Early Greek Philosophy (pre-Socratic fragments and testimony)

See Rohde, Rh. Mus. xxvi. p. 565, n. 1. The narrative in the text (Iambl. V. Pyth. 250; R. P. 59 b) goes back to Aristoxenos and Dikaiarchos (R. P. 59 a). There is no reason to suppose that their view of Pythagoras has vitiated their account of what must have been a perfectly well-known piece of history. According to the later story, Pythagoras himself was burned to death in the house of Milo, along with his disciples. This is merely a dramatic compression of the whole series of events into a single scene; we have seen that Pythagoras died at Metapontion before the final catastrophe. The valuable reference in Polybios ii. 39 (R. P. 59) to the burning of Pythagorean συνέδρια certainly implies that the disturbances went on for a very considerable time. This account has all the air of being historical. The mention of Lysis proves, however, that those events were spread over more than one generation. The coup d’état of Kroton can hardly have occurred before 450 B.C., if the teacher of Epameinondas escaped from it, and it may well have been even later. But it must have been before 410 B.C. that the Pythagoreans left Rhegion for Hellas; Philolaos was certainly at Thebes about that time. Plato, Phd. 61 d 7, e 7.

The political power of the Pythagoreans as an Order was now gone for ever, though we shall see that some of them returned to Italy at a later date. In exile they seem to have dropped the merely magical and superstitious parts of their system, and this enabled them to take their place as one of the scientific schools of Hellas. [Sidenote: Want of evidence as to the teaching of Pythagoras.]

41. Of the opinions of Pythagoras we know even less than of his life. Aristotle clearly knew nothing for certain of ethical or physical doctrines going back to the founder of the Society himself. Aristoxenos only gave a string of moral precepts. Dikaiarchos is quoted by Porphyry as asserting that hardly anything of what Pythagoras taught his disciples was known except the doctrine of transmigration, the periodic cycle, and the kinship of all living creatures. The fact is, that, like all teachers who introduce a new way of living rather than a new view of the world, Pythagoras preferred oral instruction to the dissemination of his opinions by writing, and it was not till Alexandrian times that any one ventured to forge books in his name. The writings ascribed to the earliest Pythagoreans were also forgeries of the same period. The early history of Pythagoreanism is, therefore, wholly conjectural; but we may still make an attempt to understand, in a very general way, what the position of Pythagoras in the history of Greek thought must have been.

When discussing the Pythagorean system, Aristotle always refers it to “the Pythagoreans,” not to Pythagoras himself. That this was intentional seems to be proved by the phrase οἱ καλούμενοι Πυθαγόρειοι, which occurs more than once (e.g. Met. Α, 5. 985 b 23; de Caelo, Β, 13. 293 a 20). Pythagoras himself is only thrice mentioned in the whole Aristotelian corpus, and in only one of these places (M. Mor. 1182 a 11) is any philosophical doctrine ascribed to him. We are told there that he was the first to discuss the subject of goodness, and that he made the mistake of identifying its various forms with numbers. But this is just one of the things which prove the late date of the Magna Moralia. Aristotle himself is quite clear that what he knew as the Pythagorean system belonged in the main to the days of Empedokles, Anaxagoras, and Leukippos; for, after mentioning these, he goes on to describe the Pythagoreans as “contemporary with and earlier than them” (ἐν δὲ τούτοις καὶ πρὸ τούτων, Met. Α, 5. 985 b 23). The fragments of the Πυθαγορικαὶ ἀποφάσεις of Aristoxenos are given by Diels, Vors. pp. 282 sqq. V. Pyth. 19 (R. P. 55).

See Diels, Dox. p. 150; and “Ein gefälschtes Pythagorasbuch” (Arch. iii. pp. 451 sqq.). Cf. also Bernays, Die Heraklitischen Briefe, n. 1. [Sidenote: Transmigration.]

