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, and Bertrand Russell credited him with having laid the foundations of modern logic. He is best known for his paradoxes. Elea (Velia by the Romans; see also List of traditional Greek place names) was a Greek coastal city founded around 540 BC in Lucania in southern Italy, 15 miles southeast of the Gulf of Salerno. ... Centuries: 6th century BC - 5th century BC - 4th century BC Decades: 540s BC 530s BC 520s BC 510s BC 500s BC - 490s BC - 480s BC 470s BC 460s BC 450s BC 440s BC Years: 495 BC 494 BC 493 BC 492 BC 491 BC - 490 BC - 489 BC 488 BC... Centuries: 6th century BC - 5th century BC - 4th century BC Decades: 480s BC 470s BC 460s BC 450s BC 440s BC - 430s BC - 420s BC 410s BC 400s BC 390s BC 380s BC Years: 435 BC 434 BC 433 BC 432 BC 431 BC - 430 BC - 429 BC 428 BC... Pre-Socratic philosophers are often very hard to pin down, and it is sometimes very difficult to determine the actual line of argument they used in supporting their particular views. ... A philosopher is a person who thinks deeply regarding people, society, the world, and/or the universe. ... The Eleatics were a school of pre-Socratic philosophers at Elea, a Greek colony in Lucania, Italy. ... Parmenides of Elea (Greek: , early 5th century BC) was an ancient Greek philosopher born in Elea, a Hellenic city on the southern coast of Italy. ... For other uses, see Aristotle (disambiguation). ... In classical philosophy, dialectic (Greek: διαλεκτική) is controversy, Viz. ... Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS, (18 May 1872 – 2 February 1970), was a British philosopher, logician, mathematician, advocate for social reform, and pacifist. ... “Arrow paradox” redirects here. ...

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.^[1] 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.^[2] For other uses, see Plato (disambiguation). ... Parmenides is one of the dialogues of Plato. ... The History of Athens is one of the longest of any city in Europe and in the world. ... This page is about the Classical Greek philosopher. ... Suspected of plotting to seize power in Sparta by instigating a helot uprising, Pausanias takes refuge in the Temple of Athena of the Brazen House to escape arrest. ...

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,^[3] 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. Diogenes Laërtius, the biographer of the Greek philosophers, is supposed by some to have received his surname from the town of Laerte in Cilicia, and by others from the Roman family of the Laërtii. ...

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). This article is about Proclus Diadochus, the Neoplatonist philosopher. ...

Zeno's arguments are perhaps the first examples of a method of proof called reductio ad absurdum, literally meaningto reduce to the absurd. Parmenides is said 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.^[2] Reductio ad absurdum (Latin: reduction to the absurd) also known as an apagogical argument, reductio ad impossibile, or proof by contradiction, is a type of logical argument where one assumes a claim for the sake of argument, derives an absurd or ridiculous outcome, and then concludes that the original assumption... For other uses, see Aristotle (disambiguation). ... A syllogism (Greek: — conclusion, inference), usually the categorical syllogism, is a kind of logical argument in which one proposition (the conclusion) is inferred from two others (the premises) of a certain form. ... For other uses, see Monist (disambiguation). ... Bust, traditionally thought to be Seneca, now identified by some as Hesiod. ...

Zeno's paradoxes

Main article: 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.^[4] “Arrow paradox” redirects here. ...

Notes

For other uses, see Plato (disambiguation). ... Year 1966 (MCMLXVI) was a common year starting on Saturday (link will display full calendar) of the 1966 Gregorian calendar. ... Diogenes Laërtius, the biographer of the Greek philosophers, is supposed by some to have received his surname from the town of Laerte in Cilicia, and by others from the Roman family of the Laërtii. ... For other uses, see Aristotle (disambiguation). ...

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.

For other uses, see Plato (disambiguation). ... Henry Watson Fowler (10 March 1858 – 26 December 1933) was an English schoolmaster, lexicographer and commentator on the usage of English. ... This article is about Proclus Diadochus, the Neoplatonist philosopher. ... Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS, (18 May 1872 – 2 February 1970), was a British philosopher, logician, mathematician, advocate for social reform, and pacifist. ...

See also

• Incommensurable magnitudes

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).

Jonathan Barnes (born 1942) is a British philosopher, translator and historian of ancient philosophy. ... R. Mark Sainsbury (born 1943) is a philosopher from the United Kingdom who has worked in the areas of philosophical logic, philosophy of language, reference, and the philosophies of Bertrand Russell and Gottlob Frege. ... To meet Wikipedias quality standards and make it more accessible to a general audience, this article may require cleanup. ... Gregory Vlastos (27 July 1907 - 12 October 1991) was a scholar of ancient philosophy, and author of several works on Plato and Socrates. ... Paul Edwards, born Paul Eisenstein, (September 2, 1923-December 9, 2004) was an Austrian-American moral philosopher. ...

External links

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

Zeno of Elea

• Zeno of Elea - MacTutor

Image File history File links Wikisource-logo. ... The original Wikisource logo. ... Not to be confused with New Catholic Encyclopedia. ...

External links to online texts

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