Zeno of Elea
His paradoxes, like Achilles never catching the tortoise, were meant to show that motion and plurality lead to contradictions.
Placement
Defended Parmenides with famous paradoxes against motion and plurality.
Key ideas
- Achilles and the tortoise
- Reductio ad absurdum
Teachers: Parmenides
Influence
Influenced by 1
Parmenides studied with
studied with later tradition ✓
Known only from later sources – the dramatic scene of Plato’s Parmenides (127a–128e), written decades later, and Diogenes Laertius 9.25; that Zeno’s arguments defend Parmenides is widely accepted, a teaching relation as such is not independently attested. Plato, Parmenides 127a–128e; Sophist 216a; Diogenes Laertius 9.25; SEP “Zeno of Elea”
Evidence: also in Wikidata · Wikidata
Parmenides › c. 515–450 BCE
Influenced 2
Gorgias
influenced
Gorgias’ On Not-Being reworked Zeno’s method of deriving contradictions from a thesis; the version in the pseudo-Aristotelian MXG draws on arguments of Zeno and Melissus. pseudo-Aristotle, On Melissus, Xenophanes and Gorgias (Gorgias section); R. Ioli, ‘Between Eleatics and Atomists: Gorgias’ Argument against Motion’, Archai 31 (2021); IEP “Gorgias”
Evidence: AI draft
Gorgias › c. 483–376 BCE
Democritus
influenced
Democritus answered Eleatic arguments like Zeno’s, that infinite division dissolves bodies into nothing, by positing indivisible atoms (Aristotle, On Generation and Corruption I.2). Aristotle, On Generation and Corruption I.2; SEP “Ancient Atomism”; SEP “Zeno of Elea”
Evidence: AI draft
Democritus › c. 460–370 BCE
Criticism
Criticized by 1
Henri Bergson
criticised by
Bergson traced Zeno’s paradoxes to confusing movement with the divisible line it traverses; each step of Achilles is indivisible (Matter and Memory, 1896, ch. 4). H. Bergson, Matière et mémoire (1896), ch. IV; L’Évolution créatrice (1907), ch. IV
Evidence: AI draft
Henri Bergson › 1859–1941
Position
Zeno defended Parmenides indirectly, by showing that the common-sense assumptions of plurality and motion lead to absurd consequences. In the most famous paradoxes, swift Achilles can never overtake the tortoise, because he must first reach the point where it was, by which time it has moved on; an arrow in flight is at rest at every instant; and to cross any distance one must first complete infinitely many half-distances. Aristotle called him the inventor of dialectic, the art of refuting a thesis from its own premises. His puzzles about infinity, continuity and time occupied mathematicians and philosophers for more than two thousand years.
Life & context
Zeno of Elea was a pupil and close associate of Parmenides, active in the fifth century BCE. Plato describes him visiting Athens together with his teacher. Ancient sources report that he died bravely resisting a tyrant. His book of arguments is lost; we know his paradoxes mainly through Aristotle’s Physics and later commentators.
Main works
- Paradoxes (lost book, c. 460 BCE)
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