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 about, the real things which we can directly know or of which we can definitely know something.  In some sense it must be given in our experience, if the things which are in it, and are known to be in it, are given in our experience.  How must we think of this real space?

Suppose we look at a tree at a distance.  We are conscious of a certain complex of color.  We can distinguish the kind of color; in this case, we call it blue.  But the quality of the color is not the only thing that we can distinguish in the experience.  In two experiences of color the quality may be the same, and yet the experiences may be different from each other.  In the one case we may have more of the same color—­we may, so to speak, be conscious of a larger patch; but even if there is not actually more of it, there may be such a difference that we can know from the visual experience alone that the touch object before us is, in the one case, of the one shape, and, in the other case, of another.  Thus we may distinguish between the stuff given in our experience and the arrangement of that stuff.  This is the distinction which philosophers have marked as that between “matter” and “form.”  It is, of course, understood that both of these words, so used, have a special sense not to be confounded with their usual one.