(3) The arrow in flight is at rest. For, if everything is at , rest when it occupies a space equal to itself, and what is in; flight at any given moment always occupies a space equal to itself, it cannot move.*
1 Arist. Zop~. Θ, 8. 160 Ὁ 8, Ζήνωνος (λόγος), ὅτε οὐκ ἐνδέχεται κινεῖσθαι οὐδὲ τὸ στάδιον διελθεῖν.
2 Arist. Phys. Z, 9. 239 Ὁ1ἰ (R. P. 136). Cf. Ζ, 2. 233 a 11; ἃ 21 (ΚΕ. P. 136 a).
3 Arist. Phys. Z, 9. 239 Ὁ 14 (R. P. 137).
4 Phys. Z, 9. 239 Ὁ 30 (R. P. 138); 2. 239 Ὁ 5 (R. P. 138 a). The latter passage is corrupt, though the meaning is plain. I have translated
368 Early Greek Philosophy
Here a further complication is introduced. The
moving object itself has length, and its successive
positions are not points but lines. The successive
moments in which it occupies them are still, however,
points of time. It may help to make this clear if we
remember that the flight of the arrow as represented
by the cinematograph would_be exactly of this nature.
(4) Half the time may be equal to double the time. Let us suppose three rows of bodies,! one of which (A) is at rest while the other two (B, C) are moving with equal velocity in opposite directions (Fig. 1). By the time they are all in the same part of the course, B will have passed twice as many of the bodies in C as in A (Fig. 2).
Fic, I. FIG. 2.
A. 2 @ 9 9 ΑΦ 9 @® ®
Be.e® ee --: Be ὁ ὁ ὁ
C —.. e© © @.@ Ce @ @ @
Therefore the time which it takes to pass C is twice as long as the time it takes to pass A. But the time which B and C take to reach the position of A isthe same. Therefore double the time is equal to the half.”
According to Aristotle, the paralogism here depends. upon the assumption that an equal magnitude moving
Zeller’s version of it ef γάρ, φησίν, ἠρεμεῖ πᾶν ὅταν ἢ κατὰ τὸ ἴσον, ἔστι. δ᾽ ἀεὶ τὸ φερόμενον ἐν τῷ νῦν κατὰ τὸ ἴσον, ἀκίνητον κιτ.λ. Of course del 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.
1 The word is ὄγκοι; cf. Chap. VII. p. 338, n. 1. The name is very appropriate for the Pythagorean units, which Zeno had shown to have length, breadth, and thickness (fr. 1).
2 Arist. Phys. Z, 9. 239 Ὁ 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 (/oc. cét.), 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.
es Oe ΩΣ ἢ δ
The Younger Eleatics 369
with equal velocity must move for an equal time,
whether the magnitude with which it is equal is at
rest or in motion. That is certainly so, but we are
not to suppose that this assumption is Zeno’s own.
The fourth argument is, in fact, related to the third
just as the second is to the first. The Achilles adds
a second moving point to the single moving point of
the first argument; this argument adds a second
moving line to the single moving line of the arrow
in flight. The lines, however, are represented as a
_ series of units, which is just how the Pythagoreans
_ represented them ; and it is quite true that, if lines are
a sum of discrete units, and time is similarly a series
of discrete moments, there is no other measure of
motion possible than the number of units which each
unit passes.
This argument, like the others, is intended to bring
out the absurd conclusions which follow from the
assumption that all quantity is discrete, and what
- Zeno has really done is to establish the conception of
continuous quantity by a reductio ad absurdum of the
_ other. hypothesis. If we remember that Parmenides
_ had asserted the one to be continuous (fr. 8, 25), we
_ shall see how accurate is the account of Zeno’s method
which Plato puts into the mouth of Sokrates.
Ii. Melissos of Samos
164. In his Life of Perikles, Plutarch tells us, Life.
on the authority of Aristotle, that the philosopher
Melissos, son of Ithagenes, was the Samian general
who defeated the Athenian fleet in 441/o B.C. ; and it
1 Plut. Per. 26 (R. P. 141 b), from Aristotle’s Σαμίων πολιτεία.
The Fragments.
370 Early Greek Philosophy
was no doubt for this reason that Apollodoros fixec
his forwit in Ol. LXXXIV. (444-41 B.c.).. Beyonc
this, we really know nothing about his life. He i:
said to have been, like Zeno, a disciple of Parmenides σ᾿
but, as he was a Samian, it is possible that he was
originally a member of the Ionic school, and we shal
see that certain features of his doctrine tend to bea
out this view. On the other hand, he was certainly
convinced by the Eleatic dialectic, and renounced the
Ionic doctrine in so far as it was inconsistent with
that. We note here the effect of the increased facility
of intercourse between East and West, which wa:
secured by the supremacy of Athens.
