has at last come to the same melancholy
conclusion.

[Sidenote: Doctrines of Parmenides carried out by Zeno;]

The doctrines of Parmenides were carried out by Zeno the Eleatic, who is
said to have been his adopted son. He brought into use the method of
refuting error by the _reductio ad absurdum_. His compositions were in
prose, and not in poetry, as were those of his predecessors. As it had
been the object of Parmenides to establish the existence of "the One,"
it was the object of Zeno to establish the non-existence of "the Many."
Agreeably to such principles, he started from the position that only one
thing really exists, and that all others are mere modifications or
appearances of it. He denied motion, but admitted the appearance of it;
regarding it as a name given to a series of conditions, each of which is
necessarily rest. This dogma against the possibility of motion he
maintained by four arguments; the second of them is the celebrated
Achilles puzzle. It is thus stated: "Suppose Achilles to run ten times
as fast as a tortoise, yet, if the tortoise has the start, Achilles can
never overtake him; for, if they are separated at first by an interval
of a thousand feet, when Achilles has run these thousand feet the
tortoise will have run a hundred, and when Achilles has run these
hundred the tortoise will have got on ten, and so on for ever; therefore
Achilles may run for ever without overtaking the tortoise." Such were
his arguments against the existence of motion; his proof of the
existence of One, the indivisible and infinite, may thus be stated: "To
suppose that the one is divisible is to suppose it finite. If divisible,
it must be infinitely divisible. But suppose two things to exist, then
there must necessarily be an interval between those two--something
separating and limiting them. What is that something? It is some _other_
thing. But then if not the _same_ thing, _it also_ must be separated and
limited, and so on _ad infinitum_. Thus only one thing can exist as the
substratum for all manifold appearances." Zeno furnishes us with an
illustration of the fallibility of the indications of sense in his
argument against Protagoras. It may be here introduced as a specimen of
his method: "He asked if a grain of corn, or the ten thousandth part of
a grain, would, when it fell to the ground, make a noise. Being answered
in the negative, he further asked whether, then, would a measure of
corn. This being necessarily af