Zeno of Elea

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Greek philosopher (c. 490 bc–c. 430 bc)

Zeno was born at Elea (now Velia in Italy) and in about 450 bc accompanied his teacher, Parmenides, to Athens. There he propounded the theories of the Eleatic school and became famous for his series of paradoxes and his invention of dialectic.

Little survives of Zeno's written work and this only in other authors' writings. He proposed that motion and multiplicity are unreal (thus supporting Parmenides's theories) since assumption of their existence gave rise to contradictory propositions. One of the most famous arguments against plurality and motion is that of Achilles and the tortoise: if the tortoise is given a start in a race against Achilles, when Achilles reaches the tortoise's starting position, the tortoise will have advanced a small way to a new position. Endless repetition of this argument means that Achilles can never overtake the tortoise.

Zeno's paradoxes remained unresolved for about 20 centuries, in fact until the advances in rigor of mathematical analysis (to the development of which these paradoxes may be said to have contributed). These advances included the study of convergent series (infinite series with a finite sum), the invention by Gottfried Leibniz and Isaac Newton of calculus, and Georg Cantor's theory of the infinite in the 19th century.

Following his return to Elea Zeno died while joining a coup against the tyrant Nearchus.

Zeno of Elea (born ca. 490 B.C.) was a Greek philosopher and logician. A member of the Eleatic school of philosophy, he was famous throughout antiquity for the rigorously logical and devastating arguments which he used to show the absurdities and contradictions of his opponents.

Zeno was born in the southern Italian city of Elea. Plato says that Zeno and Parmenides visited Athens about 449 B.C., where the young Socrates made their acquaintance and where Zeno made a striking impression. Ancient authorities asserted that, like Parmenides, Zeno was a Pythagorean, that he engaged in political activity in his native city, and that he was put to death for plotting against a tyrant. An oft-repeated story tells of his bravery under torture and the painful death which he endured.

It is possible that Zeno wrote more than one work, but he is best known for a single volume of epicheiremata (attacks) on the postulates of Parmenides's opponents. Only fragments of this work have survived, but a fairly clear idea of his methods may be found in the summaries given by Aristotle and the 6th-century A.D. Neoplatonist Simplicius. Zeno seems to have had no constructive theories of his own to set forth, and some of his destructive arguments seem to apply equally well to the conclusions drawn by Parmenides.

Zeno's original contribution to thought was the method of deduction which he developed to work out two sets of contradictory conclusions from a given postulate. From his argument against the pluralists, the following example is typical. Let it be postulated that everything has developed from an originally plural source (as opposed to Parmenides's One). If things are many, then they are finite since they are the number that they are. But if things are many, they are infinite since there must always be other things between them, and others between those ad infinitum.

From Zeno's arguments on motion comes the famous example which shows the impossibility of ever reaching the end of a given line. A moving body cannot reach the end because it must constantly reach the midpoint, and then another midpoint, again ad infinitum. It is unclear from the available evidence if Zeno's purpose was to offer a serious defense of the One or if he simply wanted to show that other arguments were no better. Aristotle called him the inventor of dialectic, and Zeno was undoubtedly one of the important early Greek logicians.

Further Reading

Selected passages from Zeno's work in English translation and with commentary are in Geoffrey S. Kirk and John E. Raven, The Presocratic Philosophers: A Critical History with a Selection of Texts (1957). Excellent discussions of Zeno's importance and place in the development of Greek thought are in John Burnet, Early Greek Philosophy (1892; 4th ed. 1930), and Kathleen Freeman, The Pre-Socratic Philosophers: A Companion to Diels, Fragmente der Vorsokratiker (1940; 3d ed. 1953). More generalized discussions of the Pre-Socratics and their place in Greek literature and thought appear in the standard histories of Greek literature, such as that by Albin Lesky, A History of Greek Literature (1958; trans. 1966).

