A Commentary to Kant's 'Critique of Pure Reason'

Kant · en
was the really effective influence in producing the Copernican
change.[260]

=Purely a priori and out of mere concepts.=[261]--Vaihinger’s comment
seems correct: Kant means only that neither actual experience nor pure
intuition can be resorted to. This does not contradict the complementary
assertion,[262] that the principle, everything which happens has its
cause, can be known _a priori_, not immediately from the concepts
involved in it, but only indirectly[263] through the relation of these
concepts to possible experience. “Possible experience,” even though it
stands for “something purely contingent,” is itself a concept.
Vaihinger[264] quotes Apelt upon this “mysterious” type of judgment.

     “Metaphysics is synthetic knowledge from mere concepts, not like
     mathematics from their construction in intuition, and yet these
     synthetic propositions cannot be known from bare concepts, _i.e._
     not analytically. The necessity of the connection in those
     propositions is to be apprehended through thought alone, and yet is
     not to rest upon the form of thought, the principle of
     contradiction. The conception of a kind of knowledge which arises
     from bare concepts, and yet is synthetic, eludes our grasp. The
     problem is: How can one concept be necessarily connected with
     another, without also at the same time being contained in it?”

The paragraphs in B 14 to B 17 are almost verbal transcripts from
_Prolegomena_, § 2 _c_, 2 ff.

=Mathematical judgments are one and all (insgesammt)
synthetic.=[265]--This assertion is carelessly made, and does not
represent Kant’s real view. In B 16 he himself recognises the existence
of analytic mathematical judgments, but unduly minimises their number
and importance.

=All mathematical conclusions proceed according to the principle of
contradiction.=[266]--To the objection made by Paulsen that Kant, in
admitting that mathematical judgments can be deduced from others by
means of the principle of contradiction, ought consistently to have
recognised as synthetic only axioms and principles, Vaihinger replies as
follows:[267]