Chapter 32

851. Diog. ix. 29 (R. P. 130 a). Apollodoros is not expressly referred to for Zeno’s date; but, as he is quoted for his father’s name (ix. 25; R. P. 130), there can be no doubt that he is also the source of thefloruit.

852. Plato,Parm.127 b (R. P. 111 d). The visit of Zeno to Athens is confirmed by Plut.Per.4 (R. P. 130 e), where we are told that Perikles “heard” him as well as Anaxagoras. It is also alluded to inAlc.I. 119 a, where we are told that Pythodoros, son of Isolochos, and Kallias, son of Kalliades, each paid him 100 minae for instruction.

853. Plato,Soph.241 d (R. P. 130 a).

854. Plato,Parm.,loc. cit.

855. Strabo, vi. p. 252 (R. P. 111 c).

856. Diog. ix. 26, 27, and the other passages referred to in R. P. 130 c.

857. Diog. ix. 26 (R. P. 130); Suidass.v.(R. P. 130 d).

858. Plato,Parm.128 d 6 (R. P. 130 d).

859.Berl. Sitzb., 1884, p. 359.

860. See above, p. 321,n.740. It hardly seems likely that a later writer would make Zeno argue πρὸς τοὺς φιλοσόφους, and the title given to the book at Alexandria must be based on something contained in it.

861. Arist.Phys.Η, 5. 250 a 20 (R. P. 131 a).

862. Simpl.Phys.p. 1108, 18 (R. P. 131). If this is what Aristotle refers to, it is hardly safe to attribute the κεγχρίτης λόγος to Zeno himself. It is worth noting that the existence of this dialogue is another indication of Zeno’s visit to Athens at an age when he could converse with Protagoras, which agrees very well with Plato’s representation of the matter.

863. Arist.Soph. El.170 b 22 (R. P. 130 b).

864. Chap. V. p. 231,n.512.

865. Diog. iii. 48. It is certain that the authority whom Diogenes follows here took the statement of Aristotle to mean that Alexamenos was the first writer of prose dialogues.

866. Plato,Parm.127 d. Plato speaks of the first ὑπόθεσις of the first λόγος, which shows that the book was really divided into separate sections. Proclus (in loc.) says there were forty of these λόγοι altogether.

867. Simplicius expressly says in one place (p. 140, 30; R. P. 133) that he is quoting κατὰ λέξιν. I now see no reason to doubt this, as the Academy would certainly have a copy of the work. If so, the fact that the fragments are not written in Ionic is another confirmation of Zeno’s residence at Athens.

868. Arist.Phys.Ζ, 9. 239 b 9 sqq.

869. Cf. Diog. ix. 25 (R. P. 130).

870. Plato,Parm.128 c (R. P. 130 d).

871. The technical terms used in Plato’sParmenidesseem to be as old as Zeno himself. The ὑπόθεσις is the provisional assumption of the truth of a certain statement, and takes the form εἰ πολλά ἐστι or the like. The word does not mean the assumption of something as a foundation, but the setting before one’s self of a statement as a problem to be solved (Ionic ὑποθέσθαι, Attic προθέσθαι). If the conclusions which necessarily follow from the ὑπόθεσις (τὰ συμβαίνοντα) are impossible, the ὑπόθεσις is “destroyed” (cf. Plato,Rep.533 c 8, τὰς ὑποθέσεις ἀναιροῦσα). The author of the Περὶ ἀρχαίης ἰατρικῆς (c 1) knows the word ὑπόθεσις in a similar sense.

872. The view that Zeno’s arguments were directed against Pythagoreanism has been maintained in recent times by Tannery (Science hellène, pp. 249 sqq.), and Bäumker (Das Problem der Materie, pp. 60 sqq.).

873. Zeller, p. 589 (Eng. trans. p. 612).

874. This is the view of Stallbaum in his edition of theParmenides(pp. 25 sqq.).

875.Parm.,loc. cit.

876. Chap. VI.§ 120.

877. Cf. for instance Anaxagoras, fr.3, with Zeno, fr.2; and Anaxagoras, fr.5, with Zeno, fr.3.

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 areductio ad absurdumof 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.

888. Arist.Phys.Δ, 1. 209 a 23; 3. 210 b 22 (R. P. 135 a).

889. Simpl.Phys.p. 562, 3 (R. P. 135). The version of Eudemos is given in Simpl.Phys.p. 563, 26, ἀξιοῖ γὰρ πᾶν τὸ ὂν ποῦ εἷναι· εἱ δὲ ὁ τόπος τῶν ὄντων, ποῦ ἂν εἴη· οὐκοῦν ἐν ἄλλῳ τόπῳ κἀκεῖνος δὴ ἐν ἄλλῳ καὶ οὕτως εἰς τὸ πρόσω.

