This distinction between “matter” and “form” obtains in all our experiences.  I have spoken just above of the shape of the touch object for which our visual experiences stand as signs.  What do we mean by its shape?  To the plain man real things are the touch things of which he has experience, and these touch things are very clearly distinguishable from one another in shape, in size, in position, nor are the different parts| of the things to be confounded with each other.  Suppose that, as we pass our hand over a table, all the sensations of touch and movement which we experience fused into an undistinguishable mass.  Would we have any notion of size or shape?  It is because our experiences of touch and movement do not fuse, but remain distinguishable from each other, and we are conscious of them as arranged, as constituting a system, that we can distinguish between this part of a thing and that, this thing and that.

This arrangement, this order, of what is revealed by touch and movement, we may call the “form” of the touch world.  Leaving out of consideration, for the present, time relations, we may say that the “form” of the touch world is the whole system of actual and possible relations of arrangement between the elements which make it up.  It is because there is such a system of relations that we can speak of things as of this shape or of that, as great or small, as near or far, as here or there.

Now, I ask, is there any reason to believe that, when the plain man speaks of space, the word means to him anything more than this system of actual and possible relations of arrangement among the touch things that constitute his real world?  He may talk sometimes as though space were some kind of a thing, but he does not really think of it as a thing.

This is evident from the mere fact that he is so ready to make about it affirmations that he would not venture to make about things.  It does not strike him as inconceivable that a given material object should be annihilated; it does strike him as inconceivable that a portion of space should be blotted out of existence.  Why this difference?  Is it not explained when we recognize that space is but a name for all the actual and possible relations of arrangement in which things in the touch world may stand?  We cannot drop out some of these relations and yet keep space, i.e. the system of relations which we had before.  That this is what space means, the plain man may not recognize explicitly, but he certainly seems to recognize it implicitly in what he says about space.  Men are rarely inclined to admit that space is a thing of any kind, nor are they much more inclined to regard it as a quality of a thing.  Of what could it be the quality?

And if space really were a thing of any sort, would it not be the height of presumption for a man, in the absence of any direct evidence from observation, to say how much there is of it—­to declare it infinite?  Men do not hesitate to say that space must be infinite.  But when we realize that we do not mean by space merely the actual relations which exist between the touch things that make up the world, but also the possible relations, i.e. that we mean the whole plan of the world system, we can see that it is not unreasonable to speak of space as infinite.