a way as to lead to error. Let us begin with the doctrine that
space is necessary and cannot be "thought away."

As we have seen above, it is manifestly impossible to annihilate in
thought a certain portion of space and leave the other portions intact.
There are many things in the same case. We cannot annihilate in
thought one side of a door and leave the other side; we cannot rob a
man of the outside of his hat and leave him the inside. But we can
conceive of a whole door as annihilated, and of a man as losing a whole
hat. May we or may we not conceive of space as a whole as nonexistent?

I do not say, be it observed, can we conceive of something as attacking
and annihilating space? Whatever space may be, we none of us think of
it as a something that may be threatened and demolished. I only say,
may we not think of a system of things--not a world such as ours, of
course, but still a system of things of some sort--in which space
relations have no part? May we not conceive such to be possible?

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 tr