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reached by division, for time itself is infinite from this standpoint. So the result is that it traverses the infinite in an infinite, not a finite time, and that infinites, not finites, come in contact with infinites.

vi. 9; 239 b 5. And Zeno's reasoning is fallacious. For if, he says, everything is at rest [or in motion] when it is in a space equal to itself, and the moving body is always in the present moment < in a space equal to itself, then the moving arrow is still. > This is false;

for time is not composed of present moments that are indivisible, nor indeed is any other quantity. Zeno presents four arguments concerning motion which involve puzzles to be solved, and the first of these shows that motion does not exist because the moving body must go half the distance before it goes the whole distance; of this we have spoken before (Phys. viii. 8; 263 a 5). And the second is called the Achilles argument; it is this:The slow runner will never be overtaken by the swiftest, for it is necessary that the pursuer should first reach the point from which the pursued started, so that necessarily the slower is always somewhat in advance. This argument is the same as the preceding, the only difference being that the distance is not divided each time into halves. . . . His opinion is false that the one in advance is not overtaken; he is not indeed overtaken while he is in advance; but nevertheless he is overtaken, if you will grant that he passes through the limited space. These are the first two arguments, and the third is the one that has been alluded to, that the arrow in its flight is stationary. This depends on the assumption that time is composed of present moments; there will be no syllogism if this is not granted. And the fourth argument is with reference to equal bodies moving in opposite directions past equal bodies in the stadium with equal speed, some from the end of the stadium, others from

the middle; in which case he thinks half the time equal to twice the time. The fallacy lies in the fact that while he postulates that bodies of equal size move forward with equal speed for an equal time, he compares the one with something in motion, the other with something at rest.

(c) PASSAGES RELATING TO ZENO IN THE DOXOGRAPHISTS.

Plut. Strom. 6; Dox. 581. Zeno the Eleatic brought out nothing peculiar to himself, but he started farther difficulties about these things.

Epiph. adv. Haer. iii. 11; Dox. 590. Zeno the Eleatic, a dialectician equal to the other Zeno, says that the earth does not move, and that no space is void of content. He speaks as follows :-That which is moved is moved in the place in which it is, or in the place in which it is not; it is neither moved in the place in which it is, nor in the place in which it is not; accordingly it is not moved at all.

Galen, Hist. Phil. 3; Dox. 601. Zeno the Eleatic is said to have introduced the dialectic philosophy. 7; Dox. 604. He was a skeptic.

Aet. i. 7; Dox. 303. Melissos and Zeno say that the one is universal, and that it exists alone, eternal, and unlimited. And this one is necessity [Heeren inserts here the name Empedokles], and the material of it is the four elements, and the forms are strife and love. He says that the elements are gods, and the mixture of them is the world. The uniform will be resolved into them; 1 he thinks that souls are divine, and that pure men who share these things in a pure way are divine. 23; 320. Zeno et al. denied generation and destruction, because they thought that the all is unmoved.

1

The

'Reading TρòS TAÛTA XVÕHσETaι, which, as Mr. G. D. Lord suggests to me, is probably the source of the corruption προστανλυθήσεται. Vatican vulgate combines both readings.

VIII.

THE ELEATIC SCHOOL: MELISSOS.

MELISSOS of Samos, son of Ithagenes, was a contemporary of Zeno, though he may have been slightly younger. Parmenides is said to have been his teacher, and it is possible that he may have made the acquaintance of Herakleitos. According to Diogenes, he was a respected statesman, and there seems to be good evidence (Plutarch, Perikles 26, after Aristotle) that he commanded the Samian fleet at its victory over the Athenians, 440 B.C. He wrote a book which later writers refer to under various titles.

Literature: The fragments are treated by Brandis, Commen. Eleat. iii. and by Mullach de Melisso X. G. p. 80; Pabst, de Meliss. Fragmentis, Bonn 1889, disputes the authenticity of Fr. 1-5. Spalding, Vindic. philos. Megar. Berlin 1793, first showed that the first two chapters of the book called de Xenophane, Zenone, Gorgia, refer to Melissos. Cf. also Fr. Kern, Zur Würdigung des Melissos, Festschrift d. stettin. Stadtgym. 1880.

Sources and Critical Notes.

Fr. 1-5. The passage giving these fragments, as they have been called, contains little that is not found in the remaining fragments, and in spite of the fact that it is given as a direct quotation, it seems best to regard it as a condensed statement of the opinions of Melissos. V. Zeller, Vorsokr. Phil. 607, n. 1, and Pabst, de Meliss. Fragmentis, Bonn 1889.

