Literature: Lohse, Halis 1794; Gerling, de Zenosin Paralogismis, Marburg 1825; Wellmann, Zenos Beweise, G.-Pr. Frkf. a. O. 1870; Raab, D. Zenonische Beweise, Schweinf. 1880; Schneider, Philol. xxxv. 1876; Tannery, Rev. Philos. Oct. 1885; Dunan, Les arguments de Zenon, Paris 1884; Brochard, Les arguments de Zenon, Paris 1888; Frontera, Etude sur les arguments de Zenon, Paris 1891
Ibid. 30 v 140, 27. And why is it necessary to say that there is a multiplicity of things when it is set, forth in Zeno's own book? For again in showing that, if there is a multiplicity of things, the same things are both finite and infinite, Zeno writes as follows, to use his own words: (Fr. 2) 'If there is a multiplicity of things; it is necessary that these should be just as many as exist, and not more nor fewer. If there are just as many as there are, then the number would be finite. If there is a multiplicity at all, the number is infinite, for there are always others between any two, and yet others between each pair of these. So the number of things is infinite.' So by the process of division he shows that their number is infinite. And as to magnitude, he begins, with this same argument. For first showing that (Fr. 3) 'if being did not have magnitude, it would not exist at all,' he goes on, 'if anything exists, it is necessary that each thing should have some magnitude and thickness, and that one part of it should be separated from another. The same argument applies to the thing that precedes this. That also will have magnitude and will have something before it. The same may be said of each thing once for all, for there will be no such thing as last, nor will one thing differ from another. So if there is a multiplicity of things, it is necessary that these should be great and small--small enough not to have any magnitude, and great enough to be infinite.'
Ibid. 130 v 562,.3. Zeno's argument seems to deny that place exists, putting the question as follows: (Fr. 4) [Page 116] 'If there is such a thing as place, it will be in something, for all being is in something, and that which is in something is in some place. Then this place will be in a place, and so on indefinitely. Accordingly there is no such thing as place.'
Ibid. 131 r 563, 17. Eudemos' account of Zeno's opinion runs as follows: 'Zeno's problem seems to come to the same thing. For it is natural that all being should be somewhere, and if there is a place for things, where would this place be? In some other place, and that in another, and so on indefinitely.'
Ibid. 236 v. Zeno's argument that when anything is in a space equal to itself, it is either in motion or at rest, and that nothing is moved in the present moment, and that the moving body is always in a space equal to itself at each present moment, may, I think, be put in a syllogism as follows: The arrow which is moving forward is at every present moment in a space equal to itself, accordingly it is in a space equal to itself in all time; but that which is in a space equal to itself in the present moment is not in motion. Accordingly it is in a state of rest, since it is not moved in the present moment, and that which is not moving is at rest, since everything is either in motion or at rest. So the arrow which is moving forward is at rest while it is moving forward, in every moment of its motion.
237 r. The Achilles argument is so named because Achilles is named in it as the example, and the argument shows that if he pursued a tortoise it would be impossible for him to overtake it. 255 r, Aristotle accordingly solves the problem of Zeno the Eleatic, which he propounded to Protagoras the Sophist.11 Tell me, Protagoras, said he, does one grain of millet make a noise when it falls, or does the [Page 117] ten-thousandth part of a grain? On receiving the answer that it does not, he went on: Does a measure of millet grains make a noise when it falls, or not? He answered, it does make a noise. Well, said Zeno, does not the statement about the measure of millet apply to the one grain and the ten-thousandth part of a grain? He assented, and Zeno continued, Are not the statements as to the noise the same in regard to each? For as are the things that make a noise, so are the noises. Since this is the case, if the measure of millet makes a noise, the one grain and the ten-thousandth part of a grain make a noise.
vi. 2; 233 a 21. (Time and space are continuous . . . the divisions of time and space are the same.) Accordingly Zeno's argument is erroneous, that it is not possible to traverse infinite spaces, or to come in contact with infinite spaces successively in a finite time. Both space and time can be called infinite in two ways, either absolutely as a continuous whole, or by division into the smallest parts. With infinites in point of quantity, it is not possible for anything to come in contact in a finite time, but it is possible in the case of the infinites [Page 118] 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
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 he thinks that souls are divine, and that pure
men who share these things in a pure way are divine.
28; 320. Zeno et al. denied generation and destruc-
tion, because they thought that the all is unmoved.
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. Baer. 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.
Hanover College Department of History
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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 he thinks that souls are divine, and that pure men who share these things in a pure way are divine. 28; 320. Zeno et al. denied generation and destruc- tion, because they thought that the all is unmoved.