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. 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 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 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 Topics, 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."
Read more about this topic: Zeno Of Elea
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