Early Greek Philosophy (pre-Socratic fragments and testimony)

If the one had no magnitude, it would not even be.... But, if it is, each one must have a certain magnitude and a certain thickness, and must be at a certain distance from another, and the same may be said of what is in front of it; for it, too, will have magnitude, and something will be in front of it. It is all the same to say this once and to say it always; for no such part of it will be the last, nor will one thing not be compared with another. So, if things are a many, they must be both small and great, so small as not to have any magnitude at all, and so great as to be infinite. R. P. 134. I formerly rendered “the same may be said of what surpasses it in smallness; for it too will have magnitude, and something will surpass it in smallness.” This is Tannery’s rendering, but I now agree with Diels in thinking that ἀπέχειν refers to μέγεθος and προεχειν to πάχος. Zeno is showing that the Pythagorean point has really three dimensions. Reading, with Diels and the MSS., οὔτε ἕτερον πρὸς ἕτερον οὐκ ἔσται. Gomperz’s conjecture (adopted in R. P.) seems to me arbitrary.

For if it were added to any other thing it would not make it any larger; for nothing can gain in magnitude by the addition of what has no magnitude, and thus it follows at once that what was added was nothing. But if, when this is taken away from another thing, that thing is no less; and again, if, when it is added to another thing, that does not increase, it is plain that what was added was nothing, and what was taken away was nothing. R. P. 132. Zeller marks a lacuna here. Zeno must certainly have shown that the subtraction of a point does not make a thing less; but he may have done so before the beginning of our present fragment. If things are a many, they must be just as many as they are, and neither more nor less. Now, if they are as many as they are, they will be finite in number. If things are a many, they will be infinite in number; for there will always be other things between them, and others again between these. And so things are infinite in number. R. P. 133.

This is what Aristotle calls “the argument from dichotomy” (Phys. Α, 3. 187 a 1; R. P. 134 b). If a line is made up of points, we ought to be able to answer the question, “How many points are there in a given line?” On the other hand, you can always divide a line or any part of it into two halves; so that, if a line is made up of points, there will always be more of them than any number you assign. [Sidenote: The unit.] 161. If we hold that the unit has no magnitude—and this is required by what Aristotle calls the argument from dichotomy,—then everything must be infinitely small. Nothing made up of units without magnitude can itself have any magnitude. On the other hand, if we insist that the units of which things are built up are something and not nothing, we must hold that everything is infinitely great. The line is infinitely divisible; and, according to this view, it will be made up of an infinite number of units, each of which has some magnitude. See last note. That this argument refers to points is proved by an instructive passage from Aristotle’s Metaphysics. We read there—

If the unit is indivisible, it will, according to the proposition of Zeno, be nothing. That which neither makes anything larger by its addition to it, nor smaller by its subtraction from it, is not, he says, a real thing at all; for clearly what is real must be a magnitude. And, if it is a magnitude, it is corporeal; for that is corporeal which is in every dimension. The other things, i.e. the plane and the line, if added in one way will make things larger, added in another they will produce no effect; but the point and the unit cannot make things larger in any way. Arist. Met. Β, 4. 1001 b 7. From all this it seems impossible to draw any other conclusion than that the “one” against which Zeno argued was the “one” of which a number constitute a “many,” and that is just the Pythagorean unit. [Sidenote: Space.] 162. Aristotle refers to an argument which seems to be directed against the Pythagorean doctrine of space, and Simplicius quotes it in this form:

If there is space, it will be in something; for all that is is in something, and what is in something is in space. So space will be in space, and this goes on ad infinitum, therefore there is no space. R. P. 135. Arist. Phys. Δ, 1. 209 a 23; 3. 210 b 22 (R. P. 135 a). Simpl. Phys. p. 562, 3 (R. P. 135). The version of Eudemos is given in Simpl. Phys. p. 563, 26, ἀξιοῖ γὰρ πᾶν τὸ ὂν ποῦ εἷναι· εἱ δὲ ὁ τόπος τῶν ὄντων, ποῦ ἂν εἴη· οὐκοῦν ἐν ἄλλῳ τόπῳ κἀκεῖνος δὴ ἐν ἄλλῳ καὶ οὕτως εἰς τὸ πρόσω. What Zeno is really arguing against here is the attempt to distinguish space from the body that occupies it. If we insist that body must be in space, then we must go on to ask what space itself is in. This is a “reinforcement” of the Parmenidean denial of the void. Possibly the argument that everything must be “in” something, or must have something beyond it, had been used against the Parmenidean theory of a finite sphere with nothing outside it. [Sidenote: Motion.]

163. Zeno’s arguments on the subject of motion have been preserved by Aristotle himself. The system of Parmenides made all motion impossible, and his successors had been driven to abandon the monistic hypothesis in order to avoid this very consequence. Zeno does not bring any fresh proofs of the impossibility of motion; all he does is to show that a pluralist theory, such as the Pythagorean, is just as unable to explain it as was that of Parmenides. Looked at in this way, Zeno’s arguments are no mere quibbles, but mark a great advance in the conception of quantity. They are as follows:— (1) You cannot get to the end of a race-course. You cannot traverse an infinite number of points in a finite time. You must traverse the half of any given distance before you traverse the whole, and the half of that again before you can traverse it. This goes on ad infinitum, so that there are an infinite number of points in any given space, and you cannot touch an infinite number one by one in a finite time.

(2) Achilles will never overtake the tortoise. He must first reach the place from which the tortoise started. By that time the tortoise will have got some way ahead. Achilles must then make up that, and again the tortoise will be ahead. He is always coming nearer, but he never makes up to it. Arist. Top. Θ, 8. 160 b 8, Ζήνωνος (λόγος), ὅτι οὐκ ἐνδέχεται κινεῖσθαι οὐδὲ τὸ στάδιον διελθεῖν. Arist. Phys. Ζ, 9. 239 b 11 (R. P. 136). Cf. Ζ, 2. 233 a 11; a 21 (R. P. 136 a). Arist. Phys. Ζ, 9. 239 b 14 (R. P. 137). The “hypothesis” of the second argument is the same as that in the first, namely, that the line is a series of points; but the reasoning is complicated by the introduction of another moving object. The difference, accordingly, is not a half every time, but diminishes in a constant ratio. Again, the first argument shows that no moving object can ever traverse any distance at all, however fast it may move; the second emphasises the fact that, however slowly it moves, it will traverse an infinite distance.

(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. Phys. Ζ, 9. 239 b 30 (R. P. 138); ib. 239 b 5 (R. P. 138 a). The latter passage is corrupt, though the meaning is plain. I have translated Zeller’s version of it εἰ γάρ, φησίν, ἠρεμεῖ πᾶν ὅταν ᾖ κατὰ τὸ ἴσον, ἔστι δ’ ἀεὶ τὸ φερόμενον ἐν τῷ νῦν κατὰ τὸ ἴσον, ἀκίνητον, κ.τ.λ. Of course ἀεί 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. 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). FIG. 1 A. ● ● ● ● B. ● ● ● ● → C. ← ● ● ● ● FIG. 2 A. ● ● ● ● B. ● ● ● ● C. ● ● ● ● 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 is the same. Therefore double the time is equal to the half. The word is ὄγκοι; cf. Chap. VII. p. 338, n. 794. The name is very appropriate for the Pythagorean units, which Zeno had shown to have length, breadth, and thickness (fr. 1).

Arist. Phys. Ζ, 9. 239 b 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 (loc. cit.), 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.

According to Aristotle, the paralogism here depends upon the assumption that an equal magnitude moving 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 [Sidenote: Life.]

164. In his Life of Perikles, Plutarch tells us, on the authority of Aristotle, that the philosopher Melissos, son of Ithagenes, was the Samian general who defeated the Athenian fleet in 441/0 B.C.: and it was no doubt for this reason that Apollodoros fixed his floruit in Ol. LXXXIV. (444-41 B.C.). Beyond this, we really know nothing about his life. He is said to have been, like Zeno, a disciple of Parmenides; but, as he was a Samian, it is possible that he was originally a member of the Ionic school, and we shall see that certain features of his doctrine tend to bear 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 was secured by the supremacy of Athens. Plut. Per. 26 (R. P. 141 b), from Aristotle’s Σαμίων πολιτεία. [Sidenote: The Fragments.] 165. The fragments which we have come from Simplicius, and are given, with the exception of the first, from the text of Diels.

Diog. ix. 24 (R. P. 141). It is possible, of course, that Apollodoros 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 ναυαρχία would be given with precision. See Jacoby, p. 270. Diog. ix. 24 (R. P. 141). It is no longer necessary to discuss the passages which used to appear 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 Melissi Samii fragmentis, Bonn, 1889). Almost simultaneously I had independently come to the same conclusion (see the first edition, § 138). Zeller and Diels have both accepted Pabst’s demonstration, and the supposed fragments have been relegated to the notes in the last edition of R. P. I still believe, however, that the fragment which I have numbered 1_a_ is genuine. See next note. (1_a_) If nothing is, what can be said of it as of something real?

(1) 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 a.

(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. (6_a_) (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 be all 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. Further, it is not possible either that its order should be changed; for the order which it had before does not perish, nor does that which was not come into being. But, since nothing is either added to it or passes away or is altered, how can any real thing have had its order changed? For if anything became different, that would amount to a change in its order.

Nor does it suffer pain; for a thing in pain could not all be. For a thing in pain could not be ever, nor has it the same power as what is whole. Nor would it be alike, if it were in pain; for it is only from the addition or subtraction of something that it could feel pain, and then it would no longer be alike. Nor could what is whole feel pain; for then what was whole and what was real would pass away, and what was not would come into being. And the same argument applies 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, but is full. For if there were aught empty, it would betake itself to the empty. But, since there is naught empty, it has nowhere to betake itself to. And it cannot be dense and rare; for it is not possible for what is rare to be as full as what is dense, but what is rare is at once emptier than what is dense.

This is the way in which we must distinguish between what is full and what is not full. If a thing has room for anything else, and takes it in, it is not full; but if it has no room for anything and does not take it in, it is full. Now, it must needs be full if there is naught empty, and if it is full, it does not move. R. P. 145.