(a) FRAGMENTS OF MELISSOS MAINLY FROM SIMPLICIUS ON THE PHYSICS.

Simpl. Phys. 23 × 109, 20 (Fr. 7). ὅτε τοίνυν οὐκ ἐγένετο, ἔστι δέ, ἀεὶ ἦν καὶ ἀεὶ ἔσται καὶ ἀρχὴν οὐκ ἔχει οὐδὲ τελευτήν, ἄλλ ̓ ἄπειρόν ἐστιν. εἰ μὲν γὰρ ἐγένετο, ἀρχὴν ἂν εἶχεν· ἤρξατο γὰρ ἄν ποτε γινόμενον· καὶ τελευτήν· ἐτελεύτησε γὰρ ἄν ποτε γινόμενον· εἰ δὲ μήτε ἤρξατο μήτε ἐτελεύτησεν ἀεί τε ἦν καὶ ἀεὶ ἔσται, οὐκ ἔχει ἀρχὴν οὐδὲ τελευτήν· οὐ γὰρ ἀεὶ εἶναι ἀνυστὸν ὅ τι μὴ πᾶν ἐστι. 1. 31. (Fr. 8.) ἀλλ ̓ ὥσπερ ἔστιν ἀεί, οὕτω καὶ τὸ μέγεθος ἄπειρον ἀεὶ χρὴ εἶναι. 1. 33. (Fr. 15.) εἰ γὰρ διῄρηται τὸ ἐόν, κινεῖται. κινούμενον δὲ οὐκ ἂν εἴη ἅμα.

Phys. 24 r 110, 1. (Fr. 16.) εἰ μὲν ὃν εἴη, δεῖ αὐτὸ ἓν εἶναι· ἓν δὲ ὂν δεῖ αὐτὸ σῶμα μὴ ἔχειν. (19 r 87, 6) εἰ δὲ ἔχοι πάθος, ἔχοι ἂν μόρια καὶ οὐκέτι ἓν εἴη. 1. 3. (Fr. 9.) ἀρχήν τε καὶ τέλος ἔχον οὐδὲν οὔτε ἀίδιον οὔτε ἄπειρόν ἐστιν. 1. 5. (Fr. 10.) εἰ μὴ ἓν εἴη, περανεῖ πρὸς ἄλλο.

Phys. 24 r 111, 19. (Fr. 11.) οὕτως οὖν ἀίδιόν ἐστι καὶ ἄπειρον· καὶ ἓν καὶ ὅμοιον πᾶν. καὶ οὔτ ̓ ἂν ἀπ όλοιτο οὔτε μεῖζον γίνοιτο οὔτε μετακοσμέοιτο οὔτε ἀλγεῖ οὔτε ἀνιᾶται. εἰ γάρ τι τούτων πάσχοι, οὐκ ἂν ἔτι ἓν εἴη. εἰ γὰρ ἑτεροιοῦται, ἀνάγκη τὸ ἐὸν μὴ ὅμοιον εἶναι, ἀλλὰ ἀπόλλυσθαι τὸ πρόσθεν ἐόν, τὸ δὲ οὐκ ἐὸν γίνεσθαι. εἰ τοίνυν τριχὶ μιῇ μυρίοις ἔτεσιν ἑτεροῖον γίνοιτο τὸ πᾶν,

Fr. 7. D omits καὶ . . . γινόμενον. Simplicius writes γινόμενον, Diels would restore yevóμevov regularly, and compares Spengel ad Eudem. fr. p. 18, 18. DE ἔχει, aF ἔχον.

Fr. 15. a ἅμα, Ε ἀλλὰ

Fr. 16. aD ὃν εἴη, ΕΕ οὖν εἴη, Brandis suggests ὂν ἔστι. Η δὲ μὴ ὂν· Cf. 19 r 87, 6.

X

Fr. 11. aΓ' γίγνοιτο. Ε οὐκέτι, omits ἂν. E omits de after rò. aD (F) τριχὶ μιῆ, Ε τρὶ μὴ ἦ. Vulg. from Brandis εἰ τοίνυν τρισμυρίοισι ἔτεσι. Η παρόντι for παντί.

