generally known: Wrst, that the earth is a sphere (D.L. 9. 21), and secondly,
that the Morning Star is the same as the Evening Star. Parmenides’
disowned discovery was to provide philosophers of a later generation
with a paradigm for identity statements.11
Parmenides had a pupil, Melissus, who came from Pythagoras’ island of
Samos and who was said to have studied also with Heraclitus. He was active
in politics, and rose to the rank of admiral of the Samos Xeet. In 441 bc
Samos was attacked by Athens, and though Athens was Wnally victorious in
the war Melissus is recorded as having twice inXicted defeat on the Xeet of
Pericles (Plutarch, Pericles 166c–d; D.L. 9. 4).
Melissus expounded the philosophy of Parmenides’ poem in plain prose,
arguing that the universe was unlimi ted, unchangeable, immovable, indivis-
ible, and homogeneous. He was remembered for drawing two consequences
from this monistic view: (1) pain was unreal, because it implied (impossibly)
adeWciency of being; (2) there was no such thing as a vacuum, since it would
have to be a piece of Unbeing. Local motion was therefore impossible, for the
bodies that occupy space have no room to move into (KRS 534).
Another pupil of Parmenides was Zeno of Elea. He produced a set of
more famous arguments against the possibility of motion. The Wrst
went like this: ‘There is no motion, for whatever moves must reach the
middle of its course before it reaches the end.’ To get to the far end of a
stadium, you have to run to the half-way point, to get to the half-way point
you must reach the point half-way to that, and so ad inWnitum. Better
known is the second argument, commonly known as Achilles and the
tortoise. ‘The slower’, Zeno said, ‘will never be overtaken by the swifter, for
the pursuer must Wrst reach the point from which the fugitive departed, so
that the slower must necessarily remain ahead.’ Let us suppose that Achilles
runs four times as fast as the tortoise, and that the tortoise is given a forty-
metre start when they run a hundred-metre race against each other.
According to Zeno’s argument, Achilles can never win. For by the time
he reaches the forty-metre mark, the tortoise is ahead by ten metres. By the
time Achilles has run those ten, the tortoise is still ahead by two and a half
metres. Each time Achilles makes up a gap, the tortoise opens up a new,
shorter, gap, so he can never overtake him (Aristotle, Ph.5.9.239b11–14).
11 The 19th-century philosopher Gottlob Frege used the example to introduce his celebrated
distinction between sense and reference.
PYTHAGORAS TO PLATO
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