42. In the first place, then, there can be no doubt that he really taught the doctrine of transmigration. The story told by the Greeks of the Hellespont and Pontos as to his relations with Salmoxis could never have gained currency by the time of Herodotos if he had not been known as a man who taught strange views of the life after death. Now the doctrine of transmigration is most easily to be explained as a development of the savage belief in the kinship of men and beasts, as all alike children of the Earth, a view which Dikaiarchos said Pythagoras certainly held. Further, among savages, this belief is commonly associated with a system of taboos on certain kinds of food, and the Pythagorean rule is best known for its prescription of similar forms of abstinence. This in itself goes far to show that it originated in the same ideas, and we have seen that the revival of these would be quite natural in connexion with the foundation of a new religious society. There is a further consideration which tells strongly in the same direction. In India we have a precisely similar doctrine, and yet it is not possible to assume any actual borrowing of Indian ideas at this date. The only explanation which will account for the facts is that the two systems were independently evolved from the same primitive ideas. These are found in many parts of the world; but it seems to have been only in India and in Greece that they were developed into an elaborate doctrine.

The proper Greek term for this is παλιγγενεσία, and the inaccurate μετεμψύχωσις only occurs in late writers. Hippolytos and Clement of Alexandria say μετενσωμάτωσις, which is accurate but cumbrous. See Rohde, Psyche, p. 428, n. 2. On the significance of this, see above, p. 93. Dieterich, “Mutter Erde” (Archiv für Religionswissenschaft, viii. pp. 29 and 47). [Sidenote: Abstinence.]

43. It has indeed been doubted whether we have a right to accept what we are told by such late writers as Porphyry on the subject of Pythagorean abstinence. Aristoxenos, whom we have admitted to be one of our earliest witnesses, may be cited to prove that the original Pythagoreans knew nothing of these restrictions on the use of animal flesh and beans. He undoubtedly said that Pythagoras did not abstain from animal flesh in general, but only from that of the ploughing ox and the ram. He also said that Pythagoras preferred beans to every other vegetable, as being the most laxative, and that he was partial to sucking-pigs and tender kids. Aristoxenos, however, is a witness who very often breaks down under cross-examination, and the palpable exaggeration of these statements shows that he is endeavouring to combat a belief which existed in his own day. We are therefore able to show, out of his own mouth, that the tradition which made the Pythagoreans abstain from animal flesh and beans goes back to a time long before there were any Neopythagoreans interested in upholding it. Still, it may be asked what motive Aristoxenos could have had for denying the common belief? The answer is simple and instructive. He had been the friend of the last of the Pythagoreans; and, in their time, the merely superstitious part of Pythagoreanism had been dropped, except by some zealots whom the heads of the Society refused to acknowledge. That is why he represents Pythagoras himself in so different a light from both the older and the later traditions; it is because he gives us the view of the more enlightened sect of the Order. Those who clung faithfully to the old practices were now regarded as heretics, and all manner of theories were set on foot to account for their existence. It was related, for instance, that they descended from one of the “Akousmatics,” who had never been initiated into the deeper mysteries of the “Mathematicians.” All this, however, is pure invention. The satire of the poets of the Middle Comedy proves clearly enough that, even though the friends of Aristoxenos did not practise abstinence, there were plenty of people in the fourth century, calling themselves followers of Pythagoras, who did. History has not been kind to the Akousmatics, but they never wholly died out. The names of Diodoros of Aspendos and Nigidius Figulus help to bridge the gulf between them and Apollonios of Tyana.

Aristoxenos ap. Diog. viii. 20, πάντα μὲν τὰ ἄλλα συγχωρεῖν αὐτὸν ἐσθίειν ἔμψυχα, μόνον δ’ ἀπέχεσθαι βοὸς ἀροτῆρος καὶ κριοῦ. Aristoxenos ap. Gell. iv. 11, 5, Πυθαγόρας δὲ τῶν ὀσπρίων μάλιστα τὸν κύαμον ἐδοκίμασεν· λειαντικόν τε γὰρ εἶναι καὶ διαχωρητικόν· διὸ καὶ μάλιστα κέχρηται αὐτῷ; ib. 6, “porculis quoque minusculis et haedis tenerioribus victitasse, idem Aristoxenus refert.” It is, of course, possible that Aristoxenos may be right about the taboo on beans. We know that it was Orphic, and it may have been transferred to the Pythagoreans by mistake. That, however, would not affect the general conclusion that at least some Pythagoreans practised abstinence from various kinds of food, which is all that is required. The sect of the “Akousmatics” was said to descend from Hippasos (Iambl. V. Pyth. 81; R. P. 56). Now Hippasos was the author of a μυστικὸς λόγος (Diog. viii. 7; R. P. 56 c), that is to say, of a superstitious ceremonial or ritual handbook, probably containing Akousmata like those we are about to consider; for we are told that it was written ἐπὶ διαβολῇ Πυθαγόρου.

