PYTHAGORAS TO PLATO generally known: Wrst, that the earth is a sphere (D.L 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 4) Melissus expounded the philosophy of Parmenides’ poem in plain prose, arguing that the universe was unlimited, unchangeable, immovable, indivisible, and homogeneous He was remembered for drawing two consequences from this monistic view: (1) pain was unreal, because it implied (impossibly) a deWciency 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 fortymetre 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 239b11–14) 11 The 19th-century philosopher Gottlob Frege used the example to introduce his celebrated distinction between sense and reference 19