890. Arist.Top.Θ, 8. 160 b 8, Ζήνωνος (λόγος), ὅτι οὐκ ἐνδέχεται κινεῖσθαι οὐδὲ τὸ στάδιον διελθεῖν.

891. Arist.Phys.Ζ, 9. 239 b 11 (R. P. 136). Cf. Ζ, 2. 233 a 11; a 21 (R. P. 136 a).

892. Arist.Phys.Ζ, 9. 239 b 14 (R. P. 137).

893.Phys.Ζ, 9. 239 b 30 (R. P. 138);ib.239 b 5 (R. P. 138 a). The latter passage is corrupt, though the meaning is plain. I have translated Zeller’s version of it εἰ γάρ, φησίν, ἠρεμεῖ πᾶν ὅταν ᾖ κατὰ τὸ ἴσον, ἔστι δ’ ἀεὶ τὸ φερόμενον ἐν τῷ νῦν κατὰ τὸ ἴσον, ἀκίνητον, κ.τ.λ. Of course ἀεί means “at any time,” not “always,” and κατὰ τὸ ἴσον is, literally, “on a level with a space equal (to itself).” For other readings, see Zeller, p. 598, n. 3; and Diels,Vors.p. 131, 44.

894. The word is ὄγκοι; cf. Chap. VII. p. 338,n.794. The name is very appropriate for the Pythagorean units, which Zeno had shown to have length, breadth, and thickness (fr.1).

895. Arist.Phys.Ζ, 9. 239 b 33 (R. P. 139). I have had to express the argument in my own way, as it is not fully given by any of the authorities. The figure is practically Alexander’s (Simpl.Phys.p. 1016, 14), except that he represents the ὄγκοι by letters instead of dots. The conclusion is plainly stated by Aristotle (loc. cit.), συμβαίνειν οἴεται ἴσον εἶναι χρόνον τῷ διπλασίῳ τὸν ἥμισυν, and, however we explain the reasoning, it must be so represented as to lead to this conclusion.

896. Plut.Per.26 (R. P. 141 b), from Aristotle’s Σαμίων πολιτεία.

897. Diog. ix. 24 (R. P. 141). It is possible, of course, that Apollodoros meant the first and not the fourth year of the Olympiad. That is his usual era, the foundation of Thourioi. But, on the whole, it is more likely that he meant the fourth; for the date of the ναυαρχία would be given with precision. See Jacoby, p. 270.

898. Diog. ix. 24 (R. P. 141).

899. It is no longer necessary to discuss the passages which used to appear as frs. 1-5 of Melissos, as it has been proved by A. Pabst that they are merely a paraphrase of the genuine fragments (De Melissi Samii fragmentis, Bonn, 1889). Almost simultaneously I had independently come to the same conclusion (see the first edition, § 138). Zeller and Diels have both accepted Pabst’s demonstration, and the supposed fragments have been relegated to the notes in the last edition of R. P. I still believe, however, that the fragment which I have numbered 1ais genuine. See next note.

900. These words come from the beginning of the paraphrase which was so long mistaken for the actual words of Melissos (Simpl.Phys.p. 103, 18; R. P. 142 a), and Diels has accordingly removed them along with the rest. I believe them to be genuine because Simplicius, who had access to the complete work, introduces them by the words ἄρχεται τοῦ συγγράμματος οὕτως, and because they are thoroughly Eleatic in character. It is quite natural that the first words of the book should be prefixed to the paraphrase.

901. This fragment is quoted by Simpl.de Caelo, p. 557, 16 (R. P. 144). The insertion of the word “infinite” is justified by the paraphrase (R. P. 144 a) and byM.X.G.974 a 11, πᾶν δὲ ἄπειρον ὂν <ἓν> εἶναι· εἰ γὰρ δύο ἢ πλείω εἴη, πέρατ’ ἂν εἶναι ταῦτα πρὸς ἄλληλα.

902. I have ventured to insert this, though the actual words are nowhere quoted, and it is not in Diels. It is represented in the paraphrase (R. P. 145 a) and inM.X.G.974 a 13 (R. P. 144 a).

903. Reading ὁμουρέων with Bergk. Diels keeps the MS. ὀμοῦ ῥέων; Zeller (p. 613, n. 1) conjectures ὑπ’ ἰοῦ ῥέων.

904. I read εἰ μὲν οὖν εἴη with E F for the εἰ μὲν ὂν εἴη of D. The ἐὸν which still stands in R. P. is a piece of local colour due to the editors. Diels also now reads οὖν (Vors.p. 149, 2).