(8) This argument, then, is the greatest proof that it is one alone; but the following are proofs of it also. If there were a many, these would have to be of the same kind as I say that the one is. For if there is earth and water, and air and iron, and gold and fire, and if one thing is living and another dead, and if things are black and white and all that men say they really are,—if that is so, and if we see and hear aright, each one of these must be such as we first decided, and they cannot be changed or altered, but each must be just as it is. But, as it is, we say that we see and hear and understand aright, and yet we believe that what is warm becomes cold, and what is cold warm; that what is hard turns soft, and what is soft hard; that what is living dies, and that things are born from what lives not; and that all those things are changed, and that what they were and what they are now are in no way alike. We think that iron, which is hard, is rubbed away by contact with the finger; and so with gold and stone and everything which we fancy to be strong, and that earth and stone are made out of water; so that it turns out that we neither see nor know realities. Now these things do not agree with one another. We said that there were many things that were eternal and had forms and strength of their own, and yet we fancy that they all suffer alteration, and that they change from what we see each time. It is clear, then, that we did not see aright after all, nor are we right in believing that all these things are many. They would not change if they were real, but each thing would be just what we believed it to be; for nothing is stronger than true reality. But if it has changed, what was has passed away, and what was not is come into being. So then, if there were many things, they would have to be just of the same nature as the one. R. P. 147.

(9) Now, if it were to exist, it must needs be one; but if it is one, it cannot have body; for, if it had body it would have parts, and would no longer be one. R. P. 146. (10) If what is real is divided, it moves; but if it moves, it cannot be. R. P. 144 a. These words come from the beginning of the paraphrase which was 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 with the rest. I believe them to be genuine because Simplicius, who had access to the complete work, introduces them by the words ἄρχεται τοῦ συγγράμματος οὕτως, and because they are thoroughly Eleatic in character. It is quite natural that the first words of the book should be prefixed to the paraphrase. 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 M.X.G. 974 a 11, πᾶν δὲ ἄπειρον ὂν <ἓν> εἶναι· εἰ γὰρ δύο ἢ πλείω εἴη, πέρατ’ ἂν εἶναι ταῦτα πρὸς ἄλληλα.

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 M.X.G. 974 a 13 (R. P. 144 a). Reading ὁμουρέων with Bergk. Diels keeps the MS. ὀμοῦ ῥέων; Zeller (p. 613, n. 1) conjectures ὑπ’ ἰοῦ ῥέων. I read εἰ μὲν οὖν εἴη with E F for the εἰ μὲν ὂν εἴη of D. The ἐὸν which still stands in R. P. is a piece of local colour due to the editors. Diels also now reads οὖν (Vors. p. 149, 2). Diels now reads ἀλλὰ with E for the ἅμα of F, and attaches the word to the next sentence. [Sidenote: Theory of reality.]

166. It has been pointed out that Melissos was perhaps not originally a member of the Eleatic school; but he certainly adopted all the views of Parmenides as to the true nature of reality with one remarkable exception. He appears to have opened his treatise with a reassertion of the Parmenidean “Nothing is not” (fr. 1 a), and the arguments by which he supported this view are those with which we are already familiar (fr. 1). Reality, as with Parmenides, is eternal, an attribute which Melissos expressed in a way of his own. He argued that since everything that has come into being has a beginning and an end, everything that has not come into being has no beginning or end. Aristotle is very severe upon him for this simple conversion of a universal affirmative proposition; but, of course, his belief was not founded on that. His whole conception of reality made it necessary for him to regard it as eternal. It would be a more serious matter if Aristotle were right in believing, as he seems to have done, that Melissos inferred that what is must be infinite in space, because it had neither beginning nor end in time. This, however, seems quite incredible. As we have the fragment which Aristotle interprets in this way (fr. 2), we are quite entitled to understand it for ourselves, and I cannot see anything to justify Aristotle’s assumption that the expression “without limit” means without limit in space.

Arist. Phys. Α, 3. 186 a 7 (R. P. 143 a). Aristotle finds two flaws in the Eleatic reasoning: (1) ψευδῆ λαμβάνουσιν; (2) ἀσυλλόγιστοί εἰσιν αὐτῶν οἱ λόγοι. This is the first of these flaws. It is also mentioned in Soph. El. 168 b 35 (R. P. ib.). So Eudemos ap. Simpl. Phys. p. 105, 24, οὐ γὰρ, εἰ τὸ γενόμενον ἀρχὴν ἔχει, τὸ μὴ γενόμενον ἀρχὴν οὐκ ἔχει, μᾶλλον δὲ τὸ μὴ ἔχον ἀρχὴν οὐκ ἐγένετο. The real reason is given in the paraphrase in Simpl. Phys. p. 103, 21 (R. P. 142 a), συγχωρεῖται γὰρ καὶ τοῦτο ὑπὸ τῶν φυσικῶν, though of course Melissos himself would not have put it in that way. He regarded himself as a φυσικός like the rest; but, from the time of Aristotle, it was a commonplace that the Eleatics were not φυσικοί, since they denied motion. This has been denied by Offner, “Zur Beurtheilung des Melissos” (Arch. iv. pp. 12 sqq.), but I now think he goes too far. Cf. especially Top. ix. 6, ὡς ἄμφω ταὐτὰ ὄντα τῷ ἀρχὴν ἔχειν, τό τε γεγονὸς καὶ τὸ πεπερασμένον. The same point is made in Soph. El. 167 b 13 and 181 a 27.

The words ἀλλ’ ἄπειρόν ἐστι mean simply “but it is without limit,” and this is simply a repetition of the statement that it has no beginning or end. The nature of the limit can only be determined by the context, and accordingly, when Melissos does introduce the subject of spatial infinity, he is careful to say τὸ μέγεθος ἄπειρον (fr. 3). [Sidenote: Reality spatially infinite.]

167. Melissos did indeed differ from Parmenides in holding that reality was spatially as well as temporally infinite; but he gave an excellent reason for this belief, and had no need to support it by the extraordinary argument just alluded to. What he said was that, if it were limited, it would be limited by empty space. This we know from Aristotle himself, and it marks a real advance upon Parmenides. He had thought it possible to regard reality as a finite sphere, but it would have been difficult for him to work out this view in detail. He would have had to say there was nothing outside the sphere; but no one knew better than he that there is no such thing as nothing. Melissos saw that you cannot imagine a finite sphere without regarding it as surrounded by an infinite empty space; and as, in common with the rest of the school, he denied the void (fr. 7), he was forced to say reality was spatially infinite (fr. 3). It is possible that he was influenced in this by his association with the Ionic school.

Arist. Gen. Corr. i. 8. 325 a 14, ἓν καὶ ἀκίνητον τὸ πᾶν εἶναί φασι καὶ ἄπειρον ἔνιοι· τὸ γὰρ πέρας περαίνειν ἂν πρὸς τὸ κενόν. That this refers to Melissos has been proved by Zeller (p. 612, n. 2). Note the disagreement with Zeno (§ 162). From the infinity of reality, it follows that it must be one; for, if it were not one, it would be bounded by something else (fr. 5). And, being one, it must be homogeneous throughout (fr. 6_a_), for that is what we mean by one. Reality, then, is a single, homogeneous, corporeal plenum, stretching out to infinity in space, and going backwards and forwards to infinity in time. [Sidenote: Opposition to Ionians.]

168. Eleaticism was always critical, and we are not without indications of the attitude taken up by Melissos towards contemporary systems. The flaw which he found in the Ionian theories was that they all assumed some want of homogeneity in the One, which is a real inconsistency. Further, they all allowed the possibility of change; but, if all things are one, change must be a form of coming into being and passing away. If you admit that a thing can change, you cannot maintain that it is eternal. Nor can the arrangement of the parts of reality alter, as Anaximander, for instance, had held; any such change necessarily involves a coming into being and passing away. The next point made by Melissos is somewhat peculiar. Reality, he says, cannot feel sorrow or pain; for that is always due to the addition or subtraction of something, which is impossible. It is not easy to be sure what this refers to. Perhaps it is to the theory of Herakleitos with its Want and Surfeit, perhaps to something of which no record has been preserved. Motion in general and rarefaction and condensation in particular are impossible; for both imply the existence of empty space. Divisibility is excluded for the same reason. These are the same arguments as Parmenides employed.

The view of Bäumker that Melissos admitted ἀντιπερίστασις or motion in pleno (Jahrb. f. kl. Phil., 1886, p. 541; Das Problem der Materie, p. 59) depends upon some words of Simplicius (Phys. p. 104, 13), οὐχ ὅτι μὴ δυνατὸν διὰ πλήρους κινεῖσθαι, ὡς ἐπὶ τῶν σωμάτων λέγομεν κ.τ.λ. These words were formerly turned into Ionic and passed off as a fragment of Melissos. They are, however, part of Simplicius’s own argument against Alexander, and have nothing to do with Melissos at all. [Sidenote: Opposition to Pythagoreans.]

169. In nearly all accounts of the system of Melissos, we find it stated that he denied the corporeality of what is real,—an opinion which is supported by a reference to fr. 9, which is certainly quoted by Simplicius to prove this very point. If, however, our general view as to the character of early Greek Philosophy is correct, the statement must seem incredible. And it will seem even more surprising when we find that in the Metaphysics Aristotle says that, while the unity of Parmenides seemed to be ideal, that of Melissos was material. Now the fragment, as it stands in the MSS. of Simplicius, puts a purely hypothetical case, and would most naturally be understood as a disproof of the existence of something on the ground that, if it existed, it would have to be both corporeal and one. This cannot refer to the Eleatic One, in which Melissos himself believed; and, as the argument is almost verbally the same as one of Zeno’s, it is natural to suppose that it also was directed against the Pythagorean assumption of ultimate units. The only possible objection is that Simplicius, who twice quotes the fragment, certainly took it in the sense usually given to it. But it was very natural for him to make this mistake. “The One” was an expression that had two senses in the middle of the fifth century B.C.; it meant either the whole of reality or the point as a spatial unit. To maintain it in the first sense, the Eleatics were obliged to disprove it in the second; and so it sometimes seemed that they were speaking of their own “One” when they really meant the other. We have seen that the very same difficulty was felt about Zeno’s denial of the “one.”

