It should be remarked that space relations are by no means the only ones in which we think of things as existing.  We attribute to them time relations as well.  Now, when we think of occurrences as related to each other in time, we do, in so far as we concentrate our attention upon these relations, turn our attention away from space and contemplate another aspect of the system of things.  Space is not such a necessity of thought that we must keep thinking of space when we have turned our attention to something else.  And is it, indeed, inconceivable that there should be a system of things (not extended things in space, of course), characterized by time relations and perhaps other relations, but not by space relations?

It goes without saying that we cannot go on thinking of space and at the same time not think of space.  Those who keep insisting upon space as a necessity of thought seem to set us such a task as this, and to found their conclusion upon our failure to accomplish it.  “We can never represent to ourselves the nonexistence of space,” says the German philosopher Kant (1724-1804), “although we can easily conceive that there are no objects in space.”

It would, perhaps, be fairer to translate the first half of this sentence as follows:  “We can never picture to ourselves the nonexistence of space.”  Kant says we cannot make of it a Vorstellung, a representation.  This we may freely admit, for what does one try to do when one makes the effort to imagine the nonexistence of space?  Does not one first clear space of objects, and then try to clear space of space in much the same way?  We try to “think space away,” i.e. to remove it from the place where it was and yet keep that place.

What does it mean to imagine or represent to oneself the nonexistence of material objects?  Is it not to represent to oneself the objects as no longer in space, i.e. to imagine the space as empty, as cleared of the objects?  It means something in this case to speak of a Vorstellung, or representation.  We can call before our minds the empty space.  But if we are to think of space as nonexistent, what shall we call before our minds?  Our procedure must not be analogous to what it was before; we must not try to picture to our minds the absence of space, as though that were in itself a something that could be pictured; we must turn our attention to other relations, such as time relations, and ask whether it is not conceivable that such should be the only relations obtaining within a given system.

Those who insist upon the fact that we cannot but conceive space as infinite employ a very similar argument to prove their point.  They set us a self-contradictory task, and regard our failure to accomplish it as proof of their position.  Thus, Sir William Hamilton (1788-1856) argues:  “We are altogether unable to conceive space as bounded—­as finite; that is, as a whole beyond which there is no further space.”  And Herbert Spencer echoes approvingly:  “We find ourselves totally unable to imagine bounds beyond which there is no space.”