esent in the imagination,
is composed of an infinite number of parts.

When we realize this, do we not free ourselves from the difficulties
which seemed to make the motion of a point over a line an impossible
absurdity? The line as revealed in a single experience either of sight
or of touch is not composed of an infinite number of parts. It is
composed of points seen or touched--least experiences of sight or
touch, _minima sensibilia_. These are next to each other, and the
point, in moving, takes them one by one.

But such a single experience is not what we call a line. It is but one
experience of a line. Though the experience is not infinitely
divisible, the line may be. This only means that the visual or tactual
point of the single experience may stand for, may represent, what is
not a mere point but has parts, and is, hence, divisible. Who can set
a limit to such possible substitutions? in other words, who can set a
limit to the divisibility of a _real line_?

It is only when we confuse the single experience with the real line
that we fall into absurdities. What the mathematician tells us about
real points and real lines has no bearing on the constitution of the
single experience and its parts. Thus, when he tells us that between
any two points on a line there are an infinite number of other points,
he only means that we may expand the line indefinitely by the system of
substitutions described above. We do this for ourselves within limits
every time that we approach from a distance a line drawn on a
blackboard. The mathematician has generalized our experience for us,
and that is all he has done. We should try to get at his real meaning,
and not quote him as supporting an absurdity.

[1] "Seeing and Thinking," p. 149.

CHAPTER VII

OF TIME

27. TIME AS NECESSARY, INFINITE, AND INFINITELY DIVISIBLE.--Of course, we
all know something about time; we know it as past, present, and future;
we know it as divisible into parts, all of which are successive; we know
that whatever happens must happen in time. Those who have thought a good
deal about the matter are apt to tell us that time is a necessity of
thought, we cannot but think it; that time is and must be infinite; and
that it is infinitely divisible.

These are the same statements that were made regarding space, and, as
they have to be criticised in just the same way, it is not necessary to
dwell upon them at great length. However, we must