KANT'S CRITIQUE OF TELEOLOGY IN BIOLOGICAL EXPLANATION

Infinite Judgments 67
what sense does the proposition, "The world is finite" say more than
"The world is not infinite," more than is necessary for contradiction?
The answer to this question is the resolution to the first antinomy,
to which we shall presently turn. However, in order to avoid
irrelevant complications, let me point out already here that Kant is
not casting doubt on the rule of double negation since he elsewhere
(B532) equates "non-infinite" with "finite." Moreover, the same
argument also applies to the truth relations of the following three
propositions where no double negation is involved:
3) The world is finite
4) The world is not finite
1) The world is infinite.
(3) and (4) are contradictories, but (3) and (1) are supposed to be contraries.
As we shall see, Kant is distinguishing between the negation
of a proposition (or, in singular categorical judgments, the
negation of the copula) and the negation of the predicate.
Infinite Judgments
In the Table of Judgments in the Analytic of the Critique of
Pure Reason (B95), Kant distinguishes three different "qualities" of
judgment, each of which corresponds to one of the examples cited
above. The three qualities are as follows:
Affirmative S / is / P "anima est mortalis"
Negative S / is not / P "anima non est mortalis"
Infinite S / is / not-P "anima est non-mortalis"
In an affirmative judgment the connection of a subject with a
predicate is asserted (setzen, ponere); in a negative judgment the
connection is denied (aufheben, tollere). In a so-called infinite
judgment a subject is connected with a negative predicate. "In an
affirmative judgment," says Kant in his lectures on logic as edited
by Jäsche, "the subject is thought under the sphere of a predicate, in
a negative judgment it is placed outside the sphere of the predicate
and in the infinite it is placed in the sphere of a concept which lies