etrical
judgements can in no way be 'explained'. It is not in the least
explained or made easier to accept by the supposition that objects
are 'phenomena'. These judgements must be accepted as being what we
presuppose them to be in making them, viz. the direct apprehension of
necessities of relation between real characteristics of real things.
To explain them by reference to the phenomenal character of what is
known is really--though contrary to Kant's intention--to throw doubt
upon their validity; otherwise, they would not need explanation. As a
matter of fact, it is _impossible_ to question their validity. In the
act of judging, doubt is impossible. Doubt can arise only when
we subsequently reflect and temporarily lose our hold upon the
consciousness of necessity in judging.[54] The doubt, however, since
it is non-existent in our geometrical consciousness, is really
groundless,[55] and, therefore, the problem to which it gives rise is
unreal. Moreover if, _per impossibile_, doubt could be raised, it
could not be set at rest. No vindication of a judgement in which we
are conscious of a necessity could do more than take the problem a
stage further back, by basing it upon some other consciousness of a
necessity; and since this latter judgement could be questioned for
precisely the same reason, we should only be embarking upon an
infinite process.

[54] Cf. Descartes, _Princ. Phil._ i. Sec. 13, and _Medit._ v
sub fin.

[55] The view that kinds of space other than that with which
we are acquainted are possible, though usually held and
discussed by mathematicians, belongs to them _qua_
metaphysicians, and not _qua_ mathematicians.

We may now consider Kant's conclusion in abstraction from the
arguments by which he reaches it. It raises three main difficulties.

In the first place, it is not the conclusion to be expected from
Kant's own standpoint. The phenomenal character of space is inferred,
not from the fact that we make judgements at all, but from the fact
that we make judgements of a particular kind, viz. _a priori_
judgements. From this point of view empirical judgements present no
difficulty. It should, therefore, be expected that the qualities which
we attribute to things in empirical judgements are not phenomenal, but
belong to things as they are. Kant himself implies this in drawing his
conclusion concerning the nature of space. "Space does not represent
any quality of things in thems