KANT'S CRITIQUE OF TELEOLOGY IN BIOLOGICAL EXPLANATION

98 Antinomy of Division
Antithesis
No composite thing in the world is made up of simple parts, and there
nowhere exists in the world anything simple. (B463)
The proofs that Kant thereupon provides need not concern us
as proofs; in purely formal terms they wear their invalidity on their
sleeves. Both thesis and antithesis (if we ignore the slight difference
in subject) have the logical form, "All S is P; no S is P". Thus, they
present a textbook case of contrary opposition. Consequently, the
truth of one proposition cannot be inferred from the falsity of the
other. However, the proofs, as the proofs of all the antinomies, are
conducted apagogically and are therefore invalid from the start —
independent of the later critical resolution. We can however reformulate
the antinomy in such a way that it takes on the form of an
apparent contradiction: Some bodies are simple; all bodies are nonsimple
(compounded). To display the similarity to the First Antinomy,
I shall formulate it as follows:
Thesis (affirmative judgment)
(1) The number of parts of a body is finite.
Antithesis (infinite judgment)
(2) The number of parts of a body is infinite.
If we do not want to presuppose that a material body is something
that has a determinate given amount of parts, we could say:
Resolution (negative judgment)
(3) The number of parts of a body is not finite (or infinite).
Kant expresses the state of affairs as follows:
We must therefore say that the number [Menge] of parts in a given appearance
is in itself neither finite nor infinite. For an appearance is not something
existing in itself, and its parts are first given in and through the regress
of the decomposing synthesis, a regress which is never given in absolute
completeness, either as finite or as infinite. (B533)
Kant's resolution of the second antinomy consists in calling the set
of parts indeterminately large: he says, "only the divisibility, i.e. an
in itself absolutely indeterminate number [Menge] of parts is given
— the parts themselves being given and determined only through
the subdivision" (B*554). The division can be continued in infinitum,
although the body need not be said to consist of infinitely many
parts, nor must infinitely many parts already be given. But Kant
nonetheless adheres steadfastly to the proposition that the divisible