ὀλεῖται ἂν ἐν τῷ παντὶ χρόνῳ. 1. 24. (Fr. 12.) ἀλλ' οὐδὲ μετακοσμηθῆναι ἀνυστόν· ὁ γὰρ κόσμος ὁ πρόσθεν ἐὼν ó οὐκ ἀπόλλυται οὔτε ὁ μὴ ἐὼν γίνεται. ὅτε δὲ μήτε προσγίνεται μηδὲν μήτε ἀπόλλυται μήτε ἑτεροιοῦται, πῶς ἂν μετακοσμηθὲν τῶν ἐόντων τι ᾖ; εἰ μὲν γάρ τι ἐγίνετο ἑτεροῖον, ἤδη ἂν καὶ μετακοσμηθείη· οὐδὲ ἀλγεῖ οὐ γὰρ ἂν πᾶν εἴη ἀλγέον· οὐ γὰρ ἂν δύναιτο ἀεὶ εἶναι χρῆμα ἀλγέον οὐδὲ ἔχει ἴσην δύναμιν τῷ ὑγιεῖ· οὔτ ̓ ἂν ὅμοιον εἴη, εἰ ἀλγέοι· ἀπογινομένου γάρ τευ ἂν ἀλγέοι ἢ προσγινομένου, κοὐκ ἂν ἔτι ὅμοιον εἴη. οὐδ' ἂν τὸ ὑγιὲς ἀλγῆσαι δύναιτο· ἀπὸ γὰρ ἂν ὄλοιτο τὸ ὑγιὲς καὶ τὸ ἐὸν, τὸ δὲ οὐκ ἐὸν γένοιτο. καὶ περὶ τοῦ ἀνιᾶσθαι ωὑτὸς λόγος τῷ ἀλγέοντι. 1. 6. (Fr. 14.) οὐδὲ κενεόν ἐστιν οὐδέν· τὸ γὰρ κενεὸν οὐδέν ἐστιν· οὐκ ἂν οὖν εἴη τό γε μηδέν. οὐδὲ κινεῖται· ὑποχωρῆσαι γὰρ οὐκ ἔχει οὐδαμῇ, ἀλλὰ πλέων ἐστίν. εἰ μὲν γὰρ κενεὸν ἦν, ὑπεχωρεῖ ἂν εἰς τὸ κενόν· κενοῦ δὲ μὴ ἐόντος οὐκ ἔχει ὅκῃ ὑποχωρήσει. πυκνὸν δὲ καὶ ἀραιὸν οὐκ ἂν εἴη· τὸ γὰρ ἀραιὸν οὐκ ἀνυστὸν πλέων εἶναι ὁμοίως τῷ πυκνῷ, ἀλλ ̓ ἤδη τὸ ἀραιόν γε κενεώτερον γίνεται τοῦ πυκνοῦ. κρίσιν δὲ ταύτην χρὴ ποιήσασθαι τοῦ πλέω καὶ τοῦ μὴ πλέω· εἰ μὲν οὖν χωρεῖ τι ἢ εἰσδέχεται, οὐ πλέων· εἰ δὲ μήτε χωρεῖ μήτε εἰσδέχεται, πλέων. ἀνάγκη τοίνυν πλέων εἶναι, εἰ κενὸν μὴ ἔστιν. εἰ τοίνυν πλέων ἐστίν, οὐ κινεῖται.

Phys. 34 ν 162, 24. (Fr. 6.) ἀεὶ ἦν ὅ τι ἦν καὶ ἀεὶ ἔσται. εἰ γὰρ ἐγένετο, ἀναγκαῖόν ἐστι πρὶν γενέσθαι εἶναι μηδέν. †εἰ τύχοι νῦν μηδὲν ἦν, οὐδαμὰ ἂν γένοιτο οὐδὲν ἐκ μηδενός.

Fr. 12. D μετὰ τὸ κοσμηθῆναι: a ἀπολεῖται: DF μετακοσμηθέντων ἐόντων: 2 γάρ, DFE γε: ἃ ἀλγεινόν (twice): D οὐκ for κοὐκ: DF ὠντὸς, aΕ ὁ αὐτὸς.

Fr. 14. Cf. Simpl. 40, 12. Ε πλέον et passim, Text follows aD : DF κενώτερον, Ε κοινότερον: a omits οὖν.

Fr. 6. Ε εἰ τύχοι νῦν, D εἰ τύχη, απ εἰ τοίνυν. Diels suggests ἅτε τοίνυν ; cf. 109, 20. DE οὐδὲν, aF μηδέν.

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