(fl. early 5th c. bc) The pupil and principal defender of Parmenides, Zeno was called the inventor of dialectic by Aristotle. His one book, of which we possess only fragments, contained many arguments for the unreality of the pluralistic world that we take ourselves to inhabit. The most famous of these are the four arguments against motion, known as Zeno's paradoxes. But Zeno also proposed many other antinomies, showing that objects must be both limited and unlimited in number, like and unlike, one and many, infinitesimally small and infinitely large. Zeno's own attitude to these antinomies, as to his arguments against motion, has been disputed, but he is consistently described as a convinced Parmenidean.

— Richard L. Gregory

Not to be confused with Zeno of Citium.

This article is about the Greek philosopher. For other uses, see Zeno.

Zeno of Elea[citation needed]
Born	ca. 490 BCE
Died	ca. 430 BCE
Era	Pre-Socratic philosophy
Region	Western Philosophy
School	Eleatic school
Main interests	Metaphysics, Ontology
Notable ideas	Zeno's paradoxes
Influenced by Parmenides
Influenced Plato, Aristotle, Protagoras, Gorgias

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 Bertrand Russell has described as "immeasurably subtle and profound".^[2]

Contents 1 Life 2 Works 3 Zeno's paradoxes 4 See also 5 Notes 6 References 7 Further reading 8 External links

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" (Parmenides 127b) and Socrates is "a very young man" (Parmenides 127c). 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 127b).

Other perhaps less reliable details of Zeno's life are given by Diogenes Laërtius in his Lives and Opinions of Eminent Philosophers,^[4] 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 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."^[5]

Works

Although many 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 127c). Plato also has Zeno say that this work, "meant to protect the arguments of Parmenides" (Parmenides 128c), was written in Zeno's youth, stolen, and published without his consent (Parmenides 128e). 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 127d,e).

According to Proclus in his Commentary on Plato's Parmenides, Zeno produced "not less than forty arguments revealing contradictions" (p. 29), but only nine are now known.

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. 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.^[6]

Zeno of Elea shows Youths the Doors to Truth and False (Veritas et Falsitas). Fresco in the Library of El Escorial, Madrid.

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.^[7]

See also

• Incommensurable magnitudes

Notes

1. ^ Cited in Diogenes Laërtius 8.57 and 9.25.
2. ^ Russell, p. 347: "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..."
3. ^ Plato (370 BC). Parmenides, translated by Benjamin Jowett. Internet Classics Archive.
4. ^ Diogenes Laërtius. The Lives and Opinions of Eminent Philosophers, literally translated by C.D. Yonge. London: Henry G. Bohn, 1853. Scanned and edited for Peithô's Web.
5. ^ Plutarch, Against Colotes
6. ^ Zeno in The Presocratics, Philip Wheelwright ed., The Odyssey Press, 1966, Pages 106-107.
7. ^ Aristotle (350 BCE). Physics, translated by R.P. Hardie and R.K. Gaye. Internet Classics Archive.

References

• Plato; Fowler, Harold North (1925) [1914]. Plato in twelve volumes. 8, The Statesman.(Philebus).(Ion). Loeb Classical Library. trans. W. R. M. Lamb. Cambridge, Mass.: Harvard U.P. ISBN 9780434991648. OCLC 222336129. 
• Proclus; Morrow, Glenn R.; Dillon, John M. (1992) [1987]. Proclus' Commentary on Plato's Parmenides. Princeton, N.J.: Princeton University Press. ISBN 9780691020891. OCLC 27251522. 
• Russell, Bertrand (1996) [1903]. The Principles of Mathematics. New York, NY: Norton. ISBN 9780393314045. OCLC 247299160. 

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 C. Salmon, ed. (Indianapolis, 1970).
• Zeno of Elea Gregory Vlastos in The Encyclopedia of Philosophy (Paul Edwards, ed.), (New York, 1967).

External links

Wikimedia Commons has media related to: Zeno of Elea

Wikisource has original text related to this article: Zeno

• Zeno of Elea - MacTutor
• Plato's Parmenides.
• Aristotle's Physics.
• Diogenes Laertius' Lives of Eminent Philosophers.

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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

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