Chapter V: Appendix: 263 (4)

There is left but this single path to tell thee of: namely, that being is. And on this path there are many proofs that being is without beginning and {60} indestructible; it is universal, existing alone, immovable and without end; nor ever was it nor will it be, since it now _is_, all together, one, and continuous. For what generating of it wilt thou seek out? From what did it grow, and how? I will not permit thee to say or to think that it came from not-being; for it is impossible to think or to say that not-being {65} is. What thing would then have stirred it into activity that it should arise from not-being later rather than earlier? So it is necessary that being either is absolutely or is not. Nor will the force of the argument permit that anything spring from {70} being except being itself. Therefore justice does not slacken her fetters to permit generation or destruction, but holds being firm.

(The decision as to these things comes in at this point.)

Either being exists or it does not exist. It has been decided in accordance with necessity to leave the unthinkable, unspeakable path, as this is not the true path, but that the other path exists and is true. {75} How then should being suffer destruction? How come into existence? If it came into existence, it is not being, nor will it be if it ever is to come into existence.... So its generation is extinguished, and its destruction is proved incredible.

Nor is it subject to division, for it is all alike; nor is anything more in it, so as to prevent its cohesion, nor anything less, but all is full of being; {80} therefore the all is continuous, for being is contiguous to being.

Farther it is unmoved, in the hold of great chains, without beginning or end, since generation and destruction have completely disappeared and {85} true belief has rejected them. It lies the same, abiding in the same state and by itself; accordingly it abides fixed in the same spot. For powerful necessity holds it in confining bonds, which restrain it on all sides. Therefore divine right does not permit being to have any end; but it is lacking in nothing, for if it lacked anything it would lack everything.[59]

{90} Nevertheless, behold steadfastly all absent things as present to thy mind; for thou canst not separate being in one place from contact with being in another place; it is not scattered here and there through the universe, nor is it compounded of parts.

Therefore thinking and that by reason of which {95} thought exists are one and the same thing, for thou wilt not find thinking without the _being_ from which it receives its name. Nor is there nor will there be anything apart from being; for fate has linked it together, so that it is a whole and immovable. Wherefore all these things will be but a name, all these things which mortals determined in the belief that they were true, viz. that things arise and perish, {100} that they are and are not, that they change their position and vary in colour.

But since there is a final limit, it is perfected on every side, like the mass of a rounded sphere, equally distant from the centre at every point. For {105} it is necessary that it should neither be greater at all nor less anywhere, since there is no not-being which can prevent it from arriving at equality, nor is being such that there may ever be more than what is in one part and less in another, since the whole is inviolate. For if it is equal on all sides, it abides in equality within its limits.

CONCERNING OPINIONS.

{110} At this point I cease trustworthy discourse and the thought about truth; from here on, learn the opinions of mortals, hearing of the illusive order of my verses.

Men have determined in their minds to name two principles [_lit._ forms]; but one of these they ought {115} not to name, and in so doing they have erred. They distinguish them as antithetic in character, and give them each character and attributes distinct from those of the other. On the one hand there is the aethereal flame of fire, fine, rarefied, everywhere identical with itself and not identical with its opposite; and on the other hand, opposed to the first, is {120} the second principle, flameless darkness, dense and heavy in character. Of these two principles I declare to thee every arrangement as it appears to men, so that no knowledge among mortals may surpass thine.

But since all things are called light and darkness, and the peculiar properties of these are predicated of one thing and another, everything is at the same time full of light and of obscure darkness, of both {125} equally, since neither has anything in common with the other.

And the smaller circles are filled with unmixed fire, and those next them with darkness into which their portion of light penetrates; in the midst of these is the divinity who directs the course of all. For she controls dreaded birth and coition in every {130} part of the universe, sending female to join with male, and again male to female.

First of all the gods she devised love.

Thou shalt know the nature of the heavens and {135} all signs that are in the sky, the destructive deeds of the pure bright torch of the sun and whence they arose, and thou shalt learn the wandering deeds of the round-eyed moon and its nature. Thou shalt know also the sky surrounding all, whence it arose, and how necessity took it and chained it so as to serve as {140} a limit to the courses of the stars. How earth and sun and moon and common sky and the milky way of the heavens and highest Olympos and the burning (might of the) stars began to be.

It (the moon) wanders about the earth, shining {145} at night with borrowed light. She is always gazing earnestly toward the rays of the sun.

For as at any time is the blending of very complex members in a man, so is the mind in men constituted; for that which thinks is the same in all men and in every man, _viz._ the essence of the members of the body; and the element that is in {150} excess is thought.

