[878]. Arist. Phys. Α, 3. 187 a 1 (R. P. 134 b). See below, [§ 173].
[879]. Simpl. Phys. p. 138, 32 (R. P. 134 a).
[880]. Simpl. Phys. p. 99, 13, ὡς γὰρ ἰστορεῖ, φησίν (Ἀλέξανδρος), Εὔδημος, Ζήνων ὁ Παρμενίδου γνώριμος ἐπειρᾶτο δεικνύναι ὅτι μὴ οἷόν τε τὰ ὄντα πολλὰ εἶναι τῷ μηδὲν εἶναι ἐν τοῖς οὖσιν ἕν, τὰ δὲ πολλὰ πλῆθος εἶναι ἐνάδων. This is the meaning of the statement that Zeno ἀνῄρει τὸ ἕν, which is not Alexander’s (as implied in R. P. 134 a), but goes back to no less an authority than Eudemos. It is perfectly correct when read in connexion with the words τὴν γὰρ στιγμὴν ὡς τὸ ἓν λέγει (Simpl. Phys. p. 99, 11).
[881]. It is quite in order that Mr. Bertrand Russell, from the standpoint of pluralism, should accept Zeno’s arguments as “immeasurably subtle and profound” (Principles of Mathematics, p. 347). We know from Plato, however, that Zeno meant them as a reductio ad absurdum of pluralism.
[882]. I formerly rendered “the same may be said of what surpasses it in smallness; for it too will have magnitude, and something will surpass it in smallness.” This is Tannery’s rendering, but I now agree with Diels in thinking that ἀπέχειν refers to μέγεθος and προεχειν to πάχος. Zeno is showing that the Pythagorean point has really three dimensions.
[883]. Reading, with Diels and the MSS., οὔτε ἕτερον πρὸς ἕτερον οὐκ ἔσται. Gomperz’s conjecture (adopted in R. P.) seems to me arbitrary.
[884]. Zeller marks a lacuna here. Zeno must certainly have shown that the subtraction of a point does not make a thing less; but he may have done so before the beginning of our present fragment.
[885]. This is what Aristotle calls “the argument from dichotomy” (Phys. Α, 3. 187 a 1; R. P. 134 b). If a line is made up of points, we ought to be able to answer the question, “How many points are there in a given line?” On the other hand, you can always divide a line or any part of it into two halves; so that, if a line is made up of points, there will always be more of them than any number you assign.
[886]. See last note.
[887]. Arist. Met. Β, 4. 1001 b 7.