e in mathematics and physics and the problematic
existence of such knowledge in metaphysics, and Kant's aim is to
determine the range within which _a priori_ knowledge is possible.
Thus the problem is introduced as relating to _a priori_ knowledge as
such, no distinction being drawn between its character in different
cases. Nevertheless the actual discussion of the problem in the body
of the _Critique_ implies a fundamental distinction between the nature
of _a priori_ knowledge in mathematics and its nature in physics, and
in order that a complete view of the problem may be given, this
distinction must be stated.

The 'Copernican' revolution was brought about by consideration of the
facts of mathematics. Kant accepted as an absolute starting-point the
existence in mathematics of true universal and necessary judgements.
He then asked, 'What follows as to the nature of the objects known in
mathematics from the fact that we really know them?' Further, in his
answer he accepted a distinction which he never examined or even
questioned, viz. the distinction between things in themselves and
phenomena.[19] This distinction assumed, Kant inferred from the truth
of mathematics that things in space and time are only phenomena.
According to him mathematicians are able to make the true judgements
that they do make only because they deal with phenomena. Thus Kant in
no way sought to _prove_ the truth of mathematics. On the contrary, he
argued from the truth of mathematics to the nature of the world which
we thereby know. The phenomenal character of the world being thus
established, he was able to reverse the argument and to regard the
phenomenal character of the world as _explaining_ the validity of
mathematical judgements. They are valid, because they relate to
phenomena. And the consideration which led Kant to take mathematics
as his starting-point seems to have been the self-evidence of
mathematical judgements. As we directly apprehend their necessity,
they admit of no reasonable doubt.

[19] Cf. Ch. IV. This distinction should of course have been
examined by one whose aim it was to determine how far our
knowledge can reach.

[20] For the self-evidence of mathematics to Kant compare B.
120, M. 73 and B. 200, M. 121.

On the other hand, the general principles underlying physics, e. g.
that every change must have a cause, or that in all change the quantum
of matter is constant, appeared to Kant in a differen