intervening parts shown to be infinite; therefore this one thing,
being infinitely large, is everything.

[107]

Take, again, any supposed fact, as that an arrow moves. An arrow
cannot move except in space. It cannot move in space without being in
space. At any moment of its supposed motion it must be in a particular
space. Being in that space, it must at the time during which it is in
it be at rest. But the total time of its supposed motion is made up of
the moments composing that time, and to each of these moments the same
argument applies; therefore either the arrow never was anywhere, or it
always was at rest.

Or, again, take objects moving at unequal rates, as Achilles and a
tortoise. Let the tortoise have a start of any given length, then
Achilles, however {45} much he excel in speed, will never overtake the
tortoise. For, while Achilles has passed over the originally
intervening space, the tortoise will have passed over a certain space,
and when Achilles has passed over this second space the tortoise will
have again passed over some space, and so on _ad infinitum_; therefore
in an infinite time there must always be a space, though infinitely
diminishing, between the tortoise and Achilles, _i.e._ the tortoise
must always be at least a little in front.

These will be sufficient to show the kind of arguments employed by
Zeno. In themselves they are of no utility, and Zeno never pretended
that they had any. But as against those who denied that existence as
such was a datum independent of experience, something different from a
mere sum of isolated things, his arguments were not only effective, but
substantial. The whole modern sensational or experiential school, who
derive our 'abstract ideas,' as they are called, from 'phenomena' or
'sensation,' manifest the same impatience of any analysis of what they
mean by phenomena or sensation, as no doubt Zeno's opponents manifested
of his analyses. As in criticising the one, modern critics are ready
with their answer that Zeno's quibbles are simply "a play of words on
the well-known properties of infinities," so they are quick to tell us
that sensation is an "affection of the sentient organism"; ignoring in
{46} the first case the prior question where the idea of infinity came
from, and in the second, where the idea of a sentient organism came
from.

Indirectly, as we shall see, Zeno had a great effect on subsequent
philosophies by the development of a proc