Zeno of Elea (490 B.C. — 430 B.C.)
He was an Eleatic philosopher, a native of Elea (Velia) in Italy, son of Teleutagoras, and the favorite disciple of Parmenides. He was born about 488 BCE, and at the age of forty accompanied Parmenides to Athens. Zeno was a Pre-Socratic and, as Socrates discovered philosophy, this meant he couldn't actually do proper philosophy. So instead he spent most of his life thinking of ways to reword the same paradox.
Zeno's famous paradox (and its many rewordings) tries to show that change is not possible — I suppose you have to give him credit for being original (although it was much easier back when philosophy hadn't been discovered yet). His argument goes as follows: imagine a tortoise and Achilles having a race; the tortoise is given a head start of a meter or two. But, argues Zeno, it is now impossible for Achilles to catch the tortoise because he's too busy fighting in the Trojan War to spare the time to race a bloody tortoise. Hence, nothing changes.
Zeno's contribution to Eleatic philosophy is entirely negative. He did not add anything positive to the teachings of Parmenides, but devoted himself to refuting the views of the opponents of Parmenides. Parmenides had taught that the world of sense is an illusion because it consists of motion (or change) and plurality (or multiplicity or the many).
Zeno's theory was not popular with those people that believed in change (i.e. everyone in the whole world except Zeno). As a result Zeno gave up pre-philosophy and became the world's first living statue.
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" , 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.
Sources:
· (Wales, 2008)
· (The Endless Greece Travel Guide team, 2005)
http://en.wikipedia.org/wiki/Zeno_of_Elea 