KANT'S CRITIQUE OF TELEOLOGY IN BIOLOGICAL EXPLANATION

88 The Unconditioned and the Infinite Series
The explanation of the mere subtlety of the distinction between
infinite and indefinite in the case of a progress also specifies the
conditions under which the distinction is not merely a subtlety:
wherever reason does in fact demand absolute totality, e.g. in a
regress, this distinction must be made. In this case the philosopher
must insist on his distinctions. Kant thereupon proceeds to make
the subtle distinction between the possibility of infinitely regressing
in a series and the infinite possibility of such a regress.
When the whole is empirically given, it is possible to proceed back in the
series of its inner conditions in infinitum. When the whole is not given, but
has first to be given through empirical regress, we can only say that it is
forever possible to proceed to still higher conditions of the series. (B*542)
Kant thus reproduces in the case of the regress precisely the distinction
that he rejected as "subtle" in the case of a progress. In the case
of a regress, where a distinction is made between being able to
ascend indefinitely far and being able to ascend infinitely, the decisive
factor seems to be the question whether or not the series of
conditions is given in empirical intuition:
We answer: when the whole is given in empirical intuition, the regress in the
series of its inner conditions proceeds in infinitum; but when a member only
of the series is given, starting from which the regress has to proceed to
absolute totality, the regress is only of indefinite extent (in indefinitum).
(B*540-1)
However, Kant emphasizes: "In neither case, whether the regress
be in infinitum or in indefinitum, may the series of conditions be
regarded as being given as infinite in the object." (B542) However
unclear Kant's presentation may be, it is obvious that he cannot
have meant that the series of conditions (said to be given in empirical
intuition) is given as a whole to the understanding. We shall
return to particular formulations in the next section.
What Kant is trying to say with these formulations is, I think,
something like the following: We can sensibly distinguish between
denumerating a potentially infinite series of discrete units (e.g. the
natural numbers) and the potentially infinite division of a continuum
(e.g. a line). The natural numbers can be constructed by successive
synthesis or "through repeated addition of the unit to unit"
(B456), but only as many numbers are given in our intuition as have
already been synthetically constructed. However, for a given geometrical
line a similar series can be constructed by successive synthesis,
if the line is divided, if, for instance, first one half is taken,