See, however, Bäumker, Das Problem der Materie, pp. 57 sqq., who remarks that ἐόν (or ὄν) in fr. 9 must be the predicate, as it has no article. In his fifth edition (p. 611, n. 2) Zeller has adopted the view here taken. He rightly observes that the hypothetical form εἰ μὲν ὂν εἴη speaks for it, and that the subject to εἴη must be ἕκαστον τῶν πολλῶν, as with Zeno. Met. Α, 5. 986 b 18 (R. P. 101). Brandis changed the εἴη to ἔστι, but there is no warrant for this. Cf. Zeno, fr. 1, especially the words εἰ δὲ ἔστιν, ἀνάγκη ἕκαστον μέγεθός τι ἔχειν καὶ πάχος. Simpl. Phys. pp. 87, 6, and 110, 1. See above, § 159, p. 363, n. 880. [Sidenote: Opposition to Anaxagoras.]

170. The most remarkable fragment of Melissos is, perhaps, the last (fr. 8). It seems to be directed against Anaxagoras; at least the language used seems more applicable to him than to any one else. Anaxagoras had admitted (§ 137, fin.) that, so far as our perceptions go, they do not entirely agree with his theory, though he held this was due solely to their weakness. Melissos, taking advantage of this admission, urges that, if we give up the senses as the ultimate test of reality, we are not entitled to reject the Eleatic theory. With wonderful penetration he points out that if we are to say, with Anaxagoras, that things are a many, we are bound also to say that each one of them is such as the Eleatics declared the One to be. In other words, the only consistent pluralism is the atomic theory.

Melissos has long been unduly depreciated owing to the criticisms of Aristotle; but these, we have seen, are based mainly on a somewhat pedantic objection to the false conversion in the early part of the argument. Melissos knew nothing about the rules of conversion; and if he had, he could easily have made his reasoning formally correct without modifying his system. His greatness consisted in this, that not only was he the real systematiser of Eleaticism, but he was also able to see, before the pluralists saw it themselves, the only way in which the theory that things are a many could be consistently worked out. It is significant that Polybos, the nephew of Hippokrates, reproaches those “sophists” who taught there was only one primary substance with “putting the doctrine of Melissos on its feet.” Bäumker, op. cit. p. 58, n. 3: “That Melissos was a weakling is a fable convenue that people repeat after Aristotle, who was unable to appreciate the Eleatics in general, and in particular misunderstood Melissos not inconsiderably.”

Περὶ φύσιος ἀνθρώπου, c. 1, ἀλλ’ ἔμοιγε δοκέουσιν οἱ τοιοῦτοι ἄνθρωποι αὐτοὶ ἑωυτοὺς καταβάλλειν ἐν τοῖσιν ὀνόμασι τῶν λόγων αὐτῶν ὑπὸ ἀσυνεσίης, τὸν δὲ Μελίσσου λόγον ὀρθοῦν. The metaphors are taken from wrestling, and were current at this date (cf. the καταβάλλοντες of Protagoras). Plato implies a more generous appreciation of Melissos than Aristotle’s. In Theaet. 180 e 2, he refers to the Eleatics as Μέλισσοί τε καὶ Παρμενίδαι, and in 183 e 4 he almost apologises for giving the pre-eminence to Parmenides.

LEUKIPPOS OF MILETOS [Sidenote: Leukippos and Demokritos.] 171. We have seen (§§ 31, 122) that the school of Miletos did not come to an end with Anaximenes, and it is a striking fact that the man who gave the most complete answer to the question first asked by Thales was a Milesian. It is true that the very existence of Leukippos has been called in question. Epicurus said there never was such a philosopher, and the same thing has been maintained in quite recent times. On the other hand, Aristotle and Theophrastos certainly made him the originator of the atomic theory, and it still seems possible to show they were right. Incidentally we shall see how later writers came to ignore him, and thus made possible the sally of Epicurus.

Theophrastos said he was an Eleate or a Milesian (R. P. 185), while Diogenes (ix. 30) says he was an Eleate or, according to some, an Abderite. These statements are exactly parallel to the discrepancies about the native cities of the Pythagoreans already noted (Chap. VII. p. 327, n. 763). Diogenes adds that, according to others, Leukippos was a Melian, which is a common confusion. Aetios (i. 7. 1) calls Diagoras of Melos a Milesian (cf. Dox. p. 14). Demokritos was called by some a Milesian (R. P. 186) for the same reason that Leukippos is called an Eleate. We may also compare the doubt as to whether Herodotos called himself a Halikarnassian or a Thourian. Diog. x. 13 (R. P. 185 b). The theory was revived by E. Rohde. For the literature of the controversy, see R. P. 185 b. Diels’s refutation of Rohde has convinced most competent judges. Brieger’s attempt to unsettle the question again (Hermes, xxxvi. pp. 166 sqq.) is only half-hearted, and quite unconvincing. As will be seen, however, I agree with his main contention that atomism comes after the systems of Empedokles and Anaxagoras.

The question is intimately bound up with that of the date of Demokritos, who said that he was a young man in the old age of Anaxagoras, a statement which makes it unlikely that he founded his school at Abdera before 420 B.C., the date given by Apollodoros for his floruit. Now Theophrastos stated that Diogenes of Apollonia borrowed some of his views from Anaxagoras and some from Leukippos, which can only mean that there were traces of the atomic theory in his work. Further, Apollonios is parodied in the Clouds of Aristophanes, which was produced in 423 B.C., from which it follows that the work of Leukippos must have become known considerably before that date. What that work was, Theophrastos also tells us. It was the Great Diakosmos usually attributed to Demokritos. This means further that what were known later as the works of Demokritos were really the writings of the school of Abdera, and included, as was natural, the works of its founder. They formed, in fact, a corpus comparable to that which has come down to us under the name of Hippokrates, and it was no more possible to distinguish the authors of the different treatises in the one case than it is in the other. We need not hesitate, for all that, to believe that Aristotle and Theophrastos were better informed on this point than later writers, who naturally regarded the whole mass as equally the work of Demokritos.

Diog. ix. 41 (R. P. 187). As Diels points out, the statement suggests that Anaxagoras was dead when Demokritos wrote. It is probable, too, that it was this which made Apollodoros fix the floruit of Demokritos just forty years after that of Anaxagoras (Jacoby, p. 290). We cannot make much of the other statement of Demokritos that he wrote the Μικρὸς διάκοσμος 750 years after the fall of Troy; for we cannot be sure what era he used (Jacoby, p. 292). Theophr. ap. Simpl. Phys. p. 25, 1 (R. P. 206 a).

This was stated by Thrasylos in his list of the tetralogies in which he arranged the works of Demokritos, as he did those of Plato. He gives Tetr. iii. thus: (1) Μέγας διάκοσμος (ὃν οἱ περὶ Θεόφραστον Λευκίππου φασὶν εἶναι); (2) Μικρὸς διάκοσμος; (3) Κοσμογραφίη; (4) Περὶ τῶν πλανήτων. The two διάκοσμοι would only be distinguished as μέγας and μικρός when they came to be included in the same corpus. A quotation purporting to be from the Περὶ νοῦ of Leukippos is preserved in Stob. i. 160. The phrase ἐν τοῖς Λευκίππου καλουμένοις λόγοις in M.X.G. 980 a 8 seems to refer to Arist. de Gen. Corr. 325 a 24, Λεύκιππος δ’ ἔχειν ᾠήθη λόγους κ.τ.λ., and would prove nothing in any case. Cf. Chap. II. p. 138, n. 305.

Theophrastos found Leukippos described as an Eleate in some of his authorities, and, if we may trust analogy, that means he had settled at Elea. It is possible that his emigration to the west was connected with the revolution at Miletos in 450-49 B.C. In any case, Theophrastos says distinctly that he had been a member of the school of Parmenides, and the way in which he speaks suggests that the founder of that school was still at its head. He may very well have been so, if we accept Plato’s chronology. Theophrastos also appears to have said that Leukippos “heard” Zeno, which is very credible. We shall see, at any rate, that the influence of Zeno on his thinking is unmistakable. See above, p. 380, n. 921. The aristocrats had massacred the democrats, and were overthrown in their turn by the Athenians. Cf. [Xen.] Ἀθ. πολ. 3, 11. The date is fixed by C.I.A. i. 22 a.

Theophr. ap. Simpl. Phys. p. 28, 4 (R. P. 185). Note the difference of case in κοινωνήσας Παρμενίδῃ τῆς φιλοσοφίας and κοινωνήσας τῆς Ἀναξιμένους φιλοσοφίας which is the phrase used by Theophrastos of Anaxagoras (p. 293, n. 660). The dative seems to imply a personal relationship. It is quite inadmissible to render “was familiar with the doctrine of Parmenides,” as is done in Gomperz, Greek Thinkers, vol. i. p. 345. See § 84. Cf. Diog. ix. 30, οὕτος ἤκουσε Ζήνωνος (R. P. 185 b); and Hipp. Ref. i. 12, 1, Λεύκιππος ... Ζήνωνος ἑταῖρος. Diels conjectured that the name of Zeno had been dropped in the extract from Theophrastos preserved by Simplicius (Dox. 483 a 11).

The relations of Leukippos to Empedokles and Anaxagoras are more difficult to determine. It has become part of the case for the historical reality of Leukippos that there are traces of atomism in the systems of these men; but the case is strong enough without that assumption. Besides, it lands us in serious difficulties, not the least of which is that it would require us to regard Empedokles and Anaxagoras as mere eclectics like Diogenes of Apollonia. The strongest argument for the view that Leukippos influenced Empedokles is that drawn from the doctrine of “pores”; but we have seen that this originated with Alkmaion, and it is therefore more probable that Leukippos derived it from Empedokles. We have seen too that Zeno probably wrote against Empedokles, and we know that he influenced Leukippos. Nor, is it at all probable that Anaxagoras knew anything of the theory of Leukippos. It is true that he denied the existence of the void; but it does not follow that any one had already maintained that doctrine in the atomist sense. The early Pythagoreans had spoken of a void too, though they had confused it with atmospheric air; and the experiments of Anaxagoras with the klepsydra and the inflated skins would only have had any point if they were directed against the Pythagorean theory. If he had really wished to refute Leukippos, he would have had to use arguments of a very different kind.

