"My writing is an answer to the partisans of the many... with a view to showing that the hypothesis of the many, if examined in sufficient detail, leads to even more absurd results that the hypothesis of the One."Little is known of Zeno other than that he came from Elea, in southern Italy, and that he was a dedicated disciple (some say lover) of Parmenides. Zeno is best known for his use of paradox to prove his master's thesis that being is one, indivisible and eternal. Plato's dialogue "Parmenides" describes an encounter between Zeno and Socrates, but this is not conclusive evidence that he visited Athens. The fragments of his writing are all preserved in much later texts, notably in Aristotle and Simplicius' "Commentary on Physics". Zeno's treatises consisted of a series of arguments designed to prove Parmenides' concept of unity of being.(Zeno in Plato's Dialogue "Parmenides")
His main form of argument is the paradox. Most of the paradoxes aim to prove that Being is single, finite, motionless and unchanging by examining the absurdities of the opposite "common-sense" hypothesis that several things exist. The most famous of the paradoxes, Achilles and the tortoise, is attributed to Parmenides himself. It is meant to show that motion is impossible. In a race where a tortoise is given a head start on Achilles, Achilles can never overtake the tortoise. He must first reach the place from which the tortoise started. By that time the tortoise will have got some way ahead. Achilles must then make up that and again the tortoise will be ahead. Zeno's four most discussed paradoxes have been resolved in terms of differential calculus by Bertrand Russell, who claimed that Zeno should not be dismissed as a mere inventor of ingenious puzzles. The problem the paradoxes expose is one that continues to inspire philosophical debate: how to relate appearance to reality, sense to reason.