a moving point. He writes:--

"When a point moves along a line, we know that between any two
positions of it there is an infinite number . . . of intermediate
positions. That is because the motion is continuous. Each of those
positions is where the point was at some instant or other. Between the
two end positions on the line, the point where the motion began and the
point where it stopped, there is no point of the line which does not
belong to that series. We have thus an infinite series of successive
positions of a continuously moving point, and in that series are
included all the points of a certain piece of line-room." [1]

Thus, we are told that, when a point moves along a line, between any
two positions of it there is an infinite number of intermediate
positions. Clifford does not play with the word "infinite"; he takes
it seriously and tells us that it means without any end: "_Infinite_;
it is a dreadful word, I know, until you find out that you are familiar
with the thing which it expresses. In this place it means that between
any two positions there is some intermediate position; between that and
either of the others, again, there is some other intermediate; and so
on _without any end_. Infinite means without any end."

But really, if the case is as stated, the point in question must be at
a desperate pass. I beg the reader to consider the following, and ask
himself whether he would like to change places with it:--

(1) If the series of positions is really endless, the point must
complete one by one the members of an endless series, and reach a
nonexistent final term, for a really endless series cannot have a final
term.

(2) The series of positions is supposed to be "an infinite series of
successive positions." The moving point must take them one after
another. But how can it? _Between any two positions of the point
there is an infinite number of intermediate positions_. That is to
say, no two of these successive positions must be regarded as _next to_
each other; every position is separated from every other by an infinite
number of intermediate ones. How, then, shall the point move? It
cannot possibly move from one position to the next, for there is no
next. Shall it move first to some position that is not the next? Or
shall it in despair refuse to move at all?

Evidently there is either something wrong with this doctrine of the
infinite divisibility of space, or there is something wron