Zeno of Elea
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- Zeno of Elea should not be confused with Zeno of Citium.
- In this capricious world nothing is more capricious than posthumous fame. One of the most notable victims of posterity's lack of judgement is the Eleatic Zeno. Having invented four arguments all immeasurably subtle and profound, the grossness of subsequent philosophers pronounced him to be a mere ingenious juggler, and his arguments to be one and all sophisms. After two thousand years of continual refutation, these sophisms were reinstated, and made the foundation of a mathematical renaissance...
- — Bertrand Russell, The Principles of Mathematics (1903)1
Life
Little is known for certain about Zeno's life. Although written nearly a century after Zeno's death, the primary source of biographical information about Zeno is the dialogue of Plato called the Parmenides [link]. In the dialogue, Plato describes a visit to Athens by Zeno and Parmenides, at a time when Parmenides is "about 65," Zeno is "nearly 40" and Socrates is "a very young man" (Parmenides 127). Assuming an age for Socrates of around 20, and taking the date of Socrates' birth as 470 BC, gives an approximate date of birth for Zeno of 490 BC.Plato says that Zeno was "tall and fair to look upon" and was "in the days of his youth … reported to have been beloved by Parmenides." (Parmenides 127)
Other perhaps less reliable details of Zeno's life are given in Diogenes Laertius' Lives of Eminent Philosophers [link], where it is reported that he was the son of Teleutagoras, but the adopted son of Parmenides, was "skilled to argue both sides of any question, the universal critic," and further that he was arrested and perhaps killed at the hands of a tyrant of Elea.
Works
Although several ancient writers refer to the writings of Zeno, none of these survive intact.Plato says that Zeno's writings were "brought to Athens for the first time on the occasion of" the visit of Zeno and Parmenides. Plato also has Zeno say that this work, "meant to protect the arguments of Parmenides," was written in Zeno's youth, stolen, and published without his consent. Plato has Socrates paraphrase the "first thesis of the first argument" of Zeno's work as follows: "[…]if being is many, it must be both like and unlike, and this is impossible, for neither can the like be unlike, nor the unlike like[.]"
According to Proclus in his Commentary on Plato's Parmenides, Zeno produced "not less than forty arguments revealing contradictions[.]" (p. 29)
Zeno's arguments are perhaps the first examples of a method of proof called Reductio ad absurdum, also known as proof by contradiction.
Zeno's paradoxes
- redirect
- The Dichotomy: Motion is impossible since "that which is in locomotion must arrive at the half-way stage before it arrives at the goal." (Aristotle Physics VI:9, 239b10)
A-----B3-----B2-----------B1-------------------------B
- The Achilles: "In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead." (Aristotle Physics VI:9, 239b15)
A----------------------------T1----------------T2---T3
- The Arrow: "If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless." (Aristotle Physics VI:9, 239b5)