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is Kant™s point in line 6, where he claims that for composite substances,
composition is a “contingent relation.” Now if the composition of
composite substances is only a contingent property, then it must be
possible “to remove all composition in thought,” that is, to think
the real in the composition independently of the composite. Once
all composition is abstracted away, according to the argument, all
that remains are non-composite or simple parts. Although not stated
explicitly, the argument would apply to both material and mental
substances.23
The above reasoning is valid only if being “self-subsistent” rules out
all contingent properties. But this is not obvious. From the fact that a
composite of substances must be composed of self-subsistent elements,
it does not follow that these elements could not be composite in
nature. Even if composition is a contingent property, substances could
be irreducibly composite if one conceived of self-subsistent elements
(substances) as possessing contingent properties.
22 Grier points out that despite the similarity to the earlier distinction between analytic and
synthetic wholes, Kant reserves the term “whole” or totum for the world as a whole, which was
the subject of the First Antinomy. The term “composite” or compositum applies generally
to anything in appearance made up of parts. See Grier, Kant™s Doctrine of Transcendental
Illusion, 196.
23 Grier makes this point forcefully. She criticizes Al-Azm for reading the thesis and antithe-
sis arguments as using different notions of substance, the thesis concerning only mate-
rial substance and the antithesis substances generally. See Al-Azm, The Origins of Kant™s
Arguments in the Antinomies, 46ff, and Grier, Kant™s Doctrine of Transcendental Illusion,
196“207.
Transcendental illusion II 241
A different defense is suggested by the second paragraph, where
Kant says it follows that “all things in the world are simple beings,
that composition is only an external state of these beings” (my empha-
sis). He continues: “reason must still think of them as the primary
subjects of all composition and hence think of them prior to it as
simple beings” (A436/B464). This passage appeals to the principle
of the reducibility of relations discussed in the Amphiboly. On this
view, all relations or “external determinations” are reducible to non-
relational or “inner determinations” of things. Although Kant claims
transcendental realists must endorse the reducibility of relations, he
denies that it applies to appearances in space and time. Reading the
thesis proof this way yields a valid argument. Given both that com-
position is a relation among parts and that self-subsistence implies
only non-relational properties, self-subsistent substances must be sim-
ples. A rational metaphysician could avoid the conclusion by deny-
ing either the reducibility of relations or that self-subsistent entities
have only necessary properties. As Grier points out, however, if one
accepts reason™s demand for the unconditioned, the idea of a com-
posite that is not reducible to ultimate, simple parts fails to achieve
closure.24

