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A study on eleatic conception of being

This description suggests a final position as represented in Diagram 2. Apparently, Zeno somehow meant to infer from the fact that the leading B moves past two As in the same time it moves past all four Cs that half the time is equal to its double. The challenge is to develop from this less than startling fact anything more than a facile appearance of paradox.

Since it is stressed that all the bodies are of the same size and that the moving bodies move at the same speed, Zeno would appear to have relied on some such postulate as that a body in motion proceeding at constant speed will move past bodies of the same size in the same amount of time.

The rigorous ontologism of Parmenides and Melissus

He could have argued that in the time it takes all the Cs to move past all the Bs, the leading B moves past two As or goes two lengths, and the leading B also moves past four Cs or goes four lengths. According to the postulate, then, the time the leading B travels must be the same as half the time it travels. Unfortunately, the evidence for this particular paradox does not enable us to determine just how Zeno may in fact have argued.

Aristotle also gestures toward two additional ingenious arguments by Zeno, versions of which were also known to Simplicius. The version of this argument known to Simplicius represents Zeno as engaged in a fictional argument with Protagoras, wherein he makes the point that if a large number of millet seeds makes a sound for example, when poured out in a heapthen one seed or even one ten-thousandth of a seed should also make its own sound for example, in that process Simp.

The evidence nonetheless suggests that Zeno anticipated reasoning related to that of the sorites paradox, apparently invented more than a century later. His subsequent statement of the problem is even briefer but adds one key point: Zeno would appear to have argued as follows.

Everything that is is in something, namely a place. If a place is something, then it a study on eleatic conception of being must be in something, namely some further place. If this second place is something, it must be in yet another place; and the same reasoning applies to this and each successive place ad infinitum.

Thus, if there is such a thing as place, there must be limitless places everywhere, which is absurd. Therefore, there is no such thing as place. This argument could well have formed part of a more elaborate argument against the view that there are many things, such as that if there are many things, they must be somewhere, i.

Parmenides

This is, however, only speculation. After the portion of the exchange between Socrates and Zeno quoted above sect. He, on the other hand, says there are not many things, and he too provides numerous and powerful proofs.

Zeno of Elea

With so many readers of Plato accustomed to taking Socrates as his mouthpiece in the dialogues, it is not surprising that this passage has served as the foundation for the common view of Zeno as Parmenidean legatee and defender, by his own special means, of Eleatic orthodoxy. Zeno this time replies that Socrates has not altogether grasped the truth about his book. First, he says, the book had nothing like the pretensions Socrates has ascribed to it Prm. Zeno is made to explain his actual motivation as follows: For not only does Parmenides end up examining the relation of his One to other things, which would have been impossible if his doctrine entailed their non-existence, but the relation other things have to the One actually proves responsible in a way for their existence.

Zeno cannot be supposing that his arguments against plurality entailed the doctrine of Parmenides when that doctrine is represented in this same dialogue by Parmenides himself as something altogether more involved than the simple thesis that only one thing exists. What Plato actually suggests is that Zeno aimed to show those whose superficial understanding of Parmenides had led them to charge him with flying in the face of common sense, that common sense views concerning unity and plurality are themselves riddled with latent contradictions.

Such is, essentially, the judgment of Jonathan Barnes: Many men had mocked Parmenides: Zeno mocked the mockers. His logoi were designed to reveal the inanities and ineptitudes inherent in the ordinary belief in a plural world; he wanted to startle, to amaze, to disconcert. However, whether the historical Zeno was actually involved in anything like the dialectical context Plato envisages for him must remain uncertain. The more mature Zeno seems a little embarrassed by the combative manner evident in the arguments of his younger days, as well he might since that spirit would have come to be seen as typical of the eristic controversialists who sprang up in the sophistic era.

In the Alcibiades, Socrates reports that Pythodorus and Callias each paid Zeno a hundred minae to become clever and skilled in argument Alc. Teaching for payment is of course one hallmark of the professional educators who styled themselves experts in wisdom. Precisely what Aristotle meant by this remains a matter of speculation, given that Aristotle also attributes the invention of dialectic to Socrates Arist.

For Aristotle, then, Zeno was a controversialist and paradox-monger, whose arguments were nevertheless both sophisticated enough to qualify him as the inventor of dialectic and were important for forcing clarification of concepts fundamental to natural science. A study on eleatic conception of being we a study on eleatic conception of being think of Zeno as a sophist? The skill Plutarch attributes to Zeno, still evident in the fragmentary remains of his arguments, is just the kind of skill in argument manifested in a great deal of sophistic practice.