Diels has collected these fragments in a convenient form (Vors. pp. 291 sqq.). For our purpose the most important passages are Antiphanes, fr. 135, Kock, ὥσπερ Πυθαγορίζων ἐσθίει | ἔμψυχον οὐδέν; Alexis, fr. 220, οἱ Πυθαγορίζοντες γάρ, ὡς ἀκούομεν, | οὔτ’ ὄψον ἐσθίουσιν οὔτ’ ἄλλ’ οὐδὲ ἓν | ἔμψυχον; fr. 196 (from the Πυθαγορίζουσα), ἡ δ’ ἑστίασις ἰσχάδες καὶ στέμφυλα | καὶ τυρὸς ἔσται· ταῦτα γὰρ θύειν νόμος | τοῖς Πυθαγορείοις; Aristophon, fr. 9 (from the Πυθαγοριστής), πρὸς τῶν θεῶν οἰόμεθα τοὺς πάλαι ποτέ, | τοὺς Πυθαγοριστὰς γενομένους ὄντως ῥυπᾶν | ἑκόντας ἢ φορεῖν τριβῶνας ἡδέως; Mnesimachos, fr. 1, ὡς Πυθαγοριστὶ θύομεν τῷ Λοξίᾳ | ἔμψυχον οὐδὲν ἐσθίοντες παντελῶς. See also Theokritos, xiv. 5, τοιοῦτος καὶ πρᾶν τις ἀφίκετο Πυθαγορικτάς, | ὠχρὸς κἀνυποδητός· Ἀθηναῖος δ’ ἔφατ’ ἦμεν.

We know, then, that Pythagoras taught the kinship of beasts and men, and we infer that his rule of abstinence from flesh was based, not upon humanitarian or ascetic grounds, but on taboo. This is strikingly confirmed by a fact which we are told in Porphyry’s Defence of Abstinence. The statement in question does not indeed go back to Theophrastos, as so much of Porphyry’s tract certainly does; but it is, in all probability, due to Herakleides of Pontos, and is to the effect that, though the Pythagoreans did as a rule abstain from flesh, they nevertheless ate it when they sacrificed to the gods. Now, among savage peoples, we often find that the sacred animal is slain and eaten sacramentally by its kinsmen on certain solemn occasions, though in ordinary circumstances this would be the greatest of all impieties. Here, again, we have to do with a very primitive belief; and we need not therefore attach any weight to the denials of Aristoxenos.

See Bernays, Theophrastos’ Schrift über Frömmigkeit. Porphyry’s tract, Περὶ ἀποχῆς ἐμψύχων, was doubtless saved from the general destruction of his writings by its conformity to the ascetic tendencies of the age. Even St. Jerome made constant use of it in his polemic against Iovianus, though he is careful not to mention Porphyry’s name (Theophr. Schr. n. 2). The tract is addressed to Castricius Firmus, the disciple and friend of Plotinos, who had fallen away from the strict vegetarianism of the Pythagoreans. The passage occurs De Abst. p. 58, 25 Nauck: ἱστοροῦσι δέ τινες καὶ αὐτοὺς ἅπτεσθαι τῶν ἐμψύχων τοὺς Πυθαγορείους, ὅτε θύοιεν θεοῖς. The part of the work from which this is taken comes from one Clodius, on whom see Bernay, Theophr. Schr. p. 11. He was probably the rhetorician Sextus Clodius, and a contemporary of Cicero. Bernays has shown that he made use of the work of Herakleides of Pontos (ib. n. 19). On “mystic sacrifice” generally, see Robertson Smith, Rel. Sem. i. p. 276.

Porphyry (V. Pyth. c 15) has preserved a tradition to the effect that Pythagoras recommended a flesh diet for athletes (Milo?). This story must have originated at the same time as those related by Aristoxenos, and in a similar way. In fact, Bernays has shown that it comes from Herakleides of Pontos (Theophr. Schr. n. 8). Iamblichos (V. Pyth. 5. 25) and others (Diog. viii. 13, 47) got out of this by supposing it referred to a gymnast of the same name. We see here very distinctly how the Neoplatonists for their own ends endeavoured to go back to the original form of the Pythagorean legend, and to explain away the fourth century reconstruction. [Sidenote: Akousmata.]

