Zeno of Elea's Argument from Bisection: Newly Discovered Evidence in a Hebrew Translation of Averroes

Ruth Glasner Zeno of Elea's Argument from Bisection: Newly Discovered Evidence in a Hebrew Translation of Averroes The commentary on the Physics by Alexander of Aphrodisias is no longer extant; both the Greek original and the Arabic translation are lost.1 Averroes made extensive use of the latter when he wrote his long commentary on the Physics in about 1186. The Arabic original of this commentary, too, has not survived, but the thirteenth-century Latin translation by Michael Scotus and an anonymous fourteenth-century Hebrew one are extant. The Latin translation is well known and was widely studied by medieval as well as modern scholars. The printed edition published in Venice in 1562, as a part of Averroes' works, is readily accessible.2 The Hebrew translation is less known. While We know almost nothing about the Arabic translation of Alexander's commentary. See F. E. Peters, Aristoteles Arabus (Leiden, 1968), 30-31; S. Harvey, "The Hebrew Translation of Averroes' Prooemium to his long commentary on Aristode's Physics," Proceedings ofthe American AcademyforJewish Research 52 (1983), 55—84, on p. 71 n. 2. Aleph 1 (2001) 285 studying Averroes' commentaries on the Physics I found that the two translations of the long commentary vary considerably.3 Though many passages are more or less the same, some are totally different. One such instance is comment 1.30, which includes Averroes' discussion of Physics 1.3 187al—3. The information presented in what follows is based on the Hebrew version.4 In Physics 1.2 184b25—1.3 187all Aristotle launches an attack on Eleatic monism. Zeno's name is not mentioned.5 In the concluding passage of the discussion Aristotle, referring to two Eleatic arguments, writes: Some people gave in to both arguments, to the argument that if 'is' means only one thing, all things must be one . . . , and to the argument from bisection (ek tes dichotomias) when they posited indivisible magnitudes.6 The first argument is apparently that ascribed to Parmenides and discussed earlier in this chapter.7 The second, the argument from bisection, is not mentioned in the previous discussion. For reasons that will become clear shortly, I prefer Hardie and Gay's translation "bisection" to "dichotomy," which is the rendering of Ross, Charlton, and Waterfield. The question is, what is this second argument ek tes dichotomiasì Modern commentators, following the ancient, agree in ascribing it to Zeno, but disagree as to which of Zeno's arguments is meant.8 Zeller and Ross suggest that the argument is as follows: if being were many it would have to be both infinitely small and infinitely great, both limited and unlimited, which is impossible.9 Charlton suggests that the reference is to the argument of the stadium.10 Let us look at the testimony of the ancient commentators. Simplicius, commenting on this passage, refers to the interpretations of Alexander and Themistius: 286 Ruth Glasner Alexander says that the second argument, that from bisection, is Zeno's, who says that if what is had magnitude and were divided, then what is would be a plurality and no longer one, and thus shows that the one is not an existent. Aristotelis opera cum Averrois commentatiis, vol. IV (Venice, 1562; repr. Frankfurt, 1962). The results of this study have not been published yet. Book I of the long commentary is preserved in four manuscripts. The text below is based on all four: Paris BnF MS héb. 884, numbered 31522 in the Institute for Microfilmed Hebrew Manuscripts at the National and University Library, Jerusalem (IMHM), fols. 19b25-20a23; Paris BnF MS héb. 883 (IMHM 31521), fols. 14b2715al9 ; Oxford Bodl. 1388 (IMHM 22412), fols. 22al3-22bl; Cincinnati, Hebrew Union College, MS 723, fols. 44b7-46b3. It has been suggested that the second part of the discussion (186a32-187all), which mentions no proper names, is a dialogue. This might explain the vagueness of the passage. See D. Gershenson and D. Greenberg, "Aristotle Confronts the Eleatics: Two Arguments on 'The One,'" Phronesis 7 (1962), 137-151, on p. 143. Physics 1.3 187al-3, in W. Charlton, Aristotle's Physics I, II, Translated with Introduction and Notes (Oxford, 1970), p. 7 (slightly modified). Physics 1.3...