nd through
conditioned by the mind's perceiving nature; and, consequently, if a
geometrical rule, e. g. that a three-sided figure must have three
angles, is really a law of the mind's perceiving nature, all
individual perceptions, i. e. all objects as perceived by us, will
necessarily conform to the law. Therefore, in the latter case, and in
that only, will the universal validity of geometrical judgements be
justified. Since, then, geometrical judgements are universally valid,
space, which is that of which geometrical laws are the laws, must be
merely a form of perception or a characteristic of objects as
perceived by us.

This appears to be the best form in which the substance of Kant's
argument, stripped of unessentials, can be stated. It will be
necessary to consider both the argument and its conclusion.

The argument, so stated, is undeniably plausible. Nevertheless,
examination of it reveals two fatal defects. In the first place, its
starting-point is false. To Kant the paradox of geometrical judgements
lies in the fact that they are not based upon an appeal to experience
of the things to which they relate. It is implied, therefore, that
judgements which are based on experience involve no paradox, and for
the reason that in experience we apprehend things as they are.[48] In
contrast with this, it is implied that in geometrical judgements the
connexion which we apprehend is not real, i. e. does not relate to
things as they are. Otherwise, there would be no difficulty; if in
geometry we apprehended rules of connexion relating to things as they
are, we could allow without difficulty that the things must conform to
them. No such distinction, however, can be drawn between _a priori_
and empirical judgements. For the necessity of connexion, e. g.
between being a three-sided figure and being a three-angled figure, is
as much a characteristic of things as the empirically-observed shape
of an individual body, e. g. a table. Geometrical judgements,
therefore, cannot be distinguished from empirical judgements on the
ground that in the former the mind remains within itself, and does not
immediately apprehend fact or a real characteristic of reality.[49]
Moreover, since in a geometrical judgement we do in fact think that we
are apprehending a real connexion, i. e. a connexion which applies to
things and to things as they are in themselves, to question the
reality of the connexion is to question the validity of thinking
altog