This point is important, though the argument is weakened by Brieger’s overstatement of it in Hermes, xxxvi. p. 183. He says that to assume such a reaction as Anaxagoreanism after the atomic system had once been discovered would be something unexampled in the history of Greek philosophy. Diogenes of Apollonia proves the contrary. The real point is that Empedokles and Anaxagoras were men of a different stamp. So far as Empedokles is concerned, Gomperz states the case rightly (Greek Thinkers, vol. i. p. 560). See above, Chap. V. p. 224, n. 492; and Brieger in Hermes, xxxvi. p. 171. Diels (formerly at least) maintained both these things. See above, p. 359, n. 859; and p. 382, n. 930. If, as seems probable (§ 158), Zeno wrote his book some time between 470 and 460 B.C., Leukippos can hardly have written his before 450 B.C., and even that is too late for him to have influenced Empedokles. It may well have been later still. See above, Chap. VI. § 131; and Chap. VII. § 145. [Sidenote: Theophrastos on the atomic theory.] 172. Theophrastos wrote of Leukippos as follows in the First Book of his Opinions:—

Leukippos of Elea or Miletos (for both accounts are given of him) had associated with Parmenides in philosophy. He did not, however, follow the same path in his explanation of things as Parmenides and Xenophanes did, but, as is believed, the very opposite (R. P. 185). They made the All one, immovable, uncreated, and finite, and did not even permit us to search for what is not; he assumed innumerable and ever-moving elements, namely, the atoms. And he made their forms infinite in number, since there was no reason why they should be of one kind rather than another, and because he saw that there was unceasing becoming and change in things. He held, further, that what is is no more real than what is not, and that both are alike causes of the things that come into being; for he laid down that the substance of the atoms was compact and full, and he called them what is, while they moved in the void which he called what is not, but affirmed to be just as real as what is. R. P. 194. [Sidenote: Leukippos and the Eleatics.]

173. It will be observed that Theophrastos, while noting the affiliation of Leukippos to the Eleatic school, points out that his theory is, prima facie, just the opposite of that maintained by Parmenides. Some have been led by this to deny the Eleaticism of Leukippos altogether; but this denial is really based on the view that the system of Parmenides was “metaphysical,” coupled with a great reluctance to admit that so scientific a hypothesis as the atomic theory can have had a “metaphysical” origin. It is really due to prejudice, and we must not suppose Theophrastos himself believed the two theories to be so far apart as they seem. As this is really the most important point in the history of early Greek philosophy, and as, rightly understood, it furnishes the key to the whole development, it is worth while to transcribe a passage of Aristotle which explains the historical connexion in a way that leaves nothing to be desired.

The words ὡς δοκεῖ do not imply assent to the view introduced by them; indeed they are used, far more often than not, in reference to beliefs which the writer does not accept. The translation “methinks” in Gomperz, Greek Thinkers, vol. i. p. 345, is therefore most misleading, and there is no justification for Brieger’s statement (Hermes, xxxvi. p. 165) that Theophrastos dissents from Aristotle’s view as given in the passage about to be quoted. We should be saved from many errors if we accustomed ourselves to translate δοκεῖ by “is thought” or “is believed” instead of by “seems.”

Leukippos and Demokritos have decided about all things practically by the same method and on the same theory, taking as their starting-point what naturally comes first. Some of the ancients had held that the real must necessarily be one and immovable; for, said they, empty space is not real, and motion would be impossible without empty space separated from matter; nor, further, could reality be a many, if there were nothing to separate things. And it makes no difference if any one holds that the All is not continuous, but discrete, with its parts in contact (the Pythagorean view), instead of holding that reality is many, not one, and that there is empty space. For, if it is divisible at every point there is no one, and therefore no many, and the Whole is empty (Zeno); while, if we say it is divisible in one place and not in another, this looks like an arbitrary fiction; for up to what point and for what reason will part of the Whole be in this state and be full, while the rest is discrete? And, on the same grounds, they further say that there can be no motion. In consequence of these reasonings, then, going beyond perception and overlooking it in the belief that we ought to follow the argument, they say that the All is one and immovable (Parmenides), and some of them that it is infinite (Melissos), for any limit would be bounded by empty space. This, then, is the opinion they expressed about the truth, and these are the reasons which led them to do so. Now, so far as arguments go, this conclusion does seem to follow; but, if we appeal to facts, to hold such a view looks like madness. No one who is mad is so far out of his senses that fire and ice appear to him to be one; it is only things that are right, and things that appear right from habit, in which madness makes some people see no difference.

Leukippos, however, thought he had a theory which was in harmony with sense-perception, and did not do away with coming into being and passing away, nor motion, nor the multiplicity of things. He made this concession to experience, while he conceded, on the other hand, to those who invented the One that motion was impossible without the void, that the void was not real, and that nothing of what was real was not real. “For,” said he, “that which is strictly speaking real is an absolute plenum; but the plenum is not one. On the contrary, there are an infinite number of them, and they are invisible owing to the smallness of their bulk. They move in the void (for there is a void); and by their coming together they effect coming into being; by their separation, passing away.”

This prejudice is apparent all through Gomperz’s Greek Thinkers, and seriously impairs the value of that fascinating, though somewhat imaginative work. It is amusing to notice that Brieger, from the same point of view, regards the custom of making Anaxagoras the last of the Presocratics as due to theological prepossessions (Hermes, xxxvi. p. 185). I am sorry that I cannot agree with either side; but the bitterness of the disputants bears witness to the fundamental importance of the questions raised by the early Greek philosophers. Arist. de Gen. Corr. Α, 8. 324 b 35 (R. P. 193).

It is true that in this passage Zeno and Melissos are not named, but the reference to them is unmistakable. The argument of Zeno against the Pythagoreans is clearly given; and Melissos was the only Eleatic who made reality infinite, a point which is distinctly mentioned. We are therefore justified by Aristotle’s words in explaining the genesis of Atomism and its relation to Eleaticism as follows. Zeno had shown that all pluralist systems yet known, and especially Pythagoreanism, were unable to stand before the arguments from infinite divisibility which he adduced. Melissos had used the same argument against Anaxagoras, and had added, by way of reductio ad absurdum, that, if there were many things, each one of them must be such as the Eleatics held the One to be. To this Leukippos answers, “Why not?” He admitted the force of Zeno’s arguments by setting a limit to divisibility, and to each of the atoms which he thus arrived at he ascribed all the predicates of the Eleatic One; for Parmenides had shown that if it is, it must have these predicates somehow. The same view is implied in a passage of Aristotle’s Physics. “Some,” we are there told, “surrendered to both arguments, to the first, the argument that all things are one, if the word is is used in one sense only (Parmenides), by affirming the reality of what is not; to the second, that based on dichotomy (Zeno), by introducing indivisible magnitudes.” Finally, it is only by regarding the matter in this way that we can attach any meaning to another statement of Aristotle’s to the effect that Leukippos and Demokritos, as well as the Pythagoreans, virtually make all things out of numbers. Leukippos, in fact, gave the Pythagorean monads the character of the Parmenidean One.

Arist. Phys. Α, 3. 187 a 1 (R. P. 134 b). Arist. de Caelo, Γ, 4. 303 a 8, τρόπον γάρ τινα καὶ οὕτοι (Λεύκιππος καὶ Δημόκριτος) πάντα τὰ ὄντα ποιοῦσιν ἀριθμοὺς καὶ ἐξ ἀριθμῶν. This also serves to explain what Herakleides may have meant by attributing the theory of corporeal ὄγκοι to the Pythagorean Ekphantos of Syracuse (above, p. 338, n. 794). [Sidenote: Atoms.]

174. We must observe that the atom is not mathematically indivisible, for it has magnitude; it is, however, physically indivisible, because, like the One of Parmenides, it contains in it no empty space. Each atom has extension, and all the atoms are exactly alike in substance. Therefore all differences in things must be accounted for either by the shape of the atoms or by their arrangement. It seems probable that the three ways in which differences arise, namely, shape, position, and arrangement, were already distinguished by Leukippos; for Aristotle mentions his name in connexion with them. This explains, too, why the atoms are called “forms” or “figures,” a way of speaking which seems to be of Pythagorean origin. That they are also called φύσις is quite intelligible if we remember what was said of that word in the Introduction (§ VII.). The differences in shape, order, and position just referred to account for the “opposites,” the “elements” being regarded rather as aggregates of these (πανσπερμίαι), as by Anaxagoras. The Epicureans misunderstood this point, or misrepresented it in order to magnify their own originality (see Zeller, p. 857, n. 3; Eng. trans. ii. p. 225, n. 2).

Arist. de Caelo, Α, 7. 275 b 32, τὴν δὲ φύσιν εἶναί φασιν αὐτῶν μίαν; Phys. Γ, 4. 203 a 34, αὐτῷ (Δημοκρίτῳ) τὸ κοινὸν σῶμα πάντων ἐστὶν ἀρχή. Arist. Met. Α, 4. 985 b 13 (R. P. 192); cf. de Gen. Corr. 315 b 6. As Diels suggests, the illustration from the letters of the alphabet is probably due to Demokritos. It shows, in any case, how the word στοιχεῖον came to be used later for “element.” We must read, with Wilamowitz, τὸ δὲ Ζ τοῦ Η θέσει for τὸ δὲ Ζ τοῦ Ν θέσει, the older form of the letter Ζ being just an Η laid upon its side (Diels, Elementum, p. 13, n. 1). Demokritos wrote a work, Περὶ ἰδεῶν (Sext. Math. vii. 137; R. P. 204), which Diels identifies with the Περὶ τῶν διαφερόντων ῥυσμῶν of Thrasylos, Tetr. v. 3. Theophrastos refers to Demokritos, ἐν τοῖς περὶ τῶν εἰδῶν (de Sensibus, § 51). Plut. adv. Col. 1111 a, εἶναι δὲ πάντα τὰς ἀτόμους, ἰδέας ὑπ’ αὐτοῦ καλουμένας (so the MSS.: ἰδίως, Wyttenbach; <ἢ> ἰδέας, Diels). Arist. Phys. Γ, 4. 203 a 21, (Δημόκριτος) ἐκ τῆς πανσπερμίας τῶν σχημάτων (ἄπειρα ποιεῖ τὰ στοιχεῖα). Cf. de Gen. Corr. Α, 2. 315 b 7 (R. P. 196).

