Zeno of Elea

Zeno of Elea (pronEng|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 [Cited in Diogenes Laertius 8.57 and 9.25.] , and Bertrand Russell credited him with having laid the foundations of modern logic. He is best known for his paradoxes.

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". [Plato (370 BCE). [http://classics.mit.edu/Plato/parmenides.html "Parmenides"] , translated by Benjamin Jowett. Internet Classics Archive.] 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 abouttwenty-five years younger than Parmenides."Zeno" in "The Presocratics", Philip Wheelwright ed., The Odyssey Press, 1966, Pages 106-107.]

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", [Diogenes Laertius. "The Lives and Opinions of Eminent Philosophers", literally translated by C.D. Yonge. London: Henry G. Bohn, 1853. [http://classicpersuasion.org/pw/diogenes/dlzeno-eleatic.htm Scanned and edited for Peithô's Web.] ] 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." [AGAINST COLOTES, THE DISCIPLE AND FAVORITE OF EPICURUS. - Plutarch, The Morals]

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 saidFact|date=May 2008 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."

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". [Aristotle (350 BCE). [http://classics.mit.edu/Aristotle/physics.html "Physics"] , translated by R.P. Hardie and R.K. Gaye. Internet Classics Archive.]

ee also

* Incommensurable magnitudes

Notes

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.

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).

External links

* [http://www-history.mcs.st-andrews.ac.uk/Biographies/Zeno_of_Elea.html Zeno of Elea] - MacTutor

External links to online texts

# [http://classics.mit.edu/Plato/parmenides.html Plato's "Parmenides"] .
# [http://classics.mit.edu/Aristotle/physics.html Aristotle's "Physics"] .
# [http://classicpersuasion.org/pw/diogenes/dlzeno-eleatic.htm#cite Diogenes Laertius' "Lives of Eminent Philosophers"] .

Persondata
NAME= Zeno of Elea
ALTERNATIVE NAMES=Ζήνων ὁ Ἐλεάτης;
SHORT DESCRIPTION=pre-Socratic Greek philosopher
DATE OF BIRTH=490 BC?
PLACE OF BIRTH=
DATE OF DEATH=430 BC?
PLACE OF DEATH=