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 unnecessary to consider his arguments for it. The importance
of the issue, however, requires that it should be considered in a
separate chapter.
NOTE to page 47.
The argument is not affected by the contention that, while
the totality of spaces is infinite, the totality of colours
or, at any rate, the totality of instances of some other
characteristic of objects is finite; for this difference
will involve no difference in respect of perception and
conception. In both cases the apprehension that there is a
totality will be reached in the same way, i. e. through the
_conception_ of the characteristic in general, and the
apprehension in the one case that the totality is infinite
and in the other that it is finite will depend on the
apprehension of the special nature of the characteristic in
question.
CHAPTER IV
PHENOMENA AND THINGS IN THEMSELVES