Arist. Phys. Θ, 9. 265 b 25; Simpl. Phys. p. 1318, 33, ταῦτα γὰρ (τὰ ἄτομα σώματα) ἐκεῖνοι φύσιν ἐκάλουν. Simpl. Phys. p. 36, 1 (Diels, Vors. p. 346), and R. P. 196 a. [Sidenote: The void.]

175. Leukippos affirmed the existence both of the Full and the Empty, terms which he may have borrowed from Melissos. As we have seen, he had to assume the existence of empty space, which the Eleatics had denied, in order to make his explanation of the nature of body possible. Here again he is developing a Pythagorean view. The Pythagoreans had spoken of the void, which kept the units apart; but they had not distinguished it from atmospheric air (§ 53), which Empedokles had shown to be a corporeal substance (§ 107). Parmenides, indeed, had formed a clearer conception of space, but only to deny its reality. Leukippos started from this. He admitted, indeed, that space was not real, that is to say, corporeal; but he maintained that it existed all the same. He hardly, it is true, had words to express his discovery in; for the verb “to be” had hitherto been used by philosophers only of body. But he did his best to make his meaning clear by saying that “what is not” (in the old corporealist sense) “is” (in another sense) just as much as “what is.” The void is as real as body. Arist. Met. Α, 4. 985 b 4 (R. P. 192). Cf. Melissos, fr. 7 sub fin.

It is a curious fact that the Atomists, who are commonly regarded as the great materialists of antiquity, were actually the first to say distinctly that a thing might be real without being a body. [Sidenote: Cosmology.] 176. It might seem a hopeless task to disentangle the cosmology of Leukippos from that of Demokritos, with which it is generally identified; but that very fact affords an invaluable clue. So far as we know, no one after Theophrastos was able to distinguish the doctrines of the two men, and it follows from this that all definite statements about Leukippos in later writers must, in the long run, go back to him. If we follow this up, we shall be able to give a fairly clear account of the system, and we shall even come across some views which are peculiar to Leukippos and were not adopted by Demokritos. Cf. Zeller, “Zu Leukippus” (Arch. xv. p. 138). We shall start from the fuller of the two doxographies in Diogenes, which comes from an epitome of Theophrastos. It is as follows:—

He says that the All is infinite, and that it is part full, and part empty. These (the full and the empty), he says, are the elements. From them arise innumerable worlds and are resolved into them. The worlds come into being thus. There were borne along by “abscision from the infinite” many bodies of all sorts of figures “into a mighty void,” and they being gathered together produce a single vortex. In it, as they came into collision with one another and were whirled round in all manner of ways, those which were alike were separated apart and came to their likes. But, as they were no longer able to revolve in equilibrium owing to their multitude, those of them that were fine went out to the external void, as if passed through a sieve; the rest stayed together, and becoming entangled with one another, ran down together, and made a first spherical structure. This was in substance like a membrane or skin containing in itself all kinds of bodies. And, as these bodies were borne round in a vortex, in virtue of the resistance of the middle, the surrounding membrane became thin, as the contiguous bodies kept flowing together from contact with the vortex. And in this way the earth came into being, those things which had been

borne towards the middle abiding there. Moreover, the containing membrane was increased by the further separating out of bodies from outside; and, being itself carried round in a vortex, it further got possession of all with which it had come in contact. Some of these becoming entangled, produce a structure, which was at first moist and muddy; but, when they had been dried and were revolving along with the vortex of the whole, they were then ignited and produced the substance of the heavenly bodies. The circle of the sun is the outermost, that of the moon is nearest to the earth, and those of the others are between these. And all the heavenly bodies are ignited because of the swiftness of their motion; while the sun is also ignited by the stars. But the moon only receives a small portion of fire. The sun and the moon are eclipsed.... (And the obliquity of the zodiac is produced) by the earth being inclined towards the south; and the northern parts of it have constant snow and are cold and frozen. And the sun is eclipsed rarely, and the moon continually, because their circles are unequal. And just as there are comings into being of the world, so there are growths and decays and passings away in virtue of a certain

necessity, of the nature of which he gives no clear account.

Diog. ix. 31 sqq. (R. P. 197, 197 c). This passage deals expressly with Leukippos, not with Demokritos or even “Leukippos and Demokritos.” For the distinction between the “summary” and “detailed” doxographies in Diogenes, see Appendix, § 15. As it comes substantially from Theophrastos, this passage is to be regarded as good evidence for the cosmology of Leukippos, and it is confirmed in an interesting way by certain Epicurean extracts from the Great Diakosmos. These, however, as is natural, give a specially Epicurean turn to some of the doctrines, and must therefore be used with caution. These are to be found in Aet. i. 4 (Dox. p. 289; Vors. p. 347; Usener, Epicurea, fr. 308). Epicurus himself in the second epistle (Diog. x. 88; Usener, p. 37, 7) quotes the phrase ἀποτομὴν ἔχουσα ἀπὸ τοῦ ἀπείρου. [Sidenote: Relation to Ionic cosmology.]

177. The general impression which we get from the cosmology of Leukippos is that he either ignored or had never heard of the great advance in the general view of the world which was due to the later Pythagoreans. He is as reactionary in his detailed cosmology as he was daring in his general physical theory. We seem to be reading once more of the speculations of Anaximenes or even of Anaximander, though there are traces of Empedokles and Anaxagoras too. The explanation is not hard to see. Leukippos would not learn a cosmology from his Eleatic teachers; and, even when he found it possible to construct one without giving up the Parmenidean view of reality, he was necessarily thrown back upon the older systems of Ionia. The result was unfortunate. The astronomy of Demokritos, so far as we know it, was still of this childish character. There is no reason to doubt the statement of Seneca that he did not venture to say how many planets there were. Seneca, Q. Nat. vii. 3.

This, I take it, is what gives plausibility to Gomperz’s statement that Atomism was “the ripe fruit on the tree of the old Ionic doctrine of matter which had been tended by the Ionian physiologists.” The detailed cosmology was certainly such a fruit, and it was possibly over-ripe; but the atomic theory proper, in which the real greatness of Leukippos comes out, was wholly Eleatic in its origin. Nevertheless, it will repay us to examine the cosmology too; for such an examination will serve better than anything else to bring out the true nature of the historical development of which it was the outcome. Gomperz, Greek Thinkers, vol. i. p. 323. [Sidenote: The eternal motion.]

178. Leukippos represented the atoms as having been always in motion. Aristotle puts this in his own way. The atomists, he says, “indolently” left it unexplained what was the source of motion, and they did not say what sort of motion it was. In other words, they did not decide whether it was a “natural motion” or one impressed on them “contrary to their nature.” He even went so far as to say that they made it “spontaneous,” a remark which has given rise to the erroneous view that they held it was due to chance. Aristotle does not say that, however; but only that the atomists did not explain the motion of the atoms in any of the ways in which he himself explained the motion of the elements. They neither ascribed to them a natural motion like the circular motion of the heavens and the rectilinear motion of the four elements in the sublunary region, nor did they give them a forced motion contrary to their own nature, like the upward motion which may be given to the heavy elements and the downward which may be given to the light. The only fragment of Leukippos which has survived is an express denial of chance. “Naught happens for nothing,” he said “but everything from a ground and of necessity.”

Arist. Phys. Θ, 1. 252 a 32 (R. P. 195 a); de Caelo, Γ, 2. 300 b 8 (R. P. 195); Met. Α, 4. 985 b 19 (R. P. ib.). Arist. Phys. Β, 4. 196 a 24 (R. P. 195 d). Cicero, de nat. D. i. 66 (R. P. ib.). The latter passage is the source of the phrase “fortuitous concourse” (concurrere = συντρέχειν). Aet. i. 25, 4 (Dox. p. 321), Λεύκιππος πάντα κατ’ ἀνάγκην, τὴν δ’ αὐτὴν ὑπάρχειν εἱμαρμένην. λέγει γὰρ ἐν τῷ Περὶ νοῦ· Οὐδὲν χρῆμα μάτην γίγνεται, ἀλλὰ πάντα ἐκ λόγου τε καὶ ὑπ’ ἀνάγκης.

If we put the matter historically, all this means that Leukippos did not, like Empedokles and Anaxagoras, find it necessary to assume a force to originate motion. He had no need of Love and Strife or Mind, and the reason is clear. Though Empedokles and Anaxagoras had tried to explain multiplicity and motion, they had not broken so radically as Leukippos did with the Parmenidean One. Both of them started with a condition of matter in which the “roots” or “seeds” were mixed so as to be “all together,” and they therefore required something to break up this unity. Leukippos, who started with an infinite number of Parmenidean “Ones,” so to speak, required no external agency to separate them. What he had to do was just the opposite. He had to give an explanation of their coming together, and there was nothing so far to prevent his return to the old and natural idea that motion does not require any explanation at all. Introd. § VIII.

This, then, is what seems to follow from the criticisms of Aristotle and from the nature of the case; but it will be observed that it is not consistent with Zeller’s opinion that the original motion of the atoms is a fall through infinite space, as in the system of Epicurus. Zeller’s view depends, of course, on the further belief that the atoms have weight, and that weight is the tendency of bodies to fall, so we must go on to consider whether and in what sense weight is a property of the atoms. [Sidenote: The weight of the atoms.]

179. As is well known, Epicurus held that the atoms were naturally heavy, and therefore fell continually in the infinite void. The school tradition is, however, that the “natural weight” of the atoms was an addition made by Epicurus himself to the original atomic system. Demokritos, we are told, assigned two properties to atoms, magnitude and form, to which Epicurus added a third, weight. On the other hand, Aristotle distinctly says in one place that Demokritos held the atoms were heavier “in proportion to their excess,” and this seems to be explained by the statement of Theophrastos that, according to him, weight depended on magnitude. It will be observed that, even so, it is not represented as a primary property of the atoms in the same sense as magnitude.

