Home > Zeno of Elea

"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 …"

Note: Zeno of Elea is not to be confused with Zeno of Citium

1 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 of Zeno is the dialogue of Plato called the Parmenides [1]. In the dialogue, Plato describes a visit to AthensThe history of Athens is the longest of any city in Europe: Athens has been continuously inhabited for at least 3,000 years. In the first millennium BC it became the leading city of Ancient Greece, and for a time ruled its own Athenian Empire. Its cultura by Zeno and Parmenides, at a time when Parmenides is "about 65", Zeno is "nearly 40" and SocratesThis article is about the ancient Greek philosopher. For the Byzantine church historian, see Socrates Scholasticus for the Brazilian football player, see Socrates (football player . Socrates ( June 4, 470 399 BC) ( Greek &#x;Σωκ< is "a very young man" (Parmenides 127). Assuming an age for Socrates of around 20, and taking the date of Socrates birth as 470 BCCenturies: 4th century BC 5th century BC 6th century BC Decades: 520s BC 510s BC 500s BC 490s BC 480s BC 470s BC 460s BC 450s BC 440s BC 430s BC 420s BC Years: 475 BC 474 BC 473 BC 472 BC 471 BC 470 BC 469 BC 468 BC 467 BC 466 BC 465 BC Events Births Socr, 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 127)

Other perhaps less reliable details of Zeno's life are given in Diogenes LaertiusDiogenes Laertius 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 Laertii. Of the circumstances of his life we know nothing. He must' Lives of Eminent Philosophers [2], 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.

2 Works

Although several ancient writers refer to the writings of Zeno, none 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. 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. 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".

According to ProclusProclus Lycaeus ( February 8, 412 April 17, 487), surnamed "The Successor" ( Greek Πρόκλος ὁ Διάδοχος #x50;róklo 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 absurdumReductio ad absurdum ( Latin for "reduction to the absurd", traceable back to the Greek ἡ εις το αδυνατον απαγωγη, "reduction to t also known as proof by contradiction.