On the right hand boys, on the left hand girls.

So, according to men’s opinions, did things arise, and so they are now, and from this state when they shall have reached maturity shall they perish. For each of these men has determined a name as a distinguishing mark.

{K. 150} When male and female mingle seed of Venus in the form [the body] of one, the excellence from the two different bloods, if it preserves harmony, fashions a well-formed body; but if when the seed is mingled the excellencies fight against each other and do not unite into one, they will distress the sex that is coming into existence, as the twofold seed is mingled in the body of the unfortunate woman.

With this there are fineness and heat and light and softness and brightness; and with the dense are classed cold and darkness and hardness and weight, for these are separated the ones on one side, the others on the other.

(_b_) PASSAGES RELATING TO PARMENIDES IN PLATO AND ARISTOTLE.

Plato, _Theaet._ 180 D. I almost forgot, Theodoros, that there were others who asserted opinions the very opposite of these: ‘the all is alone, unmoved; to this all names apply,’ and the other emphatic statements in opposition to those referred to, which the school of Melissos and Parmenides make, to the effect that all things are one, and that the all stands itself in itself, not having space in which it is moved.

_Ibid._ 183 E. Feeling ashamed before Melissos and the rest who assert that the all is one being, for fear we should examine the matter somewhat crudely, I am even more ashamed in view of the fact that Parmenides is one of them. Parmenides seems to me, in the words of Homer, a man to be reverenced and at the same time feared. For when I was a mere youth and he a very old man, I conversed with him, and he seemed to me to have an exceedingly wonderful depth of mind. I fear lest we may not understand what he said, and that we may fail still more to understand his thoughts in saying it; and, what is most important, I fear lest the question before us should fail to receive due consideration....[60]

_Soph._ 238 C (concluding a discussion of Parmenides). You understand then that it is really impossible to speak of not-being or to say anything about it or to conceive it by itself, but it is inconceivable, not to be spoken of or mentioned, and irrational.

_Parm._ 150 E. Accordingly the unity itself in relation to itself is as follows: Having in itself neither greatness nor littleness, it could not be exceeded by itself nor could it exceed itself, but being equal it would be equal to itself.

_Ibid._ 168 C. This statement: It does not exist, means absolutely that it does not exist anywhere in any way, nor does not-being have any share at all in being. Accordingly not-being could not exist, nor in any other way could it have a share in being.

(_Symp._ 178 B, 195 C: Reference to the stories which Hesiod and Parmenides told about the gods. Line 132 is quoted.)

Arist. _Phys._ i. 2; 184 b 16. The first principle must be one, unmoved, as Parmenides and Melissos say, ...

_Ibid._ i. 3; 186 a 4. To those proceeding after this impossible manner things seem to be one, and it is not difficult to refute them from their own statements. For both of them reason in a fallacious manner, both Parmenides and Melissos; for they make false assumptions, and at the same time their course of reasoning is not logical.... And the same sort of arguments are used by Parmenides, although he has some others of his own, and the refutation consists in showing both that he makes mistakes of fact and that he does not draw his conclusions correctly. He makes a mistake in assuming that being is to be spoken of absolutely, speaking of it thus many times; and he draws the false conclusion that, in case only whites are considered, white meaning one thing, none the less there are many whites and not one; since neither in the succession of things nor in the argument will whiteness be one. For what is predicated of white will not be the same as what is predicated of the object which is white, and nothing except white will be separated from the object; since there is no other ground of separation except the fact that the white is different from the object in which the white exists. But Parmenides had not yet arrived at the knowledge of this.

_Ibid._ i. 5; 188 a 20. Parmenides also makes heat and cold first principles; and he calls them fire and earth.

_Ibid._ iii. 6; 207 a 15. Wherefore we must regard Parmenides as a more acute thinker than Melissos, for the latter says that the infinite is the all, but the former asserts that the all is limited, equally distant from the centre [on every side].[61]

_Gen. Corr._ i. 3; 318 b 6. Parmenides says that the two exist, both being and not being—_i.e._ earth and water.

_Metaph._ i. 3; 984 b 1. None of those who have affirmed that the all is one have, it happens, seen the nature of such a cause clearly, except, perhaps, Parmenides, and he in so far as he sometimes asserts that there is not one cause alone, but two causes.