Aet. i. 3, 18 (of Epicurus), συμβεβηκέναι δὲ τοῖς σώμασι τρία ταῦτα, σχῆμα, μέγεθος, βάρος. Δημόκριτος μὲν γὰρ ἔλεγε δύο, μέγεθός τε καὶ σχῆμα, ὁ δὲ Ἐπίκουρος τούτοις καὶ τρίτον βάρος προσέθηκεν· ἀνάγκη γάρ, φησί, κινεῖσθαι τὰ σώματα τῇ τοῦ βάρους πληγῇ· ἐπεὶ (“or else”) οὐ κινηθήσεται; ib. 12, 6, Δημόκριτος τὰ πρῶτά φησι σώματα, ταῦτα δ’ ἦν τὰ ναστά, βάρος μὲν οὐκ ἔχειν, κινεῖσθαι δὲ κατ’ ἀλληλοτυπίαν ἐν τῷ ἀπείρῳ. Cic. de fato, 20, “vim motus habebant (atomi) a Democrito impulsionis quam plagam ille appellat, a te, Epicure, gravitatis et ponderis.” These passages represent the Epicurean school tradition, which would hardly venture to misrepresent Demokritos on so important a point. His works were still accessible. It is confirmed by the Academic tradition in de Fin. i. 17 that Demokritos taught the atoms moved “in infinito inani, in quo nihil nec summum nec infimum nec medium nec extremum sit.” This doctrine, we are told, was “depraved” by Epicurus. Arist. de Gen. Corr. 326 a 9, καίτοι βαρύτερόν γε κατὰ τὴν ὑπεροχήν φησιν εἶναι Δημόκριτος ἕκαστον τῶν ἀδιαιρέτων. I cannot believe this means anything else than what Theophrastos says in his fragment on sensation, § 61 (R. P. 199), βαρὺ μὲν οὖν καὶ κοῦφον τῷ μεγέθει διαιρεῖ Δημόκριτος.

It is impossible to solve this apparent contradiction without referring briefly to the history of Greek ideas about weight. It is clear that lightness and weight would be among the very first properties of body to be distinctly recognised as such. The necessity of lifting burdens must very soon have led men to distinguish them, though no doubt in some primitive and more or less animistic form. Both weight and lightness would be thought of as things that were in bodies. Now it is a remarkable feature of early Greek philosophy that from the first it was able to shake itself free from this idea. Weight is never spoken of as a “thing” as, for instance, warmth and cold are; and, so far as we can see, not one of the thinkers we have studied hitherto thought it necessary to give any explanation of it at all, or even to say anything about it. The motions and resistances which popular theory ascribes to weight are all explained in some other way. Aristotle distinctly declares that none of his predecessors had said anything of absolute weight and lightness. They had only treated of the relatively light and heavy.

In Aet. i. 12, where the placita regarding the heavy and light are given, no philosopher earlier than Plato is referred to. Parmenides (fr. 8, 59) speaks of the dark element as ἐμβριθές. I do not think that there is any other place where weight is even mentioned in the fragments of the early philosophers. Arist. de Caelo, 308 a 9, περὶ μὲν οὖν τῶν ἁπλῶς λεγομένων (βαρέων καὶ κούφων) οὐδὲν εἴρηται παρὰ τῶν πρότερον.

This way of regarding the popular notions of weight and lightness is clearly formulated for the first time in Plato’s Timaeus. There is no such thing in the world, we are told there, as “up” or “down.” The middle of the world is not “down” but “just in the middle,” and there is no reason why any point in the circumference should be said to be “above” or “below” another. It is really the tendency of bodies towards their kin that makes us call a falling body heavy and the place to which it falls “below.” Here Plato is really giving the view which was taken more or less consciously by his predecessors, and it is not till the time of Aristotle that it is questioned. For reasons which do not concern us here, he definitely identified the circumference of the heavens with “up” and the middle of the world with “down,” and equipped the four elements with natural weight and lightness that they might perform their rectilinear motions between them. As, however, Aristotle believed there was only one world, and as he did not ascribe weight to the heavens proper, the effect of this reactionary theory upon his cosmical system was not great; it was only when Epicurus tried to combine it with the infinite void that its true character emerged. It seems to me that the nightmare of Epicurean atomism can only be explained on the assumption that an Aristotelian doctrine was violently adapted to a theory which really excluded it. It is totally unlike anything we meet with in earlier days.

Plato, Tim. 61 c 3 sqq. Zeller says (p. 876) that in antiquity no one ever understood by weight anything else than the property of bodies in virtue of which they move downwards; except that in such systems as represent all forms of matter as contained in a sphere, “above” is identified with the circumference and “below” with the centre. As to that, I can only say that no such theory of weight is to be found in the fragments of the early philosophers or is anywhere ascribed to them, while Plato expressly denies it.

This brief historical survey suggests at once that it is only in the vortex that the atoms acquire weight and lightness, which are, after all, only popular names for facts which can be further analysed. We are told that Leukippos held that one effect of the vortex was that like atoms were brought together with their likes. In this way of speaking we seem to see the influence of Empedokles, though the “likeness” is of another kind. It is the finer atoms that are forced to the circumference, while the larger tend to the centre. We may express that by saying that the larger are heavy and the smaller light, and this will amply account for everything Aristotle and Theophrastos say; for there is no passage where the atoms outside the vortex are distinctly said to be heavy or light.

The Aristotelian criticisms which may have affected Epicurus are such as we find in de Caelo, 275 b 29 sqq. Aristotle there argues that, as Leukippos and Demokritos made the φύσις of the atoms one, they were bound to give them a single motion. That is just what Epicurus did, but Aristotle’s argument implies that Leukippos and Demokritos did not. Though he gave the atoms weight, Epicurus could not accept Aristotle’s view that some bodies are naturally light. The appearance of lightness is due to ἔκθλιψις, the squeezing out of the smaller atoms by the larger. In dealing with Empedokles, Aristotle expressly makes this distinction. Cf. de Caelo, Β, 13, especially 295 a 32 sqq., where he points out that Empedokles does not account for the weight of bodies on the earth (οὐ γὰρ ἥ γε δίνη πλησιάζει πρὸς ἡμᾶς), nor for the weight of bodies before the vortex arose (πρὶν γενέσθαι τὴν δίνην). Diog., loc. cit. (p. 390). This seems to be in the main the view of Dyroff, Demokritstudien (1899), pp. 31 sqq., though I should not say that lightness and weight only arose in connexion with the atoms of the earth (p. 35). If we substitute “world” for “earth,” we shall be nearer the truth.

There is a striking confirmation of the view just given in the atomist cosmology quoted above. We are told there that the separation of the larger and smaller atoms was due to the fact that they were “no longer able to revolve in equilibrium owing to their number,” which implies that they had previously been in a state of “equilibrium” or “equipoise.” Now the word ἰσορροπία has no necessary implication of weight in Greek. A ῥοπή is a mere leaning or inclination in a certain direction, which may be caused by weight or anything else. The state of ἰσορροπία is therefore that in which the tendency in one direction is exactly equal to the tendency in any other, and such a state is more naturally described as the absence of weight than as the presence of opposite weights neutralising one another. That way of looking at it may be useful from the point of view of later science, but it is not safe to attribute it to the thinkers of the fifth century B.C. See above, p. 390.

If we no longer regard the “eternal motion” of the premundane and extramundane atoms as due to their weight, there is no reason for describing it as a fall. None of our authorities do as a matter of fact so describe it, nor do they tell us in any way what it was. It is safest to say that it is simply a confused motion this way and that. It is possible that the comparison of the motion of the atoms of the soul to that of the motes in a sunbeam coming through a window, which Aristotle attributes to Demokritos, is really intended as an illustration of the original motion of the atoms still surviving in the soul. The fact that it is also a Pythagorean comparison in no way tells against this; for we have seen that there is a real connexion between the Pythagorean monads and the atoms. It is also significant that the point of the comparison appears to have been the fact that the motes in the sunbeam move even when there is no wind, so that it would be a very apt illustration indeed of the motion inherent in the atoms apart from the secondary motions produced by impact and collision. That, however, is problematical; it only serves to suggest the sort of motion which it is natural to suppose that Leukippos gave his atoms.

This view was independently advocated by Brieger (Die Urbewegung der Atome und die Weltentstehung bei Leucipp und Demokrit, 1884) and Liepmann (Die Mechanik der Leucipp-Demokritschen Atome, 1885), both of whom unnecessarily weakened their position by admitting that weight is an original property of the atoms. On the other hand, Brieger denies that the weight of the atoms is the cause of their original motion, while Liepmann says that before and outside the vortex there is only a latent weight, a Pseudoschwere, which only comes into operation in the world. It is surely simpler to say that this weight, since it produces no effect, does not yet exist. Zeller rightly argues against Brieger and Liepmann that, if the atoms have weight, they must fall; but, so far as I can see, nothing he says tells against their theory as I have restated it. Gomperz adopts the Brieger-Liepmann explanation. See also Lortzing, Jahresber., 1903, pp. 136 sqq. Arist. de An. Α, 2. 403 b 28 sqq. (R. P. 200). Ibid. Α, 2. 404 a 17 (R. P. 86 a). [Sidenote: The vortex.]

180. But what are we to say of the vortex itself which produces these effects? Gomperz observes that they seem to be “the precise contrary of what they should have been by the laws of physics”; for, “as every centrifugal machine would show, it is the heaviest substances which are hurled to the greatest distance.” Are we to suppose that Leukippos was ignorant of this fact, which was known to Anaxagoras, though Gomperz is wrong in supposing there is any reason to believe that Anaximander took account of it? Now we know from Aristotle that all those who accounted for the earth being in the centre of the world by means of a vortex appealed to the analogy of eddies in wind or water, and Gomperz supposes that the whole theory was an erroneous generalisation of this observation. If we look at the matter more closely, we can see, I think, that there is no error at all. Gomperz, Greek Thinkers, i. p. 339. For Empedokles, see Chap. V. p. 274; Anaxagoras, see Chap. VI. p. 312; and for Anaximander, Chap. I. p. 69, n. 132.