Antithesis: “No composite thing in the world consists of simple parts,
and nowhere in it does there exist anything simple” (A435/B463). The
¬rst paragraph argues that composites are not composed of simple
parts by locating composites in space:
1. Assume the opposite: suppose substances are composed of simple
parts.
2. Because composition is an “external relation between substances,”
it is possible only in space.
3. By 2, the space occupied by a composite thing must have as many
parts as the thing occupying it.
4. But space is in¬nitely divisible and does not consist of simple parts.
5. Therefore by 3 and 4 every simple part of the composite must
occupy a space.
6. By virtue of occupying space, every simple part contains parts
external to one another.
24 See Grier, Kant™s Doctrine of Transcendental Illusion, 203.
Transcendental illusion II
242
7. Hence every simple part is a composite of real substances.
8. Because 7 is self-contradictory, substances cannot be composed of
simple parts.
By contrast, the proof in the second paragraph that there are no
simples anywhere does not depend on their relation to space, but
rather on the nature of experience in general:
1. Assume that the transcendental idea of the simple applied to
appearances.
2. By 1, the empirical intuition of such an object would have to be
possible.
3. Such an intuition would contain “absolutely no manifold whose
elements are external to one another and bound into a unity”
(A437/B465).
4. Implied: spatial and temporal intuition by its nature contains a
manifold of external elements bound together in a unity.
5. But “this intuition is de¬nitely required for absolute simplicity.”
6. By 4 and 5, the simplicity of anything given in appearance “cannot
be inferred from any perception, whatever it might be.”
7. Therefore nothing simple is given in the world of sense “regarded
as the sum total of all possible experiences.”
Rather than arguing against the existence of indivisible parts, this
second proof claims only that experience could in principle offer
no evidence for their existence. Because appearances are given in
space and time, and because empirical intuition inherently contains a
manifold, intuition could offer no grounds for inferring the simplicity
of anything given in appearance. This argument is aimed against both
material and mental simples.
The ¬rst proof sides with the understanding in locating the world
of appearance in space (and time). Although the proof does not men-
tion matter per se, the ¬rst paragraph of the remark indicates that
the substances under consideration are bodies (A441/B469). As Grier
points out, it is a mistake to interpret the argument as relying on
Kant™s theory in the Aesthetic. It is true that the argument concludes
that there are no simple parts of matter, based on the fact that the
space matter occupies is in¬nitely divisible. But as we shall see, in
his resolution Kant rejects that inference. Unlike Kant, the antithe-
sis assumes that space is transcendentally real, and concludes that
substance in itself is in¬nitely divisible.
Transcendental illusion II 243
In line 2 the proof moves from the claim that composition is an
“external relation” to the claim that composite substances must exist
in space. But the claim in line 6, that the mathematical divisibility
of space entails the real divisibility of whatever occupies it, is not
obviously true. Al-Azm offers two possible defenses. One is to read
the argument as making the Leibnizian point that postulating simples
violates the Principle of Suf¬cient Reason. That is, if one admits that
the real occupying space contains a manifold of external parts, “it
would be simply arbitrary” to stop at a real thing that is indivisible.25
Since the text does not explicitly mention this principle, his second
suggestion looks more promising. According to it, line 6 assumes that
the hypothesized simple parts occupy space “in exactly the same sense
as the composite object itself is said to be in space.”26 It would follow
that all parts reached by division are “external” to each other in the
same sense that the substances making up the composite are external.
Suppose, for example, one explains the spatial extension of matter in
terms of impenetrability. To say that one half of a body occupies a
different space from the other half is to say that the parts bear this
impenetrability relation to one another. If every part of matter bears
this relation to every other part of matter, one can never arrive at a
non-divisible “simple” that stands in no impenetrability relation to
another space-occupying part.27
As the last paragraph of the remark indicates, the second proof is
also aimed against the view that the thinking self is a simple substance.
As we saw in the Paralogisms, Kant™s argument against the simple soul
depends on his idealistic principle that the thinking thing in itself is
not given in experience. Here he wants to show, independently of
transcendental idealism, that philosophers who claim to have imme-
diate awareness of a simple self are mistaken. Given that conclusion,
it is puzzling to ¬nd Kant claiming that nothing in inner sense “could
prove a manifold of elements external to one another, and hence real

25 Al-Azm, The Origins of Kant™s Arguments in the Antinomies, 63“4.
26 Al-Azm, The Origins of Kant™s Arguments in the Antinomies, 61.
27 In the MFNS of 1786, Kant argues for a dynamical theory of matter as composed of centers
of repulsive force. As Michael Friedman explains in his introduction to the translation,
“matter is explicitly taken to be continuous or in¬nitely divisible, and material substance, in
particular, is now characterized precisely by the impossibility of elementary monadic simple
elements.” Theoretical Philosophy after 1781, 174. Contrary to the antithesis argument of the
Second Antinomy, Kant™s theory depends on his transcendental idealism, and the view that
matter is only appearance and not a thing in itself.
Transcendental illusion II
244
composition” (A443/B471; my emphasis). I think his point, however,
is that the data of inner sense cannot be used either for or against
the existence of a simple self. As the stated proof points out, aware-
ness through inner sense is inherently complex and therefore cannot
support the simplicity of mental substance. On the other hand, the
manifold of inner sense cannot prove anything about the subject “con-
sidered externally, as an object of intuition” (A443/B471). In other
words, any conclusion about the real nature of mental substance must
be based on its “external” existence in relation to other things, and
not merely on inner intuition. The point of the second proof is to
refute claims that empirical intuition could support the simplicity of
mental or material substance.


