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]
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 469 bc. gives an approximate date of birth for Zeno of 490 bc. ad
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 Laertius 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 (ἐπιχείρημα). 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's paradoxes
Zeno's paradoxes have puzzled, challenged, influenced, inspired, infuriated, and amused philosophers, mathematicians, and physicists for over two millennia. The most famous are the so-called "arguments against motion" described by Aristotle in his Physics.[7]
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The Eleatic philosopher, a native of Elea (Velia) in Italy, son of Teleutagoras, and the favourite disciple of Parmenides. He was born about B.C. 488, and at the age of forty accompanied Parmenides to Athens. (See Parmenides.) He appears to have resided some time at Athens, and is said to have unfolded his doctrines to men like Pericles and Callias for the price of 100 minae. Zeno is said to have taken part in the legislation of Parmenides, to the maintenance of which the citizens of Elea had pledged themselves every year by an oath. His love of freedom is shown by the courage with which he exposed his life in order to deliver his native country from a tyrant. Whether he perished in the attempt or survived the fall of the tyrant is a point on which the authorities vary. They also state the name of the tyranny differently. Zeno devoted all his energies to explain and develop the philosophical system of Parmenides. See Zeller's Pre-Socratic Schools (1881).
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