usion? No vindication
seems possible. For how can it be possible to base the knowledge of
what things are, independently of perception, upon the knowledge of
what they look? Nevertheless, the answer is simple. In the case of the
perception of what is spatial there is no transition _in principle_
from knowledge of what things look to knowledge of what things are,
though there is continually such a transition _in respect of details_.
It is, of course, often necessary, and often difficult, to determine
the precise position, shape, &c., of a thing, and if we are to come to
a decision, we must appeal to what the thing looks or appears under
various conditions. But, from the very beginning, our consciousness of
what a thing appears in respect of spatial characteristics implies the
consciousness of it as spatial and therefore also as, in particular,
three-dimensional. If we suppose the latter consciousness absent, any
assertion as to what a thing appears in respect of spatial
characteristics loses significance. Thus, although there is a process
by which we come to learn that railway lines are really parallel,
there is no process by which we come to learn that they are really
spatial. Similarly, although there is a process by which we become
aware that a body is a cube, there is no process by which we become
aware that it has a solid shape of some kind; the process is only
concerned with the determination of the precise shape of the body.
The second difficulty is, therefore, also removed. For if assertions
concerning the apparent shape, &c. of things presuppose the
consciousness that the things _are_ spatial, to say that this
consciousness may be illusory is to say that all statements concerning
what things _appear_, in respect of spatial relations, are equally
illusory. But, since it is wholly impossible to deny that we can and
do state what things appear in this respect, the difficulty must fall
to the ground.

There remains to be answered the question whether Kant's position is
tenable in its other form, viz. that while we cannot say that reality
is spatial, we can and must say that the appearances which it produces
are spatial. This question, in view of the foregoing, can be answered
as soon as it is stated. We must allow that reality is spatial, since,
as has been pointed out, assertions concerning the apparent shape of
things presuppose that they are spatial. We must equally allow that an
appearance cannot be spatial. Fo