The doctrine of simple substances was fundamental to the Leibniz-Wolff metaphysics. Leibniz's monads provided an alternative to atomism, and thus to materialism. Although Kant was opposed to materialism and denied that there are material atoms, at the same time he rejected the argument Leibniz had used to establish the existence of monads or immaterial atoms. Examination of this argument reveals Kant's general strategy in dealing with the claims of transcendent metaphysics. It may also be interesting to compare Kant's treatment of the part/whole relation with recent mereology.
The Second Antinomy concerns "the parts of a given whole" (A418/B446) and its Thesis claims that among those parts must be simple parts, that is, parts which have no parts of their own. If parts are to be found, it is through the division of the whole. This division may be made physically, but it may also be made in thought. Reason demands that the division be completed, i.e., each part must be divided until there is nothing that can be divided any further. "Its internal conditions are its parts, and the parts of these parts remote conditions. Thus there occurs a regressive synthesis, the absolute totality of which is demanded by reason" (A413/B440). The given whole in question is a whole in appearance, rather than a thing in general (A416/B443). What is given in appearance is matter. One way of completing the synthesis is to arrive at "what is no longer matter -- namely, the simple" (A413/B440). This is the approach taken in the Thesis of the Second Antinomy.
The argument concerns the division of composite substances. A characteristic of substance is that it is a self-subsistent being. If it stands in relation to other substances to make up a composite, this relation is only accidental. The composite depends on the substantial parts, but the parts do not depend on the composite. Thus in the "Observation," Kant states that "a substantial whole . . . is composite in the strict sense of the term 'composite', that is, . . . that accidental unity of the manifold which, given as separate (at least in thought) is brought into a mutual connection, and thereby constitutes a unity" (A438/B466).
We suppose that there is a composite substance S which has no simple parts. The parts of S thus are one and all composite, as are their parts, and so on. If all composition is removed in thought, then nothing remains of the original. (As Kant had stated earlier, "the reality of matter . . . vanishes . . . into nothing" (A440/B413).) If nothing remains, then there are no substances which could serve as parts from which the original is composed, in which case the supposition that S is a composite substance is undermined. As Kant stated in the "Solution," "The assertion that if all compositeness of matter be thought away nothing at all will remain, does not appear to be compatible with the concept of a substance which is meant to be the subject of all compositeness" (A525/B553). Thus there is no composite which lacks simple parts. As the Thesis states, "every composite substance in the world is made of simple parts."
The Thesis contains a corollary, "nothing anywhere exists save the simple or what is composed of the simple." If an existing thing is not simple, it is a composite substance whose ultimate parts are simples. Even if reason is unable to discover the simples themselves, it "must think them as the primary subjects of all composition, and therefore, as simple beings, prior to all composition" (A436/B464).
Kant claimed that the problem with the argument of the Thesis is that it depends on the assumption that the given whole with which it starts is a thing in itself. In the statement of the argument, it was claimed that if all composition is removed in thought, there are no parts which together could make up a composite substance. For things in themselves, the parts are given when the whole is given. As a thing in itself, a substance is "the subject of all compositeness . . . which must persist in the elements of the composite" even if we must think it as non-spatial" (A525/B553). For appearances, the parts are given only insofar as the whole is decomposed into them. "For an appearance is not something existing in itself, and its parts are first given in and through the regress of the decomposing synthesis" (A505/B533). If we cannot arrive at a simple in the decomposition of appearances, then the decomposition proceeds to infinity. This holds for material things, because they are spatial, and space is divisible to infinity. So as extended, any given material thing is infinitely divisible. (Note that this is a difference from the First Antinomy, where the order of things in space and time is only indefinitely extensible. The reason is that this order is not given as a whole, but only composed; while in the Second Antinomy there is a given whole which is decomposed.) However, it is not composed of infinitely many parts, since the division is never completed, but only set as a task. "Only the divisibility . . . is given -- the parts themselves being given and determined only through the subdivision. In a word, the whole is not in itself already divided" (A526/B554).