_Metaph._ i. 5; 986 b 18. For Parmenides seemed to lay hold of a unity according to reason, and Melissos according to matter; wherefore the former says it is limited, the latter that it is unlimited. Xenophanes first taught the unity of things (Parmenides is said to have been his pupil), but he did not make anything clear, nor did he seem to get at the nature of either finiteness or infinity, but, looking up into the broad heavens, he said, the unity is god. These, as we said, are to be dismissed from the present investigation, two of them entirely as being somewhat more crude, Xenophanes and Melissos; but Parmenides seems to speak in some places with greater care. For believing that not-being does not exist in addition to being, of necessity he thinks that being is one and that there is nothing else, ... and being compelled to account for phenomena, and assuming that things are one from the standpoint of reason, plural from the standpoint of sense, he again asserts that there are two causes and two first principles, heat and cold, or, as he calls them, fire and earth; of these he regards heat as being, its opposite as not-being.

_Metaph._ ii. 4; 1001 a 32. There is nothing different from being, so that it is necessary to agree with the reasoning of Parmenides that all things are one, and that this is being.

(_c_) PASSAGES RELATING TO PARMENIDES IN THE DOXOGRAPHISTS.

Theophrastos, Fr. 6; Alexander _Metaph._ p. 24, 5 Bon.; _Dox._ 482. And succeeding him Parmenides, son of Pyres, the Eleatic—Theophrastos adds the name of Xenophanes—followed both ways. For in declaring that the all is eternal, and in attempting to explain the genesis of things, he expresses different opinions according to the two standpoints:—from the standpoint of truth he supposes the all to be one and not generated and spheroidal in form, while from the standpoint of popular opinion, in order to explain generation of phenomena, he uses two first principles, fire and earth, the one as matter, the other as cause and agent.

Theophrastos, Fr. 6 a; Laer. Diog. ix. 21, 22; _Dox._ 482. Parmenides, son of Pyres, the Eleatic, was a pupil of Xenophanes, yet he did not accept his doctrines.... He was the first to declare that the earth is spheroidal and situated in the middle of the universe. He said that there are two elements, fire and earth; the one has the office of demiurge, the other that of matter. Men first arose from mud; heat and cold are the elements of which all things are composed. He holds that intelligence and life are the same, as Theophrastos records in his book on physics, where he put down the opinions of almost everybody. He said that philosophy has a twofold office, to understand both the truth and also what men believe. Accordingly he says: (Vv. 28-30), ‘’Tis necessary for thee to learn all things, both the abiding essence of persuasive truth, and men’s opinions in which rests no true belief.’

Theoph. Fr. 17; Diog. Laer. viii. 48; _Dox._ 492. Theophrastos says that Parmenides was the first to call the heavens a universe and the earth spheroidal.

Theoph. _de Sens._ 3; _Dox._ 499. Parmenides does not make any definite statements as to sensation, except that knowledge is in proportion to the excess of one of the two elements. Intelligence varies as the heat or the cold is in excess, and it is better and purer by reason of heat; but nevertheless it has need of a certain symmetry. (Vv. 146-149) ‘For,’ he says, ‘as at any time is the blending of very complex members in a man, so is the mind in men constituted; for that which thinks is the same in all men and in every man, viz., the essence of the members of the body; and the element that is in excess is thought.’ He says that perceiving and thinking are the same thing, and that remembering and forgetting come from these[62] as the result of mixture, but he does not say definitely whether, if they enter into the mixture in equal quantities, thought will arise or not, nor what the disposition should be. But it is evident that he believes sensation to take place by the presence of some quality in contrast with its opposite, where he says that a corpse does not perceive light and heat and sound by reason of the absence of fire, but that it perceives cold and silence and the similar contrasted qualities, and in general that being as a whole has a certain knowledge. So in his statements he seems to do away with what is difficult by leaving it out.

Theophr. Fr. 7; Simpl. _Phys._ 25 r 115; _Dox._ 483. In the first book of his physics Theophrastos gives as the opinion of Parmenides: That which is outside of being is not-being, not-being is nothing, accordingly being is one.

Hipp. _Phil._ 11; _Dox._ 564. Parmenides supposes that the all is one and eternal, and without beginning and spheroidal in form; but even he does not escape the opinion of the many, for he speaks of fire and earth as first principles of the all, of earth as matter, and of fire as agent and cause, and he says that the earth will come to an end, but in what way he does not say. He says that the all is eternal, and not generated, and spherical, and homogeneous, not having place in itself, and unmoved, and limited.[63]

Plut. _Strom._ 5; _Dox._ 580. Parmenides the Eleatic, the companion of Xenophanes, both laid claim to his opinions, and at the same time took the opposite standpoint. For he declared the all to be eternal and immovable according to the real state of the case; for it is alone, existing alone, immovable and without beginning (v. 60); but there is a generation of the things that seem to be according to false opinion, and he excepts sense perceptions from the truth. He says that if anything exists besides being, this is not-being, but not-being does not exist at all. So there is left the being that has no beginning; and he says that the earth was formed by the precipitation of dense air.