C. The Third Antinomy: freedom and determinism
Thesis: “Causality in accordance with laws of nature is not the only
one from which all the appearances of the world can be derived. It is
also necessary to assume another causality through freedom in order
to explain them” (A444/B472). The premises are contained in the
¬rst paragraph, A444“6/B472“4, and the conclusion is spelled out in
the second:
1. Assume the opposite, that there is only causality “in accordance
with laws of nature.”
2. By 1, “everything that happens presupposes a previous state, upon
which it follows without exception according to a rule.”
3. By 2, this applies to every state of the world-series, and so on ad
in¬nitum.
4. By 3, there is no ¬rst beginning, and thus “no completeness of the
series on the side of the causes descending one from another.”
5. But “the law of nature consists just in this, that nothing happens
without a cause suf¬ciently determined a priori.”
6. Thus the assumption that “all causality is possible only in accor-
dance with laws of nature . . . contradicts itself.”
7. Therefore there must be a causality “through which something hap-
pens without its cause being further determined by another pre-
vious cause, i.e., an absolute causal spontaneity beginning from
itself . . . hence transcendental freedom.”
Transcendental illusion II 245
As the remark points out, the conclusion establishes that there must
be a ¬rst cause that has the spontaneous power to begin the series
of world states. But it also opens up the possibility that there are
spontaneous causes operating within the world-series:
because the faculty of beginning a series in time entirely on its own is thereby
proved . . . now we are permitted also to allow that in the course of the world
different series may begin on their own as far as their causality is concerned,
and to ascribe to the substances in those series the faculty of acting from
freedom. (A450/B478)

The thesis argument aims to prove the existence of transcendental
freedom, or a cause having the power to initiate an event sponta-
neously, without prior determination. But the idea of transcendental
freedom makes possible the concept of free will or practical free-
dom, the power of a rational agent to choose independently of sen-
suous determinations (A533“4/B561“2). The different series within
the world that “begin on their own as far as their causality is con-
cerned” would include consequences ensuing from such free choices.
Since such actions have “natural consequences to in¬nity, there begins
an absolutely new series, even though as far as time is concerned this
occurrence is only the continuation of a previous series” (A450/B478).
According to this conception, the events initiated by the original, tran-
scendentally free occurrence could be either causally determined or
undetermined.
The key to the argument is line 5, that causal determinism requires
that “nothing happens without a cause suf¬ciently determined a pri-
ori.” Clearly this expresses the transcendental demand that causal
explanations terminate in a complete set of suf¬cient conditions for
the given. Only on this assumption can one avoid the possibility of an
in¬nite regress of causal states. What this does, of course, is to turn the
original motive for causal explanations against itself, exploiting the
“inherent tension” in the demands of reason. While admitting that
transcendental freedom cannot be explained, its proponent claims
that this is true of causal connections themselves: “with causality in
accordance with natural laws . . . we do not in any way comprehend
how it is possible for one existence to be posited through another exis-
tence” (A448/B476). So the thesis emphasizes the demand for closure
in the causal series, and concludes that a suf¬cient account requires
Transcendental illusion II
246
a cause not subject to deterministic connections. When challenged
to explain that cause, the proponent claims to be no worse off than
the determinist, since, as Hume demonstrated, there are no a priori
explanations for causal connections.

Antithesis: “There is no freedom, but everything in the world happens
solely in accordance with laws of nature” (A445/B473). This argument
occurs in a very compressed form in the ¬rst paragraph:
1. Assume the opposite, that there is an uncaused beginning to the
causal series of appearances.
2. By 1, there would exist a ¬rst state S1 , with the power to begin abso-
lutely another state S2 , “and hence also a series of its consequences,”
S3, S4, and so on.
3. By 2, the “determination of this spontaneity itself,” the causality of
S1 “will begin absolutely, so that nothing precedes it through which
this occurring action is determined in accordance with constant
laws.”
4. But “a dynamically ¬rst beginning of action presupposes a state
that has no causal connection at all with the cause of the previous
one, i.e., in no way follows from it.”
5. Therefore “transcendental freedom is contrary to the causal law,
and is a combination between the successive states of effective
causes in accordance with which no unity of experience is pos-
sible . . . and hence is an empty thought entity.” (A445“7/B473“5)
Unlike Strawson, who sees the argument simply as endorsing the
universal principle of causality, Al-Azm notes the subtle way it explores
the notion of causal imputation. The point is to show that the idea
of a spontaneously acting cause that initiates a causally determined
series is incoherent. But the argument is not easy to make out. Line
3 states that, by de¬nition, the causal action of the transcendentally
free cause in state S1 is not determined by its antecedent states nor is
it governed by constant laws. The confusion arises with line 4, which
appears to repeat the point in line 3. Al-Azm™s account suggests the
following reconstruction.28 Suppose the dynamical ¬rst beginning of

