the universe as limited and surrounded by void space. It
is not nonsense to speak of such a state of things. It would, indeed,
appear to be nonsense to say that, if the universe is limited, it does
not lie in void space. What can we mean by void space but the system
of possible relations in which things, if they exist, must stand? To
say that, beyond a certain point, no further relations are possible,
seems absurd.

Hence, when a man has come to understand what we have a right to mean
by space, it does not imply a boundless conceit on his part to hazard
the statement that space is infinite. When he has said this, he has
said very little. What shall we say to the statement that space is
infinitely divisible?

To understand the significance of this statement we must come back to
the distinction between appearances and the real things for which they
stand as signs, the distinction discussed at length in the last chapter.

When I see a tree from a distance, the visual experience which I have
is, as we have seen, not an indivisible unit, but is a complex
experience; it has parts, and these parts are related to each other; in
other words, it has both "matter" and "form." It is, however, one
thing to say that this experience has parts, and it is another to say
that it has an infinite number of parts. No man is conscious of
perceiving an infinite number of parts in the patch of color which
represents to him a tree at a distance; to say that it is constituted
of such strikes us in our moments of sober reflection as a monstrous
statement.

Now, this visual experience is to us the sign of the reality, the real
tree; it is not taken as the tree itself. When we speak of the size,
the shape, the number of parts, of the tree, we do not have in mind the
size, the shape, the number of parts, of just this experience. We pass
from the sign to the thing signified, and we may lay our hand upon this
thing, thus gaining a direct experience of the size and shape of the
touch object.

We must recognize, however, that just as no man is conscious of an
infinite number of parts in what he sees, so no man is conscious of an
infinite number of parts in what he touches. He who tells me that,
when I pass my finger along my paper cutter, _what I perceive_ has an
infinite number of parts, tells me what seems palpably untrue. When an
object is very small, I can see it, and I cannot see that it is
composed of parts; similarly, when an ob