Epiph. _adv. Haer._ iii. 10; _Dox._ 590. Parmenides, the son of Pyres, himself also of the Eleatic school, said that the first principle of all things is the infinite.

Cic. _de Nat. Deor._ i. 11; _Dox._ 534. For Parmenides devised a sort of contrivance like a crown (he applied to it the word στεφάνη), an orb of light with continuous heat, which arched the sky, and this he called god, but in it no one could suspect a divine form or a divine sentiment, and he made many monstrosities of this sort; moreover, he raised to the rank of gods War, Discord, Desire, and many other things which disease or sleep or forgetfulness or old age destroys; and similarly with reference to the stars he expresses opinions which have been criticised elsewhere and are omitted here.

Aet. i. 3; _Dox._ 284. Parmenides, the Eleatic, son of Pyrrhes, was a companion of Xenophanes, and in his first book the doctrines agree with those of his master; for here that verse occurs: (v. 60), Universal, existing alone, immovable and without beginning. He said that the cause of all things is not earth alone, as his master said, but also fire. 7; 303. The world is immovable and limited, and spheroidal in form. 24; 320. Parmenides and Melissos did away with generation and destruction, because they thought that the all is unmoved. 25; 321. All things are controlled by necessity; this is fated, it is justice and forethought, and the producer of the world.

Aet. ii. 1; _Dox._ 327. The world is one. 4; 332. It is without beginning and eternal and indestructible. 7; 335. Parmenides taught that there were crowns encircling one another in close succession,[64] one of rarefied matter, another of dense, and between these other mixed crowns of light and darkness; and that which surrounded all was solid like a wall, and under this was a crown of fire; and the centre of all the crowns was solid, and around it was a circle of fire; and of the mixed crowns the one nearest the centre was the source of motion and generation for all, and this ‘the goddess who directs the helm and holds the keys,’[65] he calls ‘justice and necessity.’ The air is that which is separated from the earth, being evaporated by the forcible pressure of the earth; the sun and the circle of the milky way are the exhalation of fire, and the moon is the mixture of both, namely of air and fire. The aether stands highest of all and surrounding all, and beneath this is ranged the fiery element which we call the heavens, and beneath this are the things of earth. 11; 339. The revolving vault highest above the earth is the heavens. 340. The heavens are of a fiery nature. 13; 342. The stars are masses of fire. 15; 345. He ranks the morning star, which he considers the same as the evening star, first in the aether; and after this the sun, and beneath this the stars in the fiery vault which he calls the heavens. 17; 346. Stars are fed from the exhalations of the earth. 20; 349. The sun is of a fiery nature. The sun and the moon are separated from the milky way, the one from the thinner mixture, which is hot, the other from the denser, which is cold. 25; 356. The moon is of a fiery nature. 26; 357. The moon is of the same size as the sun, and derives its light from it. 30; 361. (The moon appears dark) because darkness is mingled with its fiery nature, whence he calls it the star that shines with a false light.

Aet. iii. 1; 365. The mixture of dense and thin gives its milk-like appearance to the milky way. 11; 377. Parmenides first defined the inhabited parts of the earth by the two tropical zones. 15; 380. Because the earth is equally distant on all sides from other bodies, and so rests in an equilibrium, not having any reason for swaying one way rather than another; on this account it only shakes and does not move from its place.

Aet. iv. 3; 388. The soul is of a fiery nature. 5; 391. The reason is in the whole breast. 392. Life and intelligence are the same thing, nor could there be any living being entirely without reason. 9; 397. Sensations arise part by part according to the symmetry of the pores, each particular object of sense being adapted to each sense (organ). 398. Desire is produced by lack of nourishment.

Aet. v. 7; 419. Parmenides holds the opposite opinion; males are produced in the northern part, for this shares the greater density; and females in the southern part by reason of its rarefied state. 420. Some descend from the right side to the right parts of the womb, others from the left to the left parts of the womb; but if they cross in the descent females are born. 11; 422. When the child comes from the right side of the womb, it resembles the father; when it comes from the left side, the mother. 30; 443. Old age attends the failure of heat.

VII.

