Sources and Critical Notes.
Fr. 1. D εἰ γὰρ, EF οὗ γὰρ, a οὗ γὰρ εἰ: Ἡ ἄλλων. προσγενοµένου δὲ] Zeller, Vorsokr. Phil. 591, n. 2, strikes out δὲ: F' οἴονται eis: E gives od διὰ for οὐδὲ: DEF ἀπογινόμενον.
Fr. 2. a adds καὶ πάλιν after ἂν εἴη.
Fr. 3. DF ἔχοι, aE ἔχει.
Fr. 4. E omits καὶ after ἄρα.
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(a2) SrmPLicrus’s ACCOUNT OF ZENO’S ARGUMENTS, INCLUDING THE TRANSLATION OF THE F'RAGMENTS. .
80 r 188, 90. For Eudemos says in his Physics, ‘Then does not this exist, and is there any one? This was the problem. He reports Zeno as saying that if any one explains to him the one, what it is, he can tell him what things are. But he is puzzled, it seems, because each of the senses declares that there are many things, both absolutely, and as the result of division, but no one establishes the mathematical point. He thinks that what is not increased by receiving addi- tions, or decreased as parts are taken away, 18 not one of the things that are.’ It was natural that Zeno, who, as if for the sake of exercise, argued both sides of a case (so that he is called double-tongued), should utter such statements raising difficulties about the one; but in his book which has many arguments in regard to each point, he shows that a man who affirms multiplicity naturally falls into contradictions. Among these arguments is one by which he shows that if there are many things, these _ are both small and great—great enough to be infinite in size, and small enough to be nothing in size. By this he shows that what has neither greatness nor thickness nor bulk could not even be. (Fr. 1)' ‘For if, he says, anything were added to another being, it could not make it any greater; for since greatness does not exist, it is impossible to increase the greatness of a thing by adding to it. So that which is added would be nothing. If when something is taken away that which is left is no less, and if it becomes no greater by receiving additions, evidently that which has been added or taken away is nothing.’ These things Zeno says, not denying the one, but holding that each thing has the greatness of
' Cf. Arist. Metaph. ii. 4; 1001 b8.
The Eleatic School: Zeno 115
many and infinite things, since there is always some-.
thing before that which is apprehended, by reason of its
. infinite divisibility ; and this he proves by first showing
that nothing has any greatness because each thing of
the many is identical with itself and is one.
Ibid. 830 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 thick- ness, 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. 180 v 562, 9. Zeno’s argument seems to deny ‘that place exists, putting the question as follows: (Fr. 4) ' Cf. Diels, Archiv f. d. Gesch. d. Phil. i. 245; Geller, 1.5 593 n. 1.
116 the First Philosophers of Greece
‘If there is such a thing as place, it will be in some-
thing, 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. 181r 568, 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.’
Itid. 286 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.
237r. The Achilles argument is so” named because
Achilles is named in it as the example, and the argu-
ment shows that if he pursued a tortoise it would be
impossible for him to overtake it.
255r. Aristotle accordingly solves the problem of
Zeno the Hleatic, which he propounded to Protagoras
the Sophist.' Tell me, Protagoras, said he, does one
grain of millet make a noise when it falls, or does the
' Arist. Phys. vii. 5, 250*, 20.
τηε Eleatic School: Zeno 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 state-
ments 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.
(0) ZENO’S ARGUMENTS AS DESCRIBED BY ARISTOTLE.
_ Phys. iv. 1; 209a28. Zeno’s problem demands some consideration ; if all being is in some place, evi- dently there must be a place of this place, and so on indefinitely. 3; 210 b 22. It is not difficult to solve Zeno’s problem, that if place is anything, it will be in some place ; there is no reason why the first place should not be in something else, not however as in that place, but just as health exists in warm beings as a state while warmth exists in matter as a property of it. Soit is not necessary to assume an indefinite series of places.
vi. 2; 959 8 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 nto the smallest parts. With infinites in point of quan- tity,,it is not possible for anything to come in contact in a finite time, but it is possible in the case of the infinites
118 the First Philosophers of Greece
reached by division, for time itself is infinite from this standpoint. §o 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 1s any other quantity. Zeno pre- sents 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. vill. 8; 26845). 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 neces- sarily 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 1s 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 Eleatic School: Zeno 119
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.
(ο) PassaGES RELATING TO ZENO IN THE DoxoGRAPHISTS.
Plut. Strom.6; Doz.581. Zeno the Eleatic brought
out nothing peculiar to himself, but he started farther
difficulties about these things. |
Epiph. adv. Haer. iii. 11; Doz. 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; itis 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. 8; Dox.601. Zeno the Eleatic is
said to have introduced the dialectic philosophy. 7; Dow.
604. He was a skeptic.
Aet. i. 7; Dox. 909. 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 iof 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.
23; 820. Zeno et al. denied generation and destruc-
tion, because they thought that the all is unmoved.
' Reading πρὸς ταῦτα λυθήσεται, which, as Mr. G. D. Lord suggests to me, is probably the source of the corruption προστανλυθήσεται. The Vatican vulgate combines both readings.
120 the First Philosophers of Greece
VIII. THE ELEATIC SCHOOL: MELISSOS.
Meuissos of Samos, son of Ithagenes, was a contem-
porary 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 acquaint-
ance of Herakleitos. According to Diogenes, he was a
respected statesman, and there seems to be good evidence
(Plutarch, Perikles 26, after Aristotle) that he com-
manded the Samian fleet at its victory over the Athe-
nians, 4408.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 1798, first showed
that the first two chapters of the book called de
ο... Zenone, Gorgia, refer to Melissos. Cf.
also Fr. Kern, Zur Wiirdigung des Meltssos, Fest-
schrift d. stettin. Stadtgym. 1880.