His apparent demonstrations of how the common-sense view is fraught with contradiction made him an influential precursor of sophistic antilogic and eristic disputation.

It is not surprising that someone like Isocrates should have viewed Zeno as a sophist to be classed with Protagoras and Gorgias.

  1. Furthermore, there can be no creation , for being cannot come from non-being, because a thing cannot arise from that which is different from it.
  2. Of the members, Parmenides and Melissus built arguments starting from sound premises.
  3. Even if the effort to think about what lies along the second way ends as it does in a total failure of apprehension, this non-apprehension remains unwavering. So I beg you to permit me to use this word.

While he perhaps does not fit exactly into any of these categories, still his development of sophisticated methods of argumentation to produce apparent proofs of the evidently false conclusions that motion is impossible and that there are not in fact many things made it quite natural for Plato, Aristotle, Isocrates, and others to refer to him under all these labels.

Several of the paradoxes involve no specifically mathematical notions at all. The Achilles is perhaps the best example since it employs only very ordinary notions, such as getting to where another has started from.

The other extant arguments for the most part deploy similarly prosaic notions: Where Zeno seems to have leapt ahead of earlier thinkers is in deploying specifically quantitative concepts, most notably quantitative concepts of limit peras and the lack of limit to apeiron.

Earlier Greek thinkers had tended to speak of limitedness and unlimitedness in ways suggesting a qualitative rather than a quantitative notion. They had an immediate impact on Greek physical theory. His arguments, perhaps more than anything else, forced the Greek natural philosophers to develop properly physical theories of composition as opposed to the essentially chemical theories of earlier thinkers such as Empedocles.

That mathematicians and physicists have worked ever since to develop responses to the more ingenious of his paradoxes is remarkable, though perhaps not surprising, for immunity to his paradoxes might be taken as a condition upon the adequacy of our most basic physical concepts.

He may even have offered his collection of paradoxes to provoke deeper consideration a study on eleatic conception of being the adequacy of theretofore unexamined notions. Bibliography Further Reading References in this bibliography to items prior to 1980 are more selective than those to more recent items.

For a nearly exhaustive and annotated listing of Zenonian scholarship down to 1980, consult L. Bibliographie analytique 1879—1980Volume 2, Montreal: Les Belles Lettres, 1989, pp.

Comprehensive accounts of Zeno and his arguments may be found in: Chapters 12 and 13. Cambridge University Press, 1965, Part I.

Schofield, The Presocratic Philosophers, 2nd edition, Cambridge: Cambridge University Press, 1983, Chapter 9. Cambridge University Press, 1999, pp. Cambridge University Press, 1995, Chapter 1. Vlastos, Studies in Greek Philosophy Volume 1: The PresocraticsD. Princeton University Press, 1993, pp. The Presocratics and Sophists, Oxford: Primary Sources The standard collection of the fragments of the Presocratics and sophists, together with testimonia pertaining to their lives and thought, remains: A Text a study on eleatic conception of being Translation and Notes, Cambridge: Cambridge University Press, 1936.

Cambridge University Press, 2010. Texts of the ancient authors other than Zeno referred to in the article: Diogenes Laertius, Vitae Philosophorum, M. Eudemus, Eudemos von Rhodos, F. Isocrates, Opera Omnia, B. Cambridge University Press, 2001.

Eleaticism

Reimer, 1882 and 1895. English translations of these works may be found in: The Complete Works of Aristotle: The Revised Oxford Translation, J. Princeton University Press, 1984. Harvard University Press, 1925. Harvard University Press, 1945. Plutarch, The Rise and Fall of Athens: Nine Greek Lives by Plutarch, I.

Princeton University Press, 1987. Harvard University Press, 1935. Duckworth, and Ithaca, NY: Cornell University Press, 1992. Simplicius, On Aristotle Physics 6, D.

  • Such sentences can, however, mean, 'x exists';
  • One of Plato's favorite locutions to refer to the forms eide is to ontos on, using the adverb made from the participle to intensify its meaning, literally, "the beingly being," but typically translated into English as "the really real;
  • This is discussed at length by Boman, and I shall later make some remarks about his treatment of it.

Cornell University Press, 1989. Cornell University Press, 1994. A plate of the red-figure drinking cup, Mus. Arte Tipografice Editrice, pp. Van Gorcum, 1990, pp. Clarendon Press, Chapter 5. Oxford University Press, Chapter 5. Cambridge University Press, 1954, pp. Oxford University Press, pp.