_THE ELEATIC SCHOOL: ZENO._

Zeno of Elea, son of Teleutagoras, was born early in the fifth century B.C. He was the pupil of Parmenides, and his relations with him were so intimate that Plato calls him Parmenides’s son (_Soph._ 241 D). Strabo (vi. 1, 1) applies to him as well as to his master the name Pythagorean, and gives him the credit of advancing the cause of law and order in Elea. Several writers say that he taught in Athens for a while. There are numerous accounts of his capture as party to a conspiracy; these accounts differ widely from each other, and the only point of agreement between them has reference to his determination in shielding his fellow conspirators. We find reference to one book which he wrote in prose (Plato, _Parm._ 127 C), each section of which showed the absurdity of some element in the popular belief.

Literature: Lohse, Halis 1794; Gerling, _de Zenonis
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 Zénon_, Paris 1884;
Brochard, _Les arguments de Zénon_, Paris 1888; Frontera,
_Étude sur les arguments de Zénon_, Paris 1891.

(_a_) FRAGMENTS OF ZENO, FROM SIMPLICIUS ON THE PHYSICS.

1. Simpl. _Phys._ 30 r 139, 11. εἰ γὰρ ἄλλῳ ὄντι προσγένοιτο, οὐδὲν ἂν μεῖζον ποιήσειεν· μεγέθους γὰρ μηδενὸς ὄντος, προσγενομένου δὲ οὐδὲν οἷόν τε εἰς μέγεθος ἐπιδοῦναι. καὶ οὕτως ἂν ἤδη τὸ προσγινόμενον οὐδὲν εἴη. εἰ δὲ ἀπογινομένου τὸ ἕτερον μηδὲν ἔλαττόν ἐστι, μηδὲ αὖ προσγινομένου αὐξήσεται, δῆλον ὅτι τὸ προσγενόμενον οὐδὲν ἦν οὐδὲ τὸ ἀπογενόμενον.

2. Simpl. _Phys._ 30 r 140, 29. εἰ πολλά ἐστιν, ἀνάγκη τοσαῦτα εἶναι ὅσα ἐστὶ καὶ οὔτε πλείονα αὐτῶν οὔτε ἐλάττονα. εἰ δὲ τοσαῦτά ἐστιν ὅσα ἐστί, πεπερασμένα ἂν εἴη. εἰ πολλά ἐστιν, ἄπειρα τὰ ὄντα ἐστίν. ἀεὶ γὰρ ἕτερα μεταξὺ τῶν ὄντων ἐστί, καὶ πάλιν ἐκείνων ἕτερα μεταξύ. καὶ οὕτως ἄπειρα τὰ ὄντα ἐστί.

3. Simpl. _Phys._ 30 v 141, 1. εἰ μὴ ἔχοι μέγεθος τὸ ὂν οὐδ’ ἂν εἴη, εἰ δὲ ἔστιν, ἀνάγκη ἕκαστον μέγεθός τι ἔχειν καὶ πάχος καὶ ἀπέχειν αὐτοῦ τὸ ἕτερον ἀπὸ τοῦ ἑτέρου. καὶ περὶ τοῦ προύχοντος ὁ αὐτὸς λόγος. καὶ γὰρ ἐκεῖνο ἕξει μέγεθος καὶ προέξει αὐτοῦ τι. ὅμοιον δὴ τοῦτο ἅπαξ τε εἰπεῖν καὶ ἀεὶ λέγειν· οὐδὲν γὰρ αὐτοῦ τοιοῦτον ἔσχατον ἔσται οὔτε ἕτερον πρὸς ἕτερον οὐκ ἔσται. οὕτως εἰ πολλά ἐστιν, ἀνάγκη αὐτὰ μικρά τε εἶναι καὶ μεγάλα, μικρὰ μὲν ὥστε μὴ ἔχειν μέγεθος, μεγάλα δὲ ὥστε ἄπειρα εἶναι.

4. Simpl. _Phys._ 130 ν 562, 4. εἰ ἔστιν ὁ τόπος, ἔν τινι ἔσται· πᾶν γὰρ ὂν ἔν τινι· τὸ δὲ ἔν τινι καὶ ἐν τόπῳ. ἔσται ἄρα καὶ ὁ τόπος ἐν τόπῳ καὶ τοῦτο ἐπ’ ἄπειρον· οὐκ ἄρα ἔστιν ὁ τόπος.

