But our present concern is not with Mathematics but with Physics. And
here Kant fails altogether to convince; for, taking Time and the
Perceptive Powers of the Understanding as parts of the human mind, he
shows, what indeed is clearer and clearer every day, that the principles
(so called) of Physics are indispensable Postulates, not indeed of
observing with the senses, but of comprehending with the understanding,
whatever happens. In order to give anything that can be called an
explanation of any event we must show that it falls under the general
rules which constitute the uniformity of Nature. We have no other
meaning for the words understanding or explaining an event. Thinking,
when analysed, is found to consist in bringing all that happens under
universal laws, and no phenomenon can be said to be explained in thought
except by being so related to all other phenomena. But it does not by
any means follow that events cannot happen or cannot affect our senses
without being susceptible of such explanation. To say that an event
cannot be understood, and to say either that it cannot happen or that it
cannot be observed by the senses, are two very different things. The
fact is that Mathematics and Physics do not, as Kant assumes, present
the same problem for solution, and do not therefore admit of one
solution applicable to both. It is not the case that there is a science
of abstract Physics corresponding to the science of Mathematics and
sharing in the same character of necessity. In Mathematics we have
truths which we cannot but accept, and accept as universal and
necessary: in Physics we have no such truths, nor has Kant even
endeavoured to prove that we have. The very question therefore that we
are asked to solve in regard to Mathematics does not present itself in
Physics. I am constrained to believe that two and two are four and not
five; I am not constrained to believe that if one event is followed by
another a great many times it will be so followed always. And the
question is, why, without any constraint, I nevertheless so far believe