KANT'S CRITIQUE OF TELEOLOGY IN BIOLOGICAL EXPLANATION

If , however, we replace (2) with the infinite judgment:
3a) The world is non-infinite (i.e. finite),
Tertium datur 77
we obtain a contrary opposition because (3a) says "more" than is
necessary for contradiction with (1). The Law of the Excluded
Middle applies to the conjunction of (3) and (1) — and (1) and (3a) —
only if the world belongs to the genus of things that have a
determinate size, either finite or infinite. Kant maintains that in
order to have some determinate or definite magnitude, the world as
a whole would have to be able to be given as a totality — which, he
maintains, could occur only if it were a thing in itself. Thus only on
the assumption that the world is a thing in itself does the thesis of
the First Antinomy contradict the antithesis in the strict sense. If I
deny this assumption, then the two propositions turn out to be mere
contraries. 36
If, therefore, we say, "the world is either infinite in extension or it is not
infinite (non est infinitus)," and if the former proposition is false, its contradictory
opposite, "the world is not infinite," must be true. And I should thus
remove [aufheben] an infinite world, without positing [setzen] another,
namely, a finite world. But if we had said, "the world is either infinite or
finite (non-infinite)," both statements might be false. For in that case we
should be regarding the world in itself as determined in its magnitude, and
in the counterproposition we do not merely remove the infinitude, and with
it perhaps the entire separate existence of the world, but attach a determination
to the world as a thing real in itself. This assertion may, however,
likewise be false, if, namely, the world is not given as a thing in itself at all
and thus not given as either infinite or finite with regard to size. I beg permission
to entitle this kind of opposition dialectical opposition, and that of
contradiction analytical opposition. Thus of two dialectically opposed
judgments both may be false due to the fact that the one does not merely
contradict the other, but says something more than is required for contradiction.
(B*531-2)
36 Wolff interprets this passage as follows. "Kant thus maintains that the relation
of the predicates 'infinite' and 'finite' is always contrary, while the relation
of the predicates 'infinite' and 'not infinite' is always contradictory. Kant seems
once again to attempt to base the contrariety between 'finite' and 'infinite'
independent of context on purely linguistic critieria." (Der Begriff, 54) While it is
true that Kant does indeed try to base the opposition of these predicates on purely
linguistic criteria, 1) both pairs of oppositions are considered to be 'contradictory';
2) Wolff ignores Kant's explicit distinction between "not infinite [nicht
unendlich] (non est infinitus)" and "non-infinite [nichtunendlich]"; in the first
expression the negation is part of the copula, in the second part of the predicate; 3)
here, Kant is dealing not with problems involving the oppposition of predicates but
of judgments: affirmative and infinites judgments are contraries; affirmative
and negative judgments are contradictories.