a practical and

1 Cf. above, p. 427 ff. ; below, pp. 520-1, 527-37, 541 ff. 2 A 462 = 6 490.


popular character : upon them morals and religion are based.
The latter, while conflicting with our spiritual interests, far
exceed the theses in their intellectual advantages. This

"... the zelotic passion of the one party, and the calm assurance of
the other, and why the world hails the one with eager approval,
and is implacably prejudiced against the other."

No legitimate objection could be raised against the
principles of the empirical philosopher, if he sought only
to rebuke the rashness and presumption of Reason when it

Online LibraryNorman Kemp SmithA commentary to Kant's 'Critique of pure reason,' → online text (page 59 of 72)