Zeno of Elea

Zeno of Elea was a Greek philosopher, a student and defender of Parmenides, whom Plato depicts visiting Athens with his teacher. His book of arguments is lost, and his paradoxes are known mainly through Aristotle's Physics and later commentators. Arguments such as the dichotomy and Achilles and the tortoise aimed to show that plurality and motion lead to absurdities, and they put pressure on the assumption that space and time are infinitely divisible. They have provoked responses from ancient atomists to modern mathematicians.

Key ideas

• To cross any distance one must first cross half of it, and so on without end (the dichotomy).
• Achilles can never overtake the tortoise, since he must first reach where it was.
• A flying arrow is at rest at every instant, so it never moves.
• If there are many things, they must be both infinitely small and infinitely large.

Major works

• No writings survive; arguments reported in Plato, Parmenides
• Aristotle, Physics, Book VI (record of the paradoxes of motion)
• Simplicius, Commentary on Aristotle's Physics (preserves fragments)

In the conversation

• Question Hui Shi’s Ten Theses: paradoxes for their own sake, or a theory of space? Chen Yuting · 4 replies