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NOTES AND DISCUSSIONS 537 are presented again? But no part of Protagoras' reply is even mentioned in the Meno. Why not? I can think of but one totally plausible solution to this pu~le, and that is that, contrary to the opinion of virtually all Platonic commentators, the Meno is an earlier work than the Protagoras. That fact would explain why Socrates is befuddled in the Meno and why no reference is made there to any of Protagoras' views. But if it is maintained on some other grounds that the Meno is a later work than the Protagoras , then the puzzle still remains: what is going on in the Meno? STBVEN M. CAHN University of Vermont THE ARGUMENT OF THE 'PORPHYRY TEXT' This note concerns the second of two apparently Eleatic arguments reported in Simplieius' Physics 139,27--140,6. I am not concerned with the question whether the argument originally stemmed from Zeno or from some other source. Rather, I am interested in the fallacy involved in the argument. The two points are not unconnected, of course: one would hesitate to impute an argument to Zeno if that argument contained an idiotic blunder. I quote a translation and numbering of the argument (140, 1-6) by Gregory Vlastos: x Moreover, since indeed (1) it is everywhere alike, then (2) ff it were divisible, it would be divisible everywhere alike, and not divisible here but not there. (3) Let it have been divided everywhere. (4) It is then clear once again that nothing is left, but it will vanish. (0) And if it is to have consistency, it will once again consist of nothing: (5) for if something is left, it would not yet have been divided everywhere. The object of the argument (139, 26) is to show that being is solely one, partless and indivisible. As Professor Vlastos has noted, the key point in the argument is step (3). What in the preceding two steps could even appear to justify the author of the argument in saying, "Let being have been divided everywhere"----especially as the step seems to require the accomplishment of an infinite number of dividings? And if the present argument allows of an actual infinite, one which can be gone through, can it be 1 I am quoting from notes mimeographed by Professor Vlastos from his lectures on Zeno, delivered at the Institute in Greek Philosophy and Science, Summer, 1970. The step marked (0) is so numbered because it seems to play no part in the progress of the argument. This paper originated in my worrying about problems raised in Professor Vlastos' lectures; a version was read in the course. I am grateful to Professor Vlastos for his help in the genesis and formulation of this paper. 538 HISTORY OF PHILOSOPHY plausibly ascribed to an Eleatic source? For, after all, the existence of an actual, traversible infinite would play hob with the canonical Zenonian arguments! ~ A step of the form "Let it be (constructed)" is legitimate only if we have been given the prior assurance, "It can be (constructed). ''s Thus step (3) presupposes what I shall symbolize as: (a) (p)Dp mlt is possible that, for any point p you may choose (i.e., for every point p), being is divided at p. Now neither step (1) nor step (2) nor their conjunction implies (a). The import of step (2), however, seems to be that points are logically interchangeable and indistinguishable : being could be divided at any point. There is no good reason why being should be divided at point Pl rather than at point pz. I shall symbolize this account of the meaning of step (2) as follows: (b) (p) Dp --For any point p you may choose (i.e., for every point p), it is possible that being is divided at p. I find the fallacy in the argument to lie in the confusion between (b), which is warranted by the preceding steps, and (a), which is warranted by nothing. That a statement of the form (b) does not imply a statement of the form (a) is clear from the following counter-lnstance: "Every citizen has a chance of becoming President; but it...

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Additional Information

ISSN
1538-4586
Print ISSN
0022-5053
Pages
pp. 537-539
Launched on MUSE
2008-01-01
Open Access
No
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