KANT'S CRITIQUE OF TELEOLOGY IN BIOLOGICAL EXPLANATION

Concept of Infinity 89
then 1/3, 1/4, 1/5, etc. Each line arrived at by this procedure was
already given in intuition but not given to the understanding as a
discrete quantity. 40 In both cases we are dealing with a progress so
that it would be a mere "subtlety" to insist that the series of (say)
natural numbers can only be continued in indefinitum. In cosmology
on the other hand, when dealing with the other kind of series,
the regress, there are supposed to be reasons for distinguishing
between the indefinite regress in a series of discrete units and the
infinite regress in a continuum. Kant seems also to be making some
loose correlation between this distinction and that between the category
classes quantity (extensive magnitudes) and quality (intensive
magnitudes). The main purpose of the distinction seems to be to
absolve Kant of the need to call the regress backwards in time
through discrete units potentially infinite if he wants to avoid postulating
a beginning of the world. I shall attempt to apply this distinction
to explain the resolution of the first antinomy.
2) The Antinomy of Time
Earlier in this chapter we saw how T.D. Weldon, fixated on
the name "Empiricism," simply overlooked the rationalist content of
the antithesis position. Most commentators on the antinomies seem
fixated in a similar manner on Kant's denominations, for instance,
on the fact that each thesis and each antithesis is assigned a short
piece of text entitled "Proof." The striking feature of all these proofs
is that they do not at all prove the propositions to which they
attached; rather they refute the corresponding counterproposition.
Every proof provides an argument to refute the counterproposition
and then simply asserts the proposition to be proved. As shown in
the last section, the antinomy consists not so much in the fact that
two apparently contradictory propositions have been proved, but
rather in the fact that they have both been refuted. This is why Kant
can later resolve the antinomy by showing that the opposition is one
of contrariety not contradiction, since both are false. In my discussion
of the first antinomy I shall therefore not examine the proofs as
40 The distinction between counting discrete units and dividing a continuum is
derived from Aristotle. Cf. Physics, bk. 3, chap. 7, 207a33f; cf. Wundt, Kleine
Schriften, 67ff.