KANT'S CRITIQUE OF TELEOLOGY IN BIOLOGICAL EXPLANATION

86 The Unconditioned and the Infinite Series
matical" antinomies. First let me present some examples of the
stylized technical vocabulary:
regress
from the conditioned to
the condition
retreat
ascends
regressive synthesis
on the side of the
conditions
in antecedentia
ascending line
(B438, B539-540)
progress
from the condition to the
conditioned
advance
descends
progressive synthesis
on the side of the
conditioned
in consequentia
descending line
(B438, 539-40)
While Kant is not entirely consistent in his use of this vocabulary
(for instance, he occasionally "advances" through a regress), it
will only then be possible to recognize the problems which force him
to deviate from the paradigm if we first presuppose the rule. Only
then can we distinguish between simple mistakes or infelicities of
presentation and serious difficulties with the material. In particular,
the Second Antinomy, which is essential for the discussion of
the antinomy of judgment in the next chapter, cannot be understood
without clear terminological distinctions. The subsequent analysis
will be carried out in three steps: 1) Kant's distinction between an
infinite and indefinitely continued series will be presented; 2) the
regress in indefinitum will be examined on the example of the question
of the beginning of the world, 3) some structural inconsistencies
involving the second part of the First Antinomy (size of the world)
will be exposed.
The Concept of Infinity
1) In infinitum and in indefinitum
A synthetic series is either finite or infinite in the sense that
the regress or progress in the series is either finite or can be continued
to infinity. The "infinite" of both regress and progress is a
potential infinity. The assertion that such a progress or regress can
be completed, i.e. that the set of elements in the series can actually