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.