It appears that there is no room for simplicity at all in the world of appearances. One cannot, in fact, remove all compositeness in thought from a given material thing. Each decomposition reveals another composite. This holds for material things as continuous quantities, i.e., merely as extended things, without taking into account their organization. But if we view them as discrete quantites, as being made up of definite parts (e.g. organs of an animal bodies or movements in a watch), then we may not suppose that there is an infinite regress of division. We must be prepared to find inorganic parts of organic wholes, for example.
In fact, to think that an organized body is infinitely divisible into organized parts is contradictory in the manner of the original argument. "In the case of an organic body conceived as organized in infinitum the whole is represented as already divided into parts, and as yielding to us prior to all regress, a determinate and yet infinite number of parts. This, however, is self-contradictory" (A526-7/B554-5). The notion of an organic body shares with that of a thing in itself the assumption that the parts are prior to the whole. As a result, "To view any thing as a quantum discretum, is to take the number of units in it as being determined, and therefore as being in every case equal to some number" (A527/B555).
Leibniz had given a straightforward argument for the existence of simple substances. "And there must be simple substances, since there are composites; for the composite is nothing more than a collection, or aggregate, of simples" ("Monadology," Section 2). This argument is based on a definition of 'composite,' and hence the proposition that there are simples follows analytically from the premise that there are composites. There seems to be a deficiency in this argument, however, because there is no reason given to support the claim that the simples which make up composites are simple substances (monads). All we get is another definition of 'monad' as "a simple substance that enters into composites -- simple, that is, without parts" ("Monadology," Section 1).
Baumgarten's version of the Thesis argument (Metaphysica, Sections 230-233) supplement's Leibniz's by appealing to the definitions of 'substance' and its complement 'accident.' It goes as follows: A substantial composite is defined as being composed of parts which are outside one another. The only things that could serve as parts, which really are outside one another are substances. This is because the only other possibility is that they be accidents; but accidents are in substances rather than outside substances. In fact, composite substances are strictly speaking not substances at all, for they depend on other things (the substances of which they are composed). They are merely apparent substances. Strictly speaking, they are accidents. Thus the only real substances are not composite, and what is not composite is simple, so the only real substances are simple.
Kant's reconstruction includes consideration of the notions of substance and accident. If one tries to think away all compositeness, then one either fails in the attempt or one ends up with simples. If one were to succeed in thinking away all compositeness without arriving at simples, there would be nothing of which the composites are composed. This much follows Leibniz. But Kant tries to back up this claim with the assertion that "composition, as applied to substances, is only an accidental relation in independence of which they must still persist as self-subsistent beings" (A435-6/B463-4).
Kant's presentation of the argument is very poor. The conclusion, as stated in the body of the argument, is that "a composite of substances in the world is made up of simple parts" (A436/B464). Yet the Thesis statement is that "every composite substance in the world is made up of simple parts." The key premise is that if one cannot remove all composition, then "the composite would not be made of substances," which does indeed contradict the supposition that there is a composite of substances. "Composition, as applied to substances, is only an accidental relation in independence of which they must still persist as self-subsistent beings" (A436/B464). But does the removal in thought of all composition contradict the supposition that there are composite substances? Only if a composite substance can only be a composite of substances. Baumgarten had made an argument for the connection, but in Kant it is stated nearly one hundred pages after the argument is given. The concept of substance "is meant to be the subject of all compositeness" (A525/B553). But this simply defines the substantial as the simple.
Kant did not Baumgarten's argument directly. The reason, I believe, is that he regarded it as sound when applied to things in themselves. His approach is to claim that the argument does not apply to appearances, which as spatial things are infinitely divisible. When one thinks away all compositeness in matter, there is nothing left, there is no simple. So it is possible to think away all compositeness, only not all substantial compositeness. But why not? The only thing standing in the way is definitional, and one must wonder why Kant was so willing to accept the definitions given by Baumgarten as of any consequence at all.