Arist. de Caelo, Β, 13. 295 a 10, ταύτην γὰρ τὴν αἰτίαν (sc. τὴν δίνησιν) πάντες λέγουσιν ἐκ τῶν ἐν τοῖς ὑγοῖς καὶ περὶ τὸν ἀέρα συμβαινόντων· ἐν τούτοις γὰρ ἀεὶ φέρεται τὰ μείζω καὶ τὰ βαρύτερα πρὸς τὸ μέσον τῆς δίνης. We must remember that all the parts of the vortex are in contact, and that it is just this contact (ἐπίψαυσις) by which the motion of the outermost parts is communicated to those within them. The larger bodies are more able to resist this communicated motion than the smaller, and in this way they make their way to the centre where the motion is least, and force the smaller bodies out. This resistance is surely just the ἀντέρεισις τοῦ μέσου which is mentioned in the doxography of Leukippos, and it is quite in accordance with this that, on the atomist theory, the nearer a heavenly body is to the centre, the slower is its revolution. There is no question of “centrifugal force” at all, and the analogy of eddies in air and water is quite satisfactory. Diog. ix. 32. Cf. especially the phrases ὧν κατὰ τὴν τοῦ μέσου ἀντέρεισιν περιδινουμένων, συμμενόντων ἀεὶ τῶν συνεχῶν κατ’ ἐπίψαυσιν τῆς δίνης, and συμμενόντων τῶν ἐνεχθέντων ἐπὶ τὸ μέσον. Cf. Lucr. v. 621 sqq. [Sidenote: The earth and the heavenly bodies.]

181. When we come to details, the reactionary character of the atomist cosmology is very manifest. The earth was shaped like a tambourine, and floated on the air. It was inclined towards the south because the heat of that region made the air thinner, while the ice and cold of the north made it denser and more able to support the earth. This accounts for the obliquity of the zodiac. Like Anaximander (§ 19), Leukippos held that the sun was further away than the stars, though he also held that these were further away than the moon. This certainly suggests that he made no clear distinction between the planets and the fixed stars. He does, however, appear to have known the theory of eclipses as given by Anaxagoras. Such other pieces of information as have come down to us are mainly of interest as showing that, in some important respects, the doctrine of Leukippos was not the same as that taught afterwards by Demokritos. Aet. iii. 3, 10, quoted above, p. 83, n. 168. Aet. iii. 12, 1, Λεύκιππος παρεκπεσεῖν τὴν γῆν εἰς τὰ μεσημβρινὰ μέρη διὰ τὴν ἐν τοῖς μεσημβρινοῖς ἀραιότητα, ἅτε δὴ πεπηγότων τῶν βορείων διὰ τὸ κατεψῦχθαι τοῖς κρυμοῖς, τῶν δὲ ἀντιθέτων πεπυρωμένων.

Diog. ix. 33, εἶναι δὲ τὸν τοῦ ἡλίου κύκλον ἐξώτατον, τὸν δὲ τῆς σελήνης προσγειότατον, <τοὺς δὲ> τῶν ἄλλων μεταξὺ τούτων. From Diog., loc. cit. (supra, p. 391), it appears that he dealt with the question of the greater frequency of lunar as compared with solar eclipses. It seems to have been this which led him to make the circle of the moon smaller than that of the stars. Diels pointed out that Leukippos’s explanation of thunder (πυρὸς ἐναποληφθέντος νέφεσι παχυτάτοις ἔκπτωσιν ἰσχυρὰν βροντὴν ἀποτελεῖν ἀποφαίνεται, Aet. iii. 3, 10) is quite different from that of Demokritos (Βροντὴν ... ἐκ συγκρίματος ἀνωμάλου τὸ περιειληφὸς αὐτὸ νέφος πρὸς τὴν κάτω φορὰν ἐκβιαζομένου, ib. 11). The explanation given by Leukippos is derived from that of Anaximander, while Demokritos is influenced by Anaxagoras. See Diels, 35 Philol.-Vers. 97, 7. [Sidenote: Perception.]

182. Aetios expressly attributes to Leukippos the doctrine that the objects of sense-perception exist “by law” and not by nature. This must come from Theophrastos; for, as we have seen, all later writers quote Demokritos only. A further proof of the correctness of the statement is that we also find it attributed to Diogenes of Apollonia, who, as Theophrastos tells us, derived some of his views from Leukippos. There is nothing surprising in this. Parmenides had already declared the senses to be deceitful, and said that colour and the like were only “names,” and Empedokles had also spoken of coming into being and passing away as only “names.” It is not likely that Leukippos went much further than this. It would probably be wrong to credit him with Demokritos’s clear distinction between genuine and “bastard” knowledge, or that between what are now called the primary and secondary qualities of matter. These distinctions imply a conscious epistemological theory, and all we are entitled to say is that the germs of this were already to be found in the writings of Leukippos and his predecessors. Of course, these do not make Leukippos a sceptic any more than Empedokles or Anaxagoras, whose remark on this subject (fr. 21_a_) Demokritos is said to have quoted with approval.

Aet. iv. 9, 8, οἱ μὲν ἄλλοι φύσει τὰ αἰσθητα, Λεύκιππος δὲ Δημόκριτος καὶ Ἀπολλώνιος νόμῳ. See Zeller, Arch. v. p. 444.

(p. 321) from Galilei, to the effect that tastes, smells, and colours non sieno altro che puri nomi should, therefore, have been cited to illustrate Parmenides rather than Demokritos. See p. 240, fr. 8. For these see Sext. Math. vii. 135 (R. P. 204). Sext. vii. 140, “ὄψις γὰρ ἀδήλων τὰ φαινόμενα,” ὥς φησιν Ἀναξαγόρας, ὃν ἐπὶ τούτῳ Δημόκριτος ἐπαινεῖ. There appear to be sufficient grounds for ascribing the theory of perception by means of simulacra or εἴδωλα, which played such a part in the systems of Demokritos and Epicurus, to Leukippos. It is a very natural development of the Empedoklean theory of “effluences” (§ 118). It hardly seems likely, however, that he went into great detail on the subject, and it is safer to credit Demokritos with the elaboration of the theory. [Sidenote: Importance of Leukippos.]

183. We have seen incidentally that there is a wide divergence of opinion among recent writers as to the place of Atomism in Greek thought. The question at issue is really whether Leukippos reached his theory on what are called “metaphysical grounds,” that is, from a consideration of the Eleatic theory of reality, or whether, on the contrary, it was a pure development of Ionian science. The foregoing exposition will suggest the true answer. So far as his general theory of the physical constitution of the world is concerned, it has been shown, I think, that it was derived entirely from Eleatic and Pythagorean sources, while the detailed cosmology was in the main a more or less successful attempt to make the older Ionian beliefs fit into this new physical theory. In any case, his greatness consisted in his having been the first to see how body must be regarded if we take it to be ultimate reality. The old Milesian theory had found its most adequate expression in the system of Anaximenes (§ 31), but of course rarefaction and condensation cannot be clearly represented except on the hypothesis of molecules or atoms coming closer together or going further apart in space. Parmenides had seen that very clearly (fr.2), and it was the Eleatic criticism which forced Leukippos to formulate his system as he did. Even Anaxagoras took account of Zeno’s arguments about divisibility (§ 128), but his system of qualitatively different “seeds” was lacking in that simplicity which has always been the chief attraction of atomism.

See Zeller, “Zu Leukippus” (Arch. xv. p. 138). The doctrine is attributed to him in Aet. iv. 13, 1 (Dox. p. 403); and Alexander, de Sensu, pp. 24, 14 and 56, 10, also mentions his name in connexion with it. This must come from Theophrastos.

ECLECTICISM AND REACTION [Sidenote: The “bankruptcy of science.”]

184. With Leukippos our story should properly come to an end; for he had really answered the question first asked by Thales. We have seen, however, that, though his theory of matter was of a most original and daring kind, he was not equally successful in his attempt to construct a cosmology, and this seems to have stood in the way of the recognition of the atomic theory for what it really was. We have noted the growing influence of medicine, and the consequent substitution of an interest in detailed investigation for the larger cosmological views of an earlier time, and there are several treatises in the Hippokratean corpus which give us a clear idea of the interest which now prevailed. Leukippos had shown that “the doctrine of Melissos,” which seemed to make all science impossible, was not the only conclusion that could be drawn from the Eleatic premisses, and he had gone on to give a cosmology which was substantially of the old Ionic type. The result at first was simply that all the old schools revived and had a short period of renewed activity, while at the same time some new schools arose which sought to accommodate the older views to those of Leukippos, or to make them more available for scientific purposes by combining them in an eclectic fashion. None of these attempts had any lasting importance or influence, and what we have to consider in this chapter is really one of the periodical “bankruptcies of science” which mark the close of one chapter in its history and announce the beginning of a new one.

Cf. what is said in Chap. IV. p. 167, n. 383, of the Περὶ διαίτης. The Περὶ ἀνθρώπου φύσιος and the Περὶ ἀρχαίης ἰατρικῆς are invaluable documents for the attitude of scientific men to cosmological theories at this date. Cf. Chap. VIII. p. 379, n. 919. I. HIPPON OF SAMOS 185. Hippon of Samos or Kroton belonged to the Italian school of medicine. We know very little indeed of him except that he was a contemporary of Perikles. From a scholiast on Aristophanes we learn that Kratinos satirised him in his Panoptai; and Aristotle mentions him in the enumeration of early philosophers given in the First Book of the Metaphysics, though only to say that the inferiority of his intellect deprives him of all claim to be reckoned among them. Aristoxenos said he was a Samian (R. P. 219 a). In Menon’s Iatrika he is called a Krotoniate, while others assign him to Rhegion or Metapontion. This probably means that he was affiliated to the Pythagorean medical school. The evidence of Aristoxenos is, in that case, all the more valuable. Hippon is mentioned along with Melissos in Iamblichos’s Catalogue of Pythagoreans (V. Pyth. 267). Schol. on Clouds, 94 sqq. Arist. Met. Α, 3. 984 a 3 (R. P. 219 a). [Sidenote: Moisture.]

