Zeno of Elea

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Zeno of Elea (pronounced /ˈziːnoʊ əv ˈɛliə/, Greek: Ζήνων ὁ Ἐλεάτης) (ca. 490 BC? – ca. 430 BC?) was a pre-Socratic Greek philosopher of southern Italy and a member of the Eleatic School founded by Parmenides. Aristotle called him the inventor of the dialectic.^[1] He is best known for his paradoxes, which Betrand Russell has described as "immeasurably subtle and profound".^[2]

[edit] 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.^[3] 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 has written that Zeno was about twenty-five years younger than Parmenides.^[4]

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,^[5] 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.

According to Plutarch, Zeno attempted to kill the tyrant Demylus, and failing to do so, "with his own teeth bit off his tongue, he spit it in the tyrant’s face."^[6]

[edit] Works

Although several ancient writers refer to the writings of Zeno, none of his writings 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 (Parmenides 127). 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 (Parmenides 128). 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" (Parmenides 127).

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, literally meaning to reduce to the absurd. Parmenides is said^{[citation needed]} to be the first individual to implement this style of argument. This form of argument soon became known as the epicheirema. In Book VII of his Topica, Aristotle says that an epicheirema is a dialectical syllogism. It is a connected piece of reasoning which an opponent has put forward as true. The disputant sets out to break down the dialectical syllogism. Zeno is thought to have devised forty different epicheiremata to support aspects of Parmenides' monism. This destructive method of argument was maintained by him to such a degree that Seneca the Younger commented a few centuries later, If I accede to Parmenides there is nothing left but the One; if I accede to Zeno, not even the One is left.^[4]

[edit] Zeno's paradoxes

Zeno's paradoxes have puzzled, challenged, influenced, inspired, infuriated, and amused philosophers, mathematicians, physicists and school children for over two millennia. The most famous are the so-called "arguments against motion" described by Aristotle in his Physics.^[7]

[edit] See also

• Incommensurable magnitudes

[edit] Notes

[edit] References

• Plato, Plato in Twelve Volumes, translated by H. N. Fowler, Cambridge, MA, Harvard University Press; London, William Heinemann Ltd. 1925.Vol. 4. Cratylus. Parmenides. Greater Hippias. Lesser Hippias. ISBN 0674991850.
• Proclus, Commentary on Plato's Parmenides, translated by Glenn R. Morrow and John M. Dillon, Princeton University Press; Reprint edition (1992) ISBN 0-691-02089-2.
• Russell, Bertrand, The Principles of Mathematics, W. W. Norton & Company; Reissue edition (1996) ISBN 0-393-31404-9.

[edit] Further reading

• Early Greek Philosophy Jonathan Barnes. (Harmondsworth, 1987).
• "Zeno and the Mathematicians" G. E. L. Owen. Proceedings of the Aristotelian Society (1957-8).
• Paradoxes Mark Sainsbury. (Cambridge, 1988).
• Zeno's Paradoxes Wesley Salmon, ed. (Indianapolis, 1970).
• Zeno of Elea Gregory Vlastos in The Encyclopedia of Philosophy (Paul Edwards, ed.), (New York, 1967).

[edit] External links

Wikisource has an original article from the 1913 Catholic Encyclopedia about:

Zeno of Elea

• Zeno of Elea - MacTutor

[edit] External links to online texts

1. Plato's Parmenides.
2. Aristotle's Physics.
3. Diogenes Laertius' Lives of Eminent Philosophers.