_Sources and Critical Notes._

Fr. 1. _D_ εἰ γὰρ, _EF_ οὐ γὰρ, a οὐ γὰρ εἰ: _E_ ἄλλων. προσγενομένου δὲ] Zeller, _Vorsokr. Phil._ 591, n. 2, strikes out δὲ: _F_ οἴονται εἰς: _E_ gives οὐ διὰ for οὐδὲ: _DEF_ ἀπογινόμενον.

Fr. 2. a adds καὶ πάλιν after ἂν εἴη.

Fr. 3. _DF_ ἔχοι, a_E_ ἔχει.

Fr. 4. _E_ omits καὶ after ἄρα.

(_a_) SIMPLICIUS’S ACCOUNT OF ZENO’S ARGUMENTS, INCLUDING THE TRANSLATION OF THE FRAGMENTS.

30 r 138, 30. 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 additions, or decreased as parts are taken away, is 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)[66] ‘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 many and infinite things, since there is always something 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._ 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.’[67]

_Ibid._ 130 v 562, 3. Zeno’s argument seems to deny that place exists, putting the question as follows: (Fr. 4) ‘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.[68] Tell me, Protagoras, said he, does one grain of millet make a noise when it falls, or does the 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.

(_b_) ZENO’S ARGUMENTS AS DESCRIBED BY ARISTOTLE.

_Phys._ iv. 1; 209 a 23. Zeno’s problem demands some consideration; if all being is in some place, evidently 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. So it is not necessary to assume an indefinite series of places.

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 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;[69] 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.

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.

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

Simpl. _Phys._ 23 v 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. l. 31. (Fr. 8.) ἀλλ’ ὥσπερ ἔστιν ἀεί, οὕτω καὶ τὸ μέγεθος ἄπειρον ἀεὶ χρὴ εἶναι. l. 33. (Fr. 15.) εἰ γὰρ διῄρηται τὸ ἐόν, κινεῖται. κινούμενον δὲ οὐκ ἂν εἴη ἅμα.

_Phys._ 24 r 110, 1. (Fr. 16.) εἰ μὲν ὂν 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. l. 3. (Fr. 9.) ἀρχήν τε καὶ τέλος ἔχον οὐδὲν οὔτε ἀίδιον οὔτε ἄπειρόν ἐστιν. l. 5. (Fr. 10.) εἰ μὴ ἓν εἴη, περανεῖ πρὸς ἄλλο.

_Phys._ 247 r 111, 19. (Fr. 11.) οὕτως οὖν ἀίδιόν ἐστι καὶ ἄπειρον· καὶ ἓν καὶ ὅμοιον πᾶν. καὶ οὔτ’ ἂν ἀπόλοιτο 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, ὀλεῖται ἂν ἐν τῷ παντὶ χρόνῳ. l. 24. (Fr. 12.) ἀλλ’ οὐδὲ μετακοσμηθῆναι ἀνυστόν· ὁ γὰρ κόσμος ὁ πρόσθεν ἐὼν 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. l. 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 v 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.

