re the parts of the instrument.
Everything that reaches the senses must submit to the laws of Space and
Time, that is, to the Laws of Mathematics, because Space and Time are
forms of the mind itself, and, like the kaleidoscope, arrange all things
on their way to the senses according to a pattern of their own. This
pattern is as it were super-added to the manifestations that come from
the things themselves; and if there be any manifestations of such a
nature that they could not submit to this addition, or, in other words,
could not submit to Mathematical Laws, these manifestations could not
affect our senses at all. So too our Understanding has a pattern of its
own which it imposes on all things that reach its power of perception.
What cannot be accommodated to this pattern cannot be understood at all.
Whatever things may be in themselves, their manifestations are not
within the range of our intelligence, except by passing through the
arranging process which our own mind executes upon them.

It is clear that this wonderfully ingenious speculation rests its
claims for acceptance purely on the assertion that it and it alone
explains the facts. It cannot be proved from any principle of reason. It
assumes that there is a demonstrative science of Mathematics quite
independent of experience, and that there are necessary principles of
Physics equally independent of experience. And it accounts for the
existence of these.

With Mathematics we are not now concerned, and I will pass them by with
only one remark. The ground on which Kant's theory stands is not
sufficient, for this simple reason. It accounts for one fact; it does
not account for another fact. It accounts for the fact that we attach
and cannot help attaching a conviction of necessity to all mathematical
reasoning. We not only know that two straight lines cannot enclose a
space, but we know that this is so and must be so in all places and at
all times, and we know it without any proof whatever. This fact Kant
accounts for. Space is according to him a part of our kaleidoscope; you
can always look into it and see for yourself what are the laws of it.
But there is another fact. This space of which we are speaking is
unquestionably to our minds not a thing inside of us but outside of us.
We are in it. We cannot get rid of a sense that it is independent of
ourselves. We can imagine ourselves non-existing, minds and all. We
cannot imagine space non-existing. If it be a part