If when something is taken away that which is left is no less, and if it becomes no greater by receiving additions, evidently that which has been added or taken away is nothing.’ These things Zeno says, not denying the one, but holding that each thing has the greatness of many and infinite things, since there is always something before that which is apprehended, by reason of its infinite divisibility and this he proves by first showing that nothing has any greatness because each thing of the many is identical with itself and is one. 1)9 ‘For if, he says, anything were added to another being, it could not make it any greater for since greatness does not exist, it is impossible to increase the greatness of a thing by adding to it. By this he shows that what has neither greatness nor thickness nor bulk could not even be. Among these arguments is one by which he shows that if there are many things, these are both small and great – great enough to be infinite in size, and small enough to be nothing in size. He thinks that what is not increased by receiving additions, or decreased as parts are taken away, is not one of the things that are.’ It was natural that Zeno, who, as if for the sake of exercise, argued both sides of a case (so that he is called double-tongued), should utter such statements raising difficulties about the one but in his book which has many arguments in regard to each point, he shows that a man who affirms multiplicity naturally falls into contradictions. But he is puzzled, it seems, because each of the senses declares that there are many things, both absolutely, and as the result of division, but no one establishes the mathematical point. He reports Zeno as saying that if any one explains to him the one, what it is, he can tell him what things are. For Eudemos says in his Physics, ‘Then does not this exist, and is there any one ? This was the problem. 1885 Dunan, Les arguments de Zenon, Paris 1884 Brochard, Les arguments de Zenon, Paris 1888 Frontera, Etude sur les arguments de Zenon, Paris 1891ģ0 r 138, 30. Literature: Lohse, Halis 1794 Gerling, de Zenosin Paralogismis, Marburg 1825 Wellmann, Zenos Beweise, G.-Pr. 127 c), each section of which showed the absurdity of some element in the popular belief. We find reference to one book which he wrote in prose (Plato, Parm.
There are numerous accounts of his capture as party to a conspiracy these accounts differ widely from each other, and the only point of agreement between them has reference to his determination in shielding his fellow conspirators. Several writers say that he taught in Athens for a while. 1, 1) applies to him as well as to his master the name Pythagorean, and gives him the credit of advancing the cause of law and order in Elea. He was the pupil of Parmenides, and his relations with him were so intimate that Plato calls him Parmenides’s son (Soph. Zeno of Elea, son of Teleutagoras, was born early in the-fifth century B.C. Passages relating to Zeno in the Doxographists Zeno’s arguments as described by Aristotle Simplicius’s account of Zeno’s arguments, including the translation of the Fragments Proofread and pages added by Jonathan Perry, March 2001. Scanned and proofread by Aaron Gulyas, May 1998.
0 kommentar(er)
