g with our
understanding of it, if such absurdities as these refuse to be cleared
away. Let us see where the trouble lies.

26. WHAT IS REAL SPACE?--It is plain that men are willing to make a
number of statements about space, the ground for making which is not at
once apparent. It is a bold man who will undertake to say that the
universe of matter is infinite in extent. We feel that we have the
right to ask him how he knows that it is. But most men are ready
enough to affirm that space is and must be infinite. How do they know
that it is? They certainly do not directly perceive all space, and
such arguments as the one offered by Hamilton and Spencer are easily
seen to be poor proofs.

Men are equally ready to affirm that space is infinitely divisible.
Has any man ever looked upon a line and perceived directly that it has
an infinite number of parts? Did any one ever succeed in dividing a
space up infinitely? When we try to make clear to ourselves how a
point moves along an infinitely divisible line, do we not seem to land
in sheer absurdities? On what sort of evidence does a man base his
statements regarding space? They are certainly very bold statements.

A careful reflection reveals the fact that men do not speak as they do
about space for no reason at all. When they are properly understood,
their statements can be seen to be justified, and it can be seen also
that the difficulties which we have been considering can be avoided.
The subject is a deep one, and it can scarcely be discussed
exhaustively in an introductory volume of this sort, but one can, at
least, indicate the direction in which it seems most reasonable to look
for an answer to the questions which have been raised. How do we come
to a knowledge of space, and what do we mean by space? This is the
problem to solve; and if we can solve this, we have the key which will
unlock many doors.

Now, we saw in the last chapter that we have reason to believe that we
know what the real external world is. It is a world of things which we
perceive, or can perceive, or, not arbitrarily but as a result of
careful observation and deductions therefrom, conceive as though we did
perceive it--a world, say, of atoms and molecules. It is not an
Unknowable behind or beyond everything that we perceive, or can
perceive, or conceive in the manner stated.

And the space with which we are concerned is real space, the space in
which real things exist and move abo