Simpl. _de Coelo_, 137 r; Schol. Aristot. 509 b 18; cf. Aristokl. Euseb. _Pr. Ev._ xiv. 17. (Fr. 17.) μέγιστον μὲν οὖν σημεῖον οὗτος ὁ λόγος ὅτι ἓν μόνον ἐστίν. ἀτὰρ καὶ τάδε σημεῖα· εἰ γὰρ ἦν πολλὰ, τοιαῦτα χρῆν αὐτὰ εἶναι, οἷόν περ ἐγώ φημι τὸ ἓν εἶναι. εἰ γὰρ ἔστι γῆ καὶ ὕδωρ καὶ ἀὴρ καὶ σίδηρος καὶ χρυσὸς καὶ πῦρ καὶ τὸ μὲν ζῷον τὸ δὲ τεθνηκὸς καὶ μέλαν καὶ λευκὸν καὶ τὰ ὅσα φασὶν οἱ ἄνθρωποι εἶναι ἀληθῆ,—εἰ δὴ ταῦτα ἔστι καὶ ἡμεῖς ὀρθῶς ὁρῶμεν καὶ ἀκούομεν, εἶναι χρὴ ἕκαστον τοιοῦτον οἷόν περ τὸ πρῶτον ἔδοξεν ἡμῖν, καὶ μὴ μεταπίπτειν μηδὲ γίνεσθαι ἑτεροῖον, ἀλλ’ αἰεὶ εἶναι ἕκαστον οἷόν περ ἔστιν. νῦν δέ φαμεν ὀρθῶς ὁρᾷν καὶ ἀκούειν καὶ συνιέναι, δοκεῖ δὲ ἡμῖν τό τε θερμὸν ψυχρὸν γίνεσθαι καὶ τὸ ψυχρὸν θερμὸν καὶ τὸ σκληρὸν μαλθακὸν καὶ τὸ μαλθακὸν σκληρὸν, καὶ τὸ ζῷον ἀποθνήσκειν καὶ ἐκ μὴ ζῶντος γίνεσθαι, καὶ ταῦτα πάντα ἑτεροιοῦσθαι, καὶ ὅ τι ἦν τε καὶ ὃ νῦν οὐδὲν ὅμοιον εἶναι, ἀλλ’ ὅ τε σίδηρος σκληρὸς ἐὼν τῷ δακτύλῳ κατατρίβεσθαι † ὁμοῦ ῥέων καὶ χρυσὸς καὶ λίθος καὶ ἄλλο ὅ τι ἰσχυρὸν δοκεῖ εἶναι πᾶν, ὥστε συμβαίνει μήτε ὁρᾷν μήτε τὰ ὄντα γινώσκειν· ἐξ ὕδατός τε γῆ καὶ λίθος γίνεσθαι. οὐ τοίνυν ταῦτα ἀλλήλοις ὁμολογεῖ· φαμένοις γὰρ εἶναι πολλὰ καὶ ἀίδια καὶ εἴδη τε καὶ ἴσχυν ἔχοντα, πάντα ἑτεροιοῦσθαι ἡμῖν δοκεῖ καὶ μεταπίπτειν ἐκ τοῦ ἑκάστοτε ὁρωμένου· δῆλον τοίνυν ὅτι οὐκ ὀρθῶς ἑωρῶμεν οὐδὲ ἐκεῖνα πολλὰ ὀρθῶς δοκεῖ εἶναι. οὐ γὰρ ἂν μετέπιπτεν εἰ ἀληθῆ ἦν, ἀλλ’ ἦν οἷόν περ ἐδόκει ἕκαστον τοιοῦτον· τοῦ γὰρ ἐόντος ἀληθινοῦ κρεῖσσον οὐδέν. ἢν δὲ μεταπέσῃ, τὸ μὲν ἐὸν ἀπώλετο, τὸ δὲ οὐκ ἐὸν γέγονεν. οὕτως οὖν εἰ πολλὰ εἴη, τοιαῦτα χρὴ εἶναι οἷόν περ τὸ ἕν.

_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.

Fr. 7. _D_ omits καὶ ... γινόμενον. Simplicius writes γινόμενον, Diels would restore γενόμενον regularly, and compares Spengel ad Eudem. fr. p. 18, 18. _DE_ ἔχει, a_F_ ἔχον.

Fr. 15. a_F_ ἅμα, _E_ ἀλλὰ.

Fr. 16. a_D_ ὂν εἴη, _EF_ οὖν εἴη, Brandis suggests ὂν ἔστι. _F_ δὲ μὴ ὂν· Cf. 19 r 87, 6.

Fr. 11. a_F_ γίγνοιτο. _E_ οὐκέτι, omits ἂν. _E_ omits δὲ after τὸ. a_D_ (_F_) τριχὶ μιῆ, _E_ τριᵡ μὴ ἦ. Vulg. from Brandis εἰ τοίνυν τρισμυρίοισι ἔτεσι. _F_ παρόντι for παντί.

Fr. 12. _D_ μετὰ τὸ κοσμηθῆναι: a ἀπολεῖται: _DF_ μετακοσμηθέντων ἐόντων: a γάρ, _DFE_ γε: a ἀλγεινόν (twice): _D_ οὐκ for κοὐκ: _DF_ ὠυτὸς, a_E_ ὁ αὐτὸς.

Fr. 14. Cf. Simpl. 40, 12. _E_ πλέον et passim, Text follows a_D_: _DF_ κενώτερον, _E_ κοινότερον: a omits οὖν.

Fr. 6. _E_ εἰ τύχοι νῦν, _D_ εἰ τύχη, a_F_ εἰ τοίνυν. Diels suggests ὅτε τοίνυν; cf. 109, 20. _DE_ οὐδὲν, a_F_ μηδὲν.

Fr. 17. Vulg. χρή: Simpl. ζῷον, Aristokl. ζῶν (twice): Aristokl. εἶναι ἐχρῆν, καὶ τὸ ἐὸν τοιοῦτον, οἷον πρῶτον ἔδοξεν ἡμῖν εἶναι, Simpl. omits πάντα and ἀληθῆ: Aristokl. ἕτερον, ἀλλ’ εἶναι ὅμοιον, οἷόν περ ἐστὶ ἕκαστον, Simpl. omits ἔστιν: Bergk ὁμουρέων, digito conterminus, aptatus, MSS. τὸ μέσον, corr. Brandis, _Gesch. d. Phil._ i. 403: Vulg. εἴη.