28 I have simpli¬ed his presentation; see Al-Azm, The Origins of Kant™s Arguments in the Anti-
nomies, 103“5.
Transcendental illusion II 247
action mentioned in line 4 refers to the causality of S2 rather than S1 .
Kant™s point, then, is that the deterministic causality of the series S2 ,
S3 , S4 , . . . is not imputable to its antecedent condition S1 , since S1 acts
spontaneously. Thus there are really two causal ¬rst beginnings here,
the spontaneous action of S1 on S2 , and the deterministic action of
S2 on S3 . Because S1 does not act causally by constant, deterministic
laws, it cannot cause S2 to act causally by constant, deterministic laws.
Thus the concept of a spontaneous cause initiating a deterministic
causal series is incoherent.
As Al-Azm sees it, the argument raises a question about the relation
between the spontaneous act of origination “and the agent presum-
ably ˜responsible™ for that act.”29 This suggests a tactic used by oppo-
nents of free will, who rejected the idea of undetermined choice pre-
cisely because it con¬‚icts with moral responsibility. For a spontaneous,
undetermined choice would be one not connected to antecedent con-
ditions, including the agent™s character. In that case it could not be said
to be the action of the agent. The antithesis argument here makes
the parallel point that to attribute causality to a state presupposes
that it follows from the nature (and antecedents) of the state to act in
that manner. Thus spontaneous causality cannot provide a suf¬cient
explanation of a series of causally determined states.
In the remarks on the antithesis, Kant relates the Third Antinomy
to the First Antinomy. At A449/B477 he points out that the success
of the thesis argument for a ¬rst dynamical state depends on the con-
clusion that there is a ¬rst temporal state of the world. If one admits
that substances have always existed, then “there is no dif¬culty in also
assuming that the change of their states, i.e., the series of their alter-
ations, has always existed, and hence that no ¬rst beginning, whether
mathematical or dynamical, need be sought.” Moreover, the second
paragraph picks up the point stated in the proof at A447/B475, that
admitting transcendental freedom destroys the unity of experience:
For alongside such a lawless faculty of freedom, nature could hardly be
thought any longer, because the laws of the latter would be ceaselessly mod-
i¬ed by the former, and this would render the play of appearances, which in
accordance with mere nature would be regular and uniform, confused and
disconnected. (A451/B479)

29 Al-Azm, The Origins of Kant™s Arguments in the Antinomies, 105.
Transcendental illusion II
248
In other words, the existence of transcendental freedom within
appearances would make nature indeterministic. Not only would
it be impossible to predict the consequences of events, but, as Kant
argued in the Second Analogy, it would be impossible to distinguish
between an event, an objective succession of states, and a subjective
succession of perceptions. Clearly the antithesis position sides with
the principles of the understanding.
On the above reading, the antithesis argument also appeals to the
Principle of Suf¬cient Reason. Only instead of emphasizing suf-
¬ciency in a complete set of conditions, the latter emphasizes a
suf¬cient explanation of deterministic causal connections. Corre-
sponding to each strength is a weakness: the thesis can explain neither
the source of spontaneity nor the relation between spontaneity and
determinism; the antithesis cannot give closure to the causal series.
These corresponding strengths and weaknesses illustrate both the ten-
sion in applying the Principle of Suf¬cient Reason, and the con¬‚ict
between reason and the understanding.

