Paradoxes

Zeno of Elea, a student and defender of Parmenides, is known through Aristotle's Physics and later commentators for a set of paradoxes designed to show that motion and plurality generate contradictions, defending his teacher's monism by attacking its rivals rather than by adding new positive doctrine. The most famous, Achilles and the tortoise, argues that a faster runner can never overtake a slower one given a head start, since he must first reach the point where the tortoise started, by which time it has moved further ahead, in an infinite regress; the Dichotomy paradox similarly shows that any motion requires completing infinitely many sub-motions first. Aristotle called Zeno the inventor of dialectic, and his paradoxes remained a genuine mathematical and philosophical puzzle, addressed by thinkers from Aristotle through the development of calculus limits, for over two thousand years.