must be a definite and limited amount of space.
Therefore space is finite. On the other hand, it is impossible to
conceive a limit to space. Beyond the limit there must be more space.
Therefore space is infinite. Zeno himself gave expression to this
antinomy in the form of an argument which I have not so far mentioned.
He said that everything which exists is in space. Space itself exists,
therefore space must be in space. That space must be in another space
and so _ad infinitum_. This of course is merely a quaint way of saying
that to conceive a limit to space is impossible.

But to return to the antinomy of infinite divisibility, {57} on which
most of Zeno's arguments rest, you will perhaps expect me to say
something of the different solutions which have been offered. In the
first place, we must not forget Zeno's own solution. He did not
propound this contradiction for its own sake, but to support the
thesis of Parmenides. His solution is that as multiplicity and motion
contain these contradictions, therefore multiplicity and motion cannot
be real. Therefore, there is, as Parmenides said, only one Being, with
no multiplicity in it, and excludent of all motion and becoming. The
solution given by Kant in modern times is essentially similar.
According to Kant, these contradictions are immanent in our
conceptions of space and time, and since time and space involve these
contradictions it follows that they are not real beings, but
appearances, mere phenomena. Space and time do not belong to things as
they are in themselves, but rather to our way of looking at things.
They are forms of our perception. It is our minds which impose space
and time upon objects, and not objects which impose space and time
upon our minds. Further, Kant drew from these contradictions the
conclusion that to comprehend the infinite is beyond the capacity of
human reason. He attempted to show that, wherever we try to think the
infinite, whether the infinitely large or the infinitely small, we
fall into irreconcilable contradictions. Therefore, he concluded that
human faculties are incapable of apprehending infinity. As might be
expected, many thinkers have attempted to solve the problem by denying
one or other side of the contradiction, by saying that one or other
side does not follow from the premises, that one is true and the other
false. David Hume, for example, {58} denied the infinite divisibility
of space and time, and declared that they are co