165. The fragments which we have come from
Simplicius, and are given, with the exception of the
first, from the text of Diels.’
(1a) If nothing is, what can be said of it as of something real P 4
1 Diog. ix. 24 (R. P. 141). It is possible, of course, that Apollodoro: 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 vavapxyla would be given with precision. See Jacoby, p. 270.
2 Diog. ix. 24 (R. P. 141).
3 It is no longer necessary to discuss the passages which used to appea 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 Mélisst Samdt fragmentzés Bonn, 1889). Almost simultaneously I had independently come to thi same conclusion (see the first edition, § 138). Zeller and Diels have bot! accepted Pabst’s demonstration, and the supposed fragments have bee relegated to the notes in the last edition of R. P. I still believe, however that the fragment which I have numbered Ia is genuine. See next note.
4 These words come from the beginning of the paraphrase which wa: 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 wit: the rest. I believe them to be genuine because Simplicius, who ha‘ access to the complete work, introduces them by the words ἄρχεται τοί συγγράμματος οὕτως, and because they are thoroughly Eleatic in characte). It is quite natural that the first words of the book should be prefixed t: the paraphrase.
The Younger Eleatics 371
(t) What was was ever, and ever shall be. For, if it had _ come into being, it needs must have been nothing before it came into being. Now, if it were nothing, in no wise could _ anything have arisen out of nothing. R. P. 142. (2) Since, then, it has not come into being, and since it ‘is, was ever, and ever shall be, it has no beginning or end, but is without limit. For, if it had come into being, it would have had a beginning (for it would have begun to come into being at some time or other) and an end (for it would have ceased to come into being at some time or other); but, if it _ neither began nor ended, and ever was and ever shall be, it _has no beginning or end; for it is not possible for anything to be ever without all being. R. P. 143.
(3) Further, just as it ever is, so it must ever be infinite in magnitude. R. P. 143.
(4) But nothing which has a beginning or end is either eternal or infinite. R. P. 143.
(5) If it were not one, it would be bounded by something else. R. P. 144 ἃ:
(6) For if it is (infinite), it must be one; for if it were two, it could not be infinite ; for then they would be bounded by one another.’ R. P. 144.
(6a) (And, since it is one, it is alike throughout ; for if it
were unlike, it would be many and not one.) ? (7) So then it is eternal and infinite and one and all alike. And it cannot perish nor become greater, nor does it suffer pain or grief. For, if any of these things happened to it, it would no longer be one. For if it is altered, then the real must needs not beall alike, but what was before must pass away, and what was not must come into being. Now, if it changed by so much as a single hair in ten thousand years, it would all perish in the whole of time.
1 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 by ALX.G. 974 a 11, πᾶν δὲ ἄπειρον ὃν <év> εἷναι " εἰ γὰρ δύο ἢ πλείω εἴη, πέρατ᾽ ἂν εἶναι ταῦτα πρὸς ἄλληλα.
_ 2 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 in 47.X.G. 974 a 13 (R. P. 144 a).
372 Early Greek Philosophy
Further, it is not possible either that its order should b changed ; for the order which it had before does not perisl nor does that which was not come into being. Βυΐ, sinc nothing is either added to it or passes away or is altered, ho can any real thing have had its order changed? For if anythin became different, that would amount to a change ‘in its orde
Nor does it suffer pain; for a thing in pain could not a be. For a thing in pain could not be ever, nor has it th same power as what is whole. Nor would it be alike, if. were in pain; for it is only from the addition or subtraction ς something that it could feel pain, and then it would no longe be alike. Nor could what is whole feel pain ; for then whz was whole and what was real would pass away, and what we not would come into being. And the same argument applic to grief as to pain.
Nor is anything empty. For what is empty is nothing What is nothing cannot be.
Nor does it move ; for it has nowhere to betake itself to, bu is full. For if there were aught empty, it would betake itself t the empty. But, since there is naught empty, it has nowher to betake itself to.
And it cannot be dense and rare; for it is not possible fo what is rare to be as full as what is dense, but what is rare i at once emptier than what is dense.
This is the way in which we must pe SOE between wha is full and what is not full. Ifa thing has room for anythin else, and takes it in, it is not full; but if it has no room fo anything and does not take it in, it is full.
Now, it must needs be full if there is naught empty, and : it is full, it does not move. R. P. 145.
(8) This argument, then, is the greatest proof that it is on alone ; but the following are proofs of it also. If there were many, these would have to be of the same kind as I say thi. the one is. For if there is earth and water, and air and iror: and gold and fire, and if one thing is living and another deac| and if things are black and white and all that men say the; really are,—if that is so, and if we see and hear aright, eact one of these must be such as we first decided, and they cannv’ be changed or altered, but each must be just as it is. But, ἐ.