are equal, are common
examples. Into the ground of these axioms the geometrician does not
enquire. That is the business of philosophy. Not that philosophers
affect to doubt the truth of these axioms. But surely it is a very
strange thing, and a fact quite worthy of study, that there are some
statements of which we feel that we must give the most laborious
proofs, and others in the case of which we feel no such necessity. How
is it that some propositions can be self-evident and others must be
proved? What is the ground of this distinction? And when one comes to
think of it, it is a very extraordinary property of mind that it
should be able to make the most universal and unconditional statements
about things, without a jot of evidence or proof. When we say that two
straight lines cannot enclose a space, we do not mean merely that this
has been found true in regard to all the particular pairs of straight
lines with which we have tried the experiment. We mean that it never
can be and never has been otherwise. We mean that a million million
years ago two straight lines did not enclose a space, and that it will
be the same a million million years hence, and that it is just as true
on those stars, if there are any, which are invisible even to the
greatest telescopes. But we have no experience of what will {5} happen
a million million years hence, or of what can take place among those
remote stars. And yet we assert, with absolute confidence, that our
axiom is and must be equally true everywhere and at all times.
Moreover, we do not found this on probabilities gathered from
experience. Nobody would make experiments or use telescopes to prove
such axioms. How is it that they are thus self-evident, that the mind
can make these definite and far-reaching assertions without any
evidence at all? Geometricians do not consider these questions. They
take the facts for granted. To solve these problems is for philosophy.

Again, the physical sciences take the existence of matter for granted.
But philosophy asks what matter is. At first sight it might appear
that this question is one for the physicist and not the philosopher.
For the problem of "the constitution of matter" is a well-known
physical problem. But a little consideration will show that this is
quite a different question from the one the philosopher propounds. For
even if it be shown that all matter is ether, or electricity, or
vortex-atoms, or other such, this does not help