y 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."

Now, whatever one may be inclined to think about the infinity of space,
it is clear that this argument is an absurd one. Let me write it out
more at length: "We are altogether unable to conceive space as
bounded--as finite; that is, as a whole _in the space_ beyond which
there is no further space." "We find ourselves totally unable to
imagine bounds, _in the space_ beyond which there is no further space."
The words which I have added were already present implicitly. What can
the word "beyond" mean if it does not signify space beyond? What Sir
William and Mr. Spencer have asked us to do is to imagine a limited
space with a _beyond_ and yet _no beyond_.

There is undoubtedly some reason why men are so ready to affirm that
space is infinite, even while they admit that they do not know that the
world of material thi