Grice, "Notes on Zeno of Elea", The Grice Archive

Item in folder, along with notes on Socrates --.

From wiki:

"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 Falsity (Veritas et Falsitas). Fresco in the Library of El Escorial, Madrid.
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.
[edit] 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.
[edit] 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).