44. We shall now know what to think of the various Pythagorean rules and precepts which have come down to us. These are of two kinds, and have very different sources. Some of them, derived from the collection of Aristoxenos, and for the most part preserved by Iamblichos, are mere precepts of morality. They do not pretend to go back to Pythagoras himself; they are only the sayings which the last generation of “Mathematicians” heard from their predecessors. The second class is of a very different nature, and the sayings which belong to it are called Akousmata, which points to their being the property of that sect of Pythagoreans which had faithfully preserved the old customs. Later writers interpret them as “symbols” of moral truth; but their interpretations are extremely far-fetched, and it does not require a very practised eye to see that they are genuine taboos of a thoroughly primitive type. I give a few examples in order that the reader may judge what the famous Pythagorean rule of life was really like.

1. To abstain from beans. 2. Not to pick up what has fallen. 3. Not to touch a white cock. 4. Not to break bread. 5. Not to step over a crossbar. 6. Not to stir the fire with iron. 7. Not to eat from a whole loaf. 8. Not to pluck a garland. 9. Not to sit on a quart measure. 10. Not to eat the heart. 11. Not to walk on highways. 12. Not to let swallows share one’s roof. 13. When the pot is taken off the fire, not to leave the mark of it in the ashes, but to stir them together. 14. Do not look in a mirror beside a light. 15. When you rise from the bedclothes, roll them together and smooth out the impress of the body. For these see Diels, Vors. pp. 282 sqq. There is an excellent collection of Ἀκούσματα καὶ σύμβολα in Diels, Vors. pp. 279 sqq., where the authorities will be found. It is impossible to discuss these in detail here, but students of folklore will see at once to what order of ideas they belong.

It would be easy to multiply proofs of the close connexion between Pythagoreanism and primitive modes of thought, but what has been said is really sufficient for our purpose. The kinship of men and beasts, the abstinence from flesh, and the doctrine of transmigration all hang together and form a perfectly intelligible whole from the point of view which has been indicated. [Sidenote: Pythagoras as a man of science.]

45. Were this all, we should be tempted to delete the name of Pythagoras from the history of philosophy altogether, and relegate him to the class of “medicine-men” (γόητες) along with Epimenides and Onomakritos. This, however, would be quite wrong. As we shall see, the Pythagorean Society became one of the chief scientific schools of Hellas, and it is certain that Pythagorean science as well as Pythagorean religion originated with the master himself. Herakleitos, who is not partial to him, says that Pythagoras had pursued scientific investigation further than other men, though he also says that he turned his much learning into an art of mischief. Herodotos called Pythagoras “by no means the weakest sophist of the Hellenes,” a title which at this date does not imply the slightest disparagement. Aristotle even said that Pythagoras first busied himself with mathematics and numbers, and that it was later on he attached himself to the miracle-mongering of Pherekydes. Is it possible for us to trace any connexion between these two sides of his activity?

Herakl. fr. 17 (R. P. 31 a). The word ἱστορίη is in itself quite general. What it chiefly means here we see from a valuable notice preserved by Iamblichos, V. Pyth. 89, ἐκαλεῖτο δὲ ἡ γεωμετρία πρὸς Πυθαγόρου ἱστορία. Tannery’s interpretation of this statement is based on a misunderstanding, and need not be discussed here. Herod. iv. 95. Arist. Περὶ τῶν Πυθαγορείων, fr. 186, 1510 a 39, Πυθαγόρας Μνησάρχου υἱὸς τὸ μὲν πρῶτον διεπονεῖτο περὶ τὰ μαθήματα καὶ τοὺς ἀριθμούς, ὕστερον δέ ποτε καὶ τῆς Φερεκύδου τερατοποιΐας οὐκ ἀπέστη.