SIMPLICIUS’S ACCOUNT OF MELISSOS, INCLUDING THE TRANSLATION OF THE FRAGMENTS.

22; 103, 13. Now let us glance at Melissos’ argument, which we ran across a few lines back. Melissos, making use of the axioms of the physicists, in regard to generation and destruction, begins his book as follows: (Fr. 1) If nothing is, how could this be spoken of as though something is? And if anything is, either it has come into being, or else it always has been. If it came into being, it sprung either from being or from not-being; but it is impossible that any such thing should have sprung from not-being (for nothing else that is could have sprung from it, much less pure being); nor could it have sprung from being, for in that case it <would simply be, and> would not have come into existence. So then being is not generated; being always is, nor will it be destroyed. For being could not be changed into not-being (this also is conceded by the physicists), nor into being; for then it would abide as it is, and would not be destroyed. Accordingly being was not generated, nor will it be destroyed; so it always was and always will be. (Fr. 2) But while that which comes into existence has a beginning, that which does not come into existence does not have a beginning, and being which did not come into existence would not have a beginning. Farther, that which is destroyed has an end; but if anything is not subject to destruction, it does not have an end; and that which has neither beginning nor end is of course infinite; so being is infinite. (Fr. 3) And if it is infinite, it is one; for if being were two, both parts could not be infinite, but each would be limited by the other. But being is infinite; there could not be several beings; accordingly being is one. (Fr. 4) Farther, if being is one it does not move; for the one is always homogeneous [_lit._ like itself]; and that which is homogeneous could not perish or become greater or change its arrangement or suffer pain or annoyance. If it experienced any of these things it would not be one; for that which is moved with any sort of motion changes something from one thing into something different; but there is nothing else except being, so this will not be moved. (Fr. 5) To follow another line of argument: there is no place void of being, for the void is nothing; but that which is nothing could not exist; so then being is not moved: it is impossible for it to go anywhere, if there is no void. Nor is it possible for it to contract into itself, for in that case different degrees of density would arise, and this is impossible; for it is impossible that the rare should be as full as the dense; but the rare is more empty than the dense, and there is no such thing as emptiness. It is necessary to judge whether being is full or not by its capacity to receive something else: if it will not receive anything it is full; if it will receive something it is not full. Now if the void does not exist, it must of necessity be full; and if this is the case it does not move, not because it is impossible for it to move through space already filled, as we say of bodies, but because all being cannot be moved into being (for there is nothing besides itself), nor can being be moved into not-being, for not-being does not exist.

23; 109, 7. Melissos also is blamed because in his frequent references to the beginning he does not use the word to mean a beginning in time which applies to that which comes into existence, but rather to mean a logical beginning which does not apply to the things that are changing collectively. He seems to have seen clearly before Aristotle that all matter, even that which is eternal, being limited has a limited capacity, and in itself is always at the end of time, and because of the ever-moving beginning of that which passes, it is always at the beginning, and remains eternal, so that that which has beginning and end in quantity has also beginning and end in time, and the reverse; for that which has beginning and end in time is not everything simultaneously. So he bases his proof on beginning and end in time. Accordingly he says that that which is not everything—_i.e._ which is not the whole simultaneously—is not without beginning or end; what applies to things that are indivisible and infinite in their being, applies so much the more to pure being; and that all applies to being. Melissos puts it as follows: (Fr. 7) Since then it did not come into being but _is_, it always was and always will be, and has neither beginning nor end, but is infinite. For if it had come into existence it would have had a beginning (for that which once came into existence would have a beginning) and an end (for that which once came into existence would come to an end); if it neither had a beginning nor came to an end, it always was and always will be; it has not beginning or end; but it is impossible that anything which is not the whole should always exist.... l. 31. (Fr. 8) But as it always exists, so it is necessary also that it be always infinite in magnitude. l. 33. (Fr. 15) If being is separated it moves; and that which moves could not exist simultaneously.

24; 110, 1 (Fr. 16) If being exists it must be one, and being one it is necessary that it should not itself have body; (19; 87, 6) and if it should have thickness, it would have parts and would no longer be a unity. l. 3 (Fr. 9) Nothing which has beginning and end is either eternal or infinite. l. 5 (Fr. 10) If it were not one, it would be bounded by something else.[70]