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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
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 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 process of ingenious verbal
distinction, which in the hands of so-called sophists and others became a
weapon of considerable, if temporary, power.
A History of Greek Philosophy /
THE ELEATICS /
ZENO