With regard to his views, the most precise statement is that of Alexander, who doubtless follows Theophrastos. It is to the effect that he held the primary substance to be Moisture, without deciding whether it was Water or Air. We have the authority of Aristotle and Theophrastos, represented by Hippolytos, for saying that this theory was supported by physiological arguments of the kind common at the time. His other views belong to the history of Medicine. Alexander in Met. p. 26, 21 (R. P. 219). Arist. de An. Α, 2. 405 b 2 (R. P. 220). Hipp. Ref. i. 16 (R. P. 221). Till quite recently no fragment of Hippon was known to exist, but a single one has now been recovered from the Geneva Scholia on Homer. It is directed against the old assumption that the “waters under the earth” are an independent source of moisture, and runs thus:

The waters we drink are all from the sea; for if wells were deeper than the sea, then it would not, doubtless, be from the sea that we drink, for then the water would not be from the sea, but from some other source. But as it is, the sea is deeper than the waters, so all the waters that are above the sea come from it. R. P. 219 b. We observe here the universal assumption that water tends to rise from the earth, not to sink into it. Along with Hippon, Idaios of Himera may just be mentioned. We really know nothing of him except that he held air to be the primary substance. The fact that he was of Sicilian origin is, however, suggestive. Schol. Genav. p. 197, 19. Cf. Diels in Arch. iv. p. 653. The extract comes from the Ὁμηρικά of Krates of Mallos. Sext. adv. Math. ix. 360. II. DIOGENES OF APOLLONIA [Sidenote: Date.] 186. After discussing the three great representatives of the Milesian school, Theophrastos went on to say:

And Diogenes of Apollonia, too, who was almost the latest of those who gave themselves up to these studies, wrote most of his work in an eclectic fashion, agreeing in some points with Anaxagoras and in others with Leukippos. He, too, says that the primary substance of the universe is Air infinite and eternal, from which by condensation, rarefaction, and change of state, the form of everything else arises. R. P. 206 a. On this passage see Diels, “Leukippos und Diogenes von Apollonia” (Rhein. Mus. xlii. pp. 1 sqq.). Natorp’s view that the words are merely those of Simplicius (ib. xli. pp. 349 sqq.) can hardly be maintained. This passage shows that the Apolloniate was somewhat later in date than the statement in Laertios Diogenes that he was contemporary with Anaxagoras would lead us to suppose, and the fact that he is satirised in the Clouds of Aristophanes points in the same direction. Of his life we know next to nothing. He was the son of Apollothemis, and came from Apollonia in Crete. The Ionic dialect in which he wrote is no objection to this; it was the regular dialect for cosmological works.

Diog. ix. 57 (R. P. 206). The statement of Antisthenes, the writer of Successions, that he had “heard” Anaximenes is due to the usual confusion. He was doubtless, like Anaxagoras, “an associate of the philosophy of Anaximenes.” Cf. Chap. VI. § 122. Aristoph. Clouds, 227 sqq., where Sokrates speaks of “mixing his subtle thought with the kindred air,” and especially the words ἡ γῆ βίᾳ | ἕλκει πρὸς αὑτὴν τὴν ἱκμάδα τῆς φροντίδος. For the ἱκμάς, see Beare, p. 259. Cf. also Eur. Tro. 884, ὦ γῆς ὄχημα κἀπὶ γῆς ἕδραν ἔχων κ.τ.λ. Diog. ix. 57 (R. P. 206). Cf. Chap. VII. pp. 327 sqq. The fact that Diogenes was parodied in the Clouds suggests that he had found his way to Athens; and we have the excellent authority of Demetrios Phalereus for saying that the Athenians treated him in the usual way. He excited so great dislike as nearly to imperil his life. Diog. ix. 57, τοῦτόν φησιν ὁ Φαληρεὺς Δημήτριος ἐν τῇ Σωκράτους ἀπολογίᾳ διὰ μέγαν φθόνον μικροῦ κινδυνεῦσαι Ἀθήνησιν. Diels follows Volkmann in holding that this is a note on Anaxagoras which has been inserted in the wrong place. I do not think this is necessary, though it is certainly possible. [Sidenote: Writings.]

187. Simplicius affirms that Diogenes wrote several works, though he allows that only one survived till his own day, namely, the Περὶ φύσεως. This statement is based upon references in the surviving work itself, and is not to be lightly rejected. In particular, it is very credible that he wrote a tract Against the Sophists, that is to say, the pluralist cosmologists of the day. That he wrote a Meteorology and a book called The Nature of Man is also quite probable. This would be a physiological or medical treatise, and perhaps the famous fragment about the veins comes from it. Simpl. Phys. p. 151, 24 (R. P. 207 a). Simplicius says Πρὸς φυσιολόγους, but he adds that Diogenes called them σοφισταί, which is the older word. This is, so far, in favour of the genuineness of the work. Diels gives this as fr. 6 (Vors. p. 350). I have omitted it, as it really belongs to the history of Medicine. [Sidenote: The Fragments.] 188. The work of Diogenes seems to have been preserved in the Academy; practically all the fairly extensive fragments which we still have are derived from Simplicius. I give them as they are arranged by Diels:—

(1) In beginning any discourse, it seems to me that one should make one’s starting-point something indisputable, and one’s expression simple and dignified. R. P. 207. (2) My view is, to sum it all up, that all things are differentiations of the same thing, and are the same thing. And this is obvious; for, if the things which are now in this world—earth, and water, and air and fire, and the other things which we see existing in this world,—if any one of these things, I say, were different from any other, different, that is, by having a substance peculiar to itself; and if it were not the same thing that is often changed and differentiated, then things could not in any way mix with one another, nor could they do one another good or harm. Neither could a plant grow out of the earth, nor any animal nor anything else come into being unless things were composed in such a way as to be the same. But all these things arise from the same thing; they are differentiated and take different forms at different times, and return again to the same thing. R. P. 208.

(3) For it would not be possible for it to be divided as it is without intelligence, so as to keep the measures of all things, of winter and summer, of day and night, of rains and winds and fair weather. And any one who cares to reflect will find that everything else is disposed in the best possible manner. R. P. 210. (4) And, further, there are still the following great proofs. Men and all other animals live upon air by breathing it, and this is their soul and their intelligence, as will be clearly shown in this work; while, when this is taken away, they die, and their intelligence fails. R. P. 210.

(5) And my view is, that that which has intelligence is what men call air, and that all things have their course steered by it, and that it has power over all things. For this very thing I hold to be a god, and to reach everywhere, and to dispose everything, and to be in everything; and there is not anything which does not partake in it. Yet no single thing partakes in it just in the same way as another; but there are many modes both of air and of intelligence. For it undergoes many transformations, warmer and colder, drier and moister, more stable and in swifter motion, and it has many other differentiations in it, and an infinite number of colours and savours. And the soul of all living things is the same, namely, air warmer than that outside us and in which we are, but much colder than that near the sun. And this warmth is not alike in any two kinds of living creatures, nor, for the matter of that, in any two men; but it does not differ much, only so far as is compatible with their being alike. At the same time, it is not possible for any of the things which are differentiated to be exactly like one another till they all once more become the same.

(6) Since, then, differentiation is multiform, living creatures are multiform and many, and they are like one another neither in appearance nor in intelligence, because of the multitude of differentiations. At the same time, they all live, and see, and hear by the same thing, and they all have their intelligence from the same source. R. P. 211. (7) And this itself is an eternal and undying body, but of those things some come into being and some pass away. (8) But this, too, appears to me to be obvious, that it is both great, and mighty, and eternal, and undying, and of great knowledge. R. P. 209. The MSS. of Simplicius have ἔθος, not θεός; but I adopt Usener’s certain correction. It is confirmed by the statement of Theophrastos, that the air within us is “a small portion of the god” (de Sens. 42); and by Philodemos (Dox. p. 536), where we read that Diogenes praises Homer, τὸν ἀέρα γὰρ αὐτὸν Δία νομίζειν φησίν, ἐπειδὴ πᾶν εἰδέναι τὸν Δία λέγει (cf. Cic. Nat. D. i. 12, 29). The MSS. of Simplicius have τῷ δέ, but surely the Aldine τῶν δέ is right.

That the chief interest of Diogenes was a physiological one, is clear from his elaborate account of the veins, preserved by Aristotle. It is noticeable, too, that one of his arguments for the underlying unity of all substances is that without this it would be impossible to understand how one thing could do good or harm to another (fr. 2). In fact, the writing of Diogenes is essentially of the same character as a good deal of the pseudo-Hippokratean literature, and there is much to be said for the view that the writers of these curious tracts made use of him very much as they did of Anaxagoras and Herakleitos. Arist. Hist. An. Γ, 2. 511 b 30. See Weygoldt, “Zu Diogenes von Apollonia” (Arch. i. pp. 161 sqq.). Hippokrates himself represented just the opposite tendency to that of those writers. His great achievement was the separation of medicine from philosophy, a separation most beneficial to both (Celsus, i. pr.). This is why the Hippokratean corpus contains some works in which the “sophists” are denounced and others in which their writings are pillaged. To the latter class belong the Περὶ διαίτης and the Περὶ φυσῶν; to the former, especially the Περὶ ἀρχαίης ἰατρικῆς. [Sidenote: Cosmology.]

189. Like Anaximenes, Diogenes regarded Air as the primary substance; but we see from his arguments that he lived at a time when other views had become prevalent. He speaks clearly of the four Empedoklean elements (fr. 2), and he is careful to attribute to Air the attributes of Nous as taught by Anaxagoras (fr. 4). The doxographical tradition as to his cosmological views is fairly preserved:— Diogenes of Apollonia makes air the element, and holds that all things are in motion, and that there are innumerable worlds. And he describes the origin of the world thus. When the All moves and becomes rare in one place and dense in another, where the dense met together it formed a mass, and then the other things arose in the same way, the lightest parts occupying the highest position and producing the sun. [Plut.] Strom. fr. 12 (R. P. 215). Nothing arises from what is not nor passes away into what is not. The earth is round, poised in the middle, having received its shape through the revolution proceeding from the warm and its solidification from the cold. Diog. ix. 57 (R. P. 215).

The heavenly bodies were like pumice-stone. He thinks they are the breathing-holes of the world, and that they are red-hot. Aet. ii. 13, 5 = Stob. i. 508 (R. P. 215). The sun was like pumice-stone, and into it the rays from the aether fix themselves. Aet. ii. 20, 10. The moon was a pumice-like conflagration. Ib. ii. 25, 10. Along with the visible heavenly bodies revolve invisible stones, which for that very reason are nameless; but they often fall and are extinguished on the earth like the stone star which fell down flaming at Aigospotamos. Ib. ii. 13, 9. See Chap. VI. p. 292, n. 657.