905. Diels now reads ἀλλὰ with E for the ἅμα of F, and attaches the word to the next sentence.

906. Arist.Phys.Α, 3. 186 a 7 (R. P. 143 a). Aristotle finds two flaws in the Eleatic reasoning: (1) ψευδῆ λαμβάνουσιν; (2) ἀσυλλόγιστοί εἰσιν αὐτῶν οἱ λόγοι. This is the first of these flaws. It is also mentioned inSoph. El.168 b 35 (R. P.ib.). So Eudemosap.Simpl.Phys.p. 105, 24, οὐ γὰρ, εἰ τὸ γενόμενον ἀρχὴν ἔχει, τὸ μὴ γενόμενον ἀρχὴν οὐκ ἔχει, μᾶλλον δὲ τὸ μὴ ἔχον ἀρχὴν οὐκ ἐγένετο.

907. The real reason is given in the paraphrase in Simpl.Phys.p. 103, 21 (R. P. 142 a), συγχωρεῖται γὰρ καὶ τοῦτο ὑπὸ τῶν φυσικῶν, though of course Melissos himself would not have put it in that way. He regarded himself as a φυσικός like the rest; but, from the time of Aristotle, it was a commonplace that the Eleatics were not φυσικοί, since they denied motion.

908. This has been denied by Offner,“Zur Beurtheilung des Melissos”(Arch.iv. pp. 12 sqq.), but I now think he goes too far. Cf. especiallyTop.ix. 6, ὡς ἄμφω ταὐτὰ ὄντα τῷ ἀρχὴν ἔχειν, τό τε γεγονὸς καὶ τὸ πεπερασμένον. The same point is made inSoph. El.167 b 13 and 181 a 27.

909. The words ἀλλ’ ἄπειρόν ἐστι mean simply “but it is without limit,” and this is simply a repetition of the statement that it has no beginning or end. The nature of the limit can only be determined by the context, and accordingly, when Melissos does introduce the subject of spatial infinity, he is careful to say τὸ μέγεθος ἄπειρον (fr.3).

910. Arist.Gen. Corr.i. 8. 325 a 14, ἓν καὶ ἀκίνητον τὸ πᾶν εἶναί φασι καὶ ἄπειρον ἔνιοι· τὸ γὰρ πέρας περαίνειν ἂν πρὸς τὸ κενόν. That this refers to Melissos has been proved by Zeller (p. 612, n. 2).

911. Note the disagreement with Zeno (§ 162).

912. The view of Bäumker that Melissos admitted ἀντιπερίστασις or motionin pleno(Jahrb. f. kl. Phil., 1886, p. 541;Das Problem der Materie, p. 59) depends upon some words of Simplicius (Phys.p. 104, 13), οὐχ ὅτι μὴ δυνατὸν διὰ πλήρους κινεῖσθαι, ὡς ἐπὶ τῶν σωμάτων λέγομεν κ.τ.λ. These words were formerly turned into Ionic and passed off as a fragment of Melissos. They are, however, part of Simplicius’s own argument against Alexander, and have nothing to do with Melissos at all.

913. See, however, Bäumker,Das Problem der Materie, pp. 57 sqq., who remarks that ἐόν (or ὄν) in fr. 9 must be the predicate, as it has no article. In his fifth edition (p. 611, n. 2) Zeller has adopted the view here taken. He rightly observes that the hypothetical form εἰ μὲν ὂν εἴη speaks for it, and that the subject to εἴη must be ἕκαστον τῶν πολλῶν, as with Zeno.

914.Met.Α, 5. 986 b 18 (R. P. 101).

915. Brandis changed the εἴη to ἔστι, but there is no warrant for this.

916. Cf. Zeno, fr.1, especially the words εἰ δὲ ἔστιν, ἀνάγκη ἕκαστον μέγεθός τι ἔχειν καὶ πάχος.

917. Simpl.Phys.pp. 87, 6, and 110, 1.

918. See above,§ 159, p. 363,n.880.

919. Bäumker,op. cit.p. 58, n. 3: “That Melissos was a weakling is afable convenuethat people repeat after Aristotle, who was unable to appreciate the Eleatics in general, and in particular misunderstood Melissos not inconsiderably.”

920. Περὶ φύσιος ἀνθρώπου, c. 1, ἀλλ’ ἔμοιγε δοκέουσιν οἱ τοιοῦτοι ἄνθρωποι αὐτοὶ ἑωυτοὺς καταβάλλειν ἐν τοῖσιν ὀνόμασι τῶν λόγων αὐτῶν ὑπὸ ἀσυνεσίης, τὸν δὲ Μελίσσου λόγον ὀρθοῦν. The metaphors are taken from wrestling, and were current at this date (cf. the καταβάλλοντες of Protagoras). Plato implies a more generous appreciation of Melissos than Aristotle’s. InTheaet.180 e 2, he refers to the Eleatics as Μέλισσοί τε καὶ Παρμενίδαι, and in 183 e 4 he almost apologises for giving the pre-eminence to Parmenides.

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