KANT'S CRITIQUE OF TELEOLOGY IN BIOLOGICAL EXPLANATION

66 Kant's Logic
For the true opposition that takes place here contains neither more nor less
than belongs to opposition. According to the Principle of the Excluded
Middle therefore both of the contradictory judgments cannot be true, but
also both of them can just as little be false. Thus if the one is true the other
is false and vice versa. (Logic, §48; W 3,547f)
Contraries on the one hand say "more" than is necessary for
true opposition, and both can be false. Subcontraries say "less" than
is necessary and can both be true. The only thing somewhat
unusual about Kant's conception of these types of logical opposition
is that he is not so much interested in the logical form of the propositions
in the strict sense, that is, in their identity or difference in
quantity and quality. Although in his lectures on logic (§48-50), he
introduces them in the traditional manner, in practice he is interested
only in the truth relations of the propositions: whether both
can at once be true or both false, etc. Contraries thus need not be
universal propositions, subcontraries need not be particular, and
contradictories need not differ in quantity. They need only have the
appropriate truth relations.
The distinction between these various kinds of opposition is
significant when dealing with immediate inference and indirect
proof, and it is in this context that Kant introduces them in his lectures
on logic. The important point is that the so-called apagogical
or indirect proof, in which the truth of a proposition is inferred from
the falsity of its opposite, is legitimate only when the two propositions
involved are true contradictories. If they are merely contraries,
no conclusions about the truth or falsity of one can be drawn
from the falsity of the other without introducing further assumptions.
As for subcontraries, although one can indeed in traditional
logic, infer the truth of one proposition from the falsity of the other,
one cannot infer the falsity of a proposition from the truth of its
subcontrary.
Returning to our original example, we can see that Kant is
asserting that, of the three propositions,
1) The world is infinite,
2) The world is not infinite,
3) The world is finite,
(1) and (2) are contradictories but (1) and (3) are contraries, that is,
that while either (1) or (2) must be true, both (1) and (3) can be false
(and according to Kant they are false). What is the difference? In