We have seen that the aim of the Orphic and other Orgia was to obtain release from the “wheel of birth” by means of “purifications,” which were generally of a very primitive type. The new thing in the Society founded by Pythagoras seems to have been that, while it admitted all these half-savage customs, it at the same time suggested a more exalted idea of what “purification” really was. Aristoxenos tells us that the Pythagoreans employed music to purge the soul as they used medicine to purge the body, and it is abundantly clear that Aristotle’s famous theory of κάθαρσις is derived from Pythagorean sources. Such methods of purifying the soul were familiar in the Orgia of the Korybantes, and will serve to explain the Pythagorean interest in Harmonics. But there is more than this. If we can trust Herakleides so far, it was Pythagoras who first distinguished the “three lives,” the Theoretic, the Practical, and the Apolaustic, which Aristotle made use of in the Ethics. The general theory of these lives is clear, and it is impossible to doubt that in substance it belongs to the very beginning of the school. It is to this effect. We are strangers in this world, and the body is the tomb of the soul, and yet we must not seek to escape by self-murder; for we are the chattels of God who is our herdsman, and without his command we have no right to make our escape. In this life, there are three kinds of men, just as there are three sorts of people who come to the Olympic Games. The lowest class is made up of those who come to buy and sell, and next above them are those who come to compete. Best of all, however, are those who come simply to look on (θεωρεῖν). The greatest purification of all is, therefore, disinterested science, and it is the man who devotes himself to that, the true philosopher, who has most effectually released himself from the “wheel of birth.” It would be rash to say that Pythagoras expressed himself exactly in this manner; but all these ideas are genuinely Pythagorean, and it is only in some such way that we can bridge the gulf which separates Pythagoras the man of science from Pythagoras the religious teacher. We must now endeavour to discover how much of the later Pythagorean science may reasonably be ascribed to Pythagoras himself.

Its immediate source is to be found in Plato, Laws, 790 d 2 sqq., where the Korybantic rites are adduced as an instance. For a full account see Rohde, Psyche, p. 336, n. 2. Plato gives this as the Pythagorean view in Phd. 62 b, for the interpretation of which cf. Espinas in Arch. viii. pp. 449 sqq. Plato distinctly implies that it was not merely the theory of Philolaos, but something older.

See Döring in Arch. v. pp. 505 sqq. There seems to be a reference to the theory of the “three lives” in Herakleitos, fr. 111. It was apparently taught in the Pythagorean Society of Phleious; for Herakleides made Pythagoras expound it in a conversation with the tyrant of Phleious (Cic. Tusc. v. 3; Diog. pr. 12, viii. 8), and it is developed by Plato in a dialogue which is, as it were, dedicated to Echekrates. If it should be thought that this is interpreting Pythagoras too much in the light of Schopenhauer, it may be answered that even the Orphics came very near such a theory. The soul must not drink of Lethe, but go past it and drink of the water of Memory, before it can claim to become one of the heroes. This has obvious points of contact with Plato’s ἀνάμνησις, and the only question is how much of the Phaedo we are to ascribe to Pythagorean sources. A great deal, I suspect. See Prof. Stewart’s Myths of Plato, pp. 152 sqq. [Sidenote: Arithmetic.]

46. In his treatise on Arithmetic, Aristoxenos said that Pythagoras was the first to carry that study beyond the needs of commerce, and his statement is confirmed by everything we otherwise know. By the end of the fifth century B.C., we find that there is a widespread interest in such subjects and that these are studied for their own sake. Now this new interest cannot have been wholly the work of a school; it must have originated with some great man, and there is no one but Pythagoras to whom we can refer it. As, however, he wrote nothing, we have no sure means of distinguishing his own teaching from that of his followers in the next generation or two. All we can safely say is that, the more primitive any Pythagorean doctrine appears, the more likely it is to be that of Pythagoras himself, and all the more so if it can be shown to have points of contact with views which we know to have been held in his own time or shortly before it. In particular, when we find the later Pythagoreans teaching things that were already something of an anachronism in their own day, we may be reasonably sure that we are dealing with survivals which only the authority of the master’s name could have preserved. Some of these must be mentioned at once, though the developed system belongs to a later part of our story. It is only by separating its earliest form from its later that the true place of Pythagoreanism in Greek thought can be made clear, though we must always remember that no one can now pretend to draw the line between its successive stages with any certainty.

Stob. i. p. 20, 1, ἐκ τῶν Ἀριστοξένου περὶ ἀριθμητικῆς, Τὴν δὲ περὶ τοὺς ἀριθμοὺς