erceived. Kant himself lays this down.
"The proposition 'all objects are beside one another in space'
is valid under[59] the limitation that these things are taken as
objects of our sensuous perception. If I join the condition to the
perception, and say 'all things, as external phenomena, are beside
one another in space', the rule is valid universally, and without
limitation."[60] Kant, then, is in effect allowing that it is possible
for geometricians to make judgements, of the necessity of which
they are convinced, and yet to be wrong; and that, therefore, the
apprehension of the necessity of a judgement is no ground of its
truth. It follows that the truth of geometrical judgements can no
longer be accepted as a starting-point of discussion, and, therefore,
as a ground for inferring the phenomenal character of space.

[59] A. reads 'only under'

[60] B. 43, M. 27.

There seems, indeed, one way of avoiding this consequence, viz. to
suppose that for Kant it was an absolute starting-point, which nothing
would have caused him to abandon, that only those judgements of which
we apprehend the necessity are true. It would, of course, follow that
geometricians would be unable to apprehend the necessity of
geometrical judgements, and therefore to make such judgements, until
they had discovered that things as spatial were only phenomena. It
would not be enough that they should think that the phenomenal or
non-phenomenal character of things as spatial must be left an open
question for the theory of knowledge to decide. In this way the
necessity of admitting the illusory character of geometry would be
avoided. The remedy, however, is at least as bad as the disease.
For it would imply that geometry must be preceded by a theory of
knowledge, which is palpably contrary to fact. Nor could Kant accept
it; for he avowedly bases his theory of knowledge, i. e. his view
that objects as spatial are phenomena, upon the truth of geometry;
this procedure would be circular if the making of true geometrical
judgements was allowed to require the prior adoption of his theory of
knowledge.

The third difficulty is the most fundamental. Kant's conclusion (and
also, of course, his argument) presupposes the validity of the
distinction between phenomena and things in themselves. If, then, this
distinction should prove untenable in principle, Kant's conclusion
with regard to space must fail on general grounds, and it will even
have been unn