- Malcolm Schofield
Zeno (1), of Elea is portrayed by *Plato(1) (Prm. 127b) as the pupil and friend of *Parmenides, and junior to him by 25 years. Their fictional meeting with a ‘very young’ *Socrates (ibid.) gives little basis for firm chronology. We may conclude only that Zeno was active in the early part of the 5th cent. bce. Whether the work from which Plato makes him read was his only book is uncertain.
The most famous of Zeno's arguments are the four paradoxes about motion paraphrased by *Aristotle (Ph. 6. 9), which have intrigued thinkers down to Bertrand Russell in our era. The Achilles paradox proposes that a quicker can never overtake a slower runner who starts ahead of him, since he must always first reach the place the slower has already occupied. His task is in truth an infinite sequence of tasks, and can therefore never be completed. The Arrow paradox argues that in the present a body in motion occupies a place just its own size, and is therefore at rest. But since it is in the present throughout its movement, it is always at rest. The Dichotomy raises the same issues about infinite divisibility as the Achilles; the Arrow and the Stadium (an obscure puzzle about the relative motion of bodies) are perhaps directed against the implicit assumption of indivisible minima.