D. The Fourth Antinomy: contingency and necessity
Thesis: “To the world there belongs something that, either as a part
of it or as its cause, is an absolutely necessary being” (A452/B480).
The thesis states that something absolutely necessary exists within
the world. The proof consists of two parts, the ¬rst arguing for an
absolutely necessary being, and the second arguing that this being
must exist in the world. The ¬rst part consists of these steps:
1. The sensible world as the whole of appearances contains a series
of alterations.
2. “Every alteration, however, stands under its condition, which pre-
cedes it in time, and under which it is necessary” (A452/B480).
3. Every given conditioned presupposes a complete series up to the
unconditioned, “which alone is absolutely necessary.”
4. “Thus there must exist something absolutely necessary, if an alter-
ation exists as its consequence.”
The second part argues that this necessary being cannot be outside
the world of appearances:
5. Assume the opposite, that the absolutely necessary being is outside
the world of sense.
Transcendental illusion II 249
6. By 5, the series of alterations in the world “would derive from it,
without this necessary cause itself belonging to the world of sense”
(A452“4/B480“2).
7. But “the beginning of a time-series can be determined only through
what precedes it in time.”
8. By 7, “the supreme condition of the beginning of a series of
changes” must exist in the time before the series comes into exis-
tence.
9. By 8, the absolutely necessary cause of the series “belongs to time,
hence to appearance (in which alone time is possible, as its form);
consequently it cannot be thought as detached from the world of
sense.”
Although the argument seems straightforward, it turns out to be
more complicated than it appears on the surface. The main issue is
how it differs from the Third Antinomy argument for a transcen-
dentally free cause. Commentators such as Kemp Smith and Bennett
claim this proof is redundant, since the necessary being argued for
here is just the ¬rst, uncaused cause at issue in the preceding Anti-
nomy.30 Although the second part suggests this reading, Grier argues
persuasively that the two arguments have different purposes.31 First,
there is the obvious point that the two proofs involve different cat-
egories, the Third Antinomy causality, and the fourth the modal
concepts of necessity and contingency. As Kant explains in discussing
the ontological argument in the next section, the nominal de¬nition
of an absolutely necessary being is one whose non-being is impossible
(A592“3/B620“1). Notice that on this de¬nition, even if the necessary
being exists in time, there could be no time at which it did not exist.
That alone would rule out the idea that it is merely the ¬rst tempo-
ral state of a causal series. The natural application of this notion to
appearances would be to substance: rather than taking the necessary

30 See Kemp Smith, Commentary, 495, and Bennett, Kant™s Dialectic, 241.
31 See Grier, Kant™s Doctrine of Transcendental Illusion, 219“27. I am not as convinced, however,
by her claim that the Third Antinomy also does not involve the notion of a ¬rst causal
state in time. She cites as evidence Kant™s claim in the remark on the thesis that “here we
are talking of an absolute beginning not, as far as time is concerned, but as far as causality
is concerned” (A450/B478). See Grier, 220“1. She is right that the issue there is whether
deterministic causality must be conditioned by transcendental freedom. As we saw above,
however, at least the antithesis position takes the thesis argument to presuppose a ¬rst causal
state in time. Whether she is right about the Third Antinomy, her point seems stronger with
respect to the Fourth.
Transcendental illusion II
250
being as a ¬rst state of the series, it makes more sense to take it as some-
thing substantial existing permanently in time. In fact, in the solution
Kant says, “Here we deal not with unconditioned causality, but with
the unconditioned existence of the substance itself” (A559/B587).
Grier also points out that the references to cause in the Fourth Anti-
nomy can be construed in terms of immanent rather than transitive
causation. As Spinoza distinguished them, transitive causation occurs
between really distinct things, for example in a collision in which one
body causes another to move. An immanent cause, by contrast, is a
ground of something, inseparable from its effect. The numbers 1 and
2 can be seen as the “immanent causes” of the number 4, for exam-
ple, insofar as they are contained in it.32 Thus Grier maintains the
Fourth Antinomy treats necessary existence as the immanent cause of
all contingent existence in appearances rather than a temporally ¬rst,
transitive cause.
The ¬rst part argues directly from the contingency of appearances
to an absolutely necessary being. The description of appearances as a
series of alterations establishes their contingency, since, as line 2 spells
out, an alteration is an event necessitated by a temporally prior con-
dition. Although this presupposes a causal account, what is relevant
to the argument is the contingency. Moreover, we should note that
the necessity obtaining between empirical causes and effects is relative
rather than absolute. That is, if an empirical state follows necessar-
ily from a prior state, then its existence is not absolutely necessary
in Kant™s sense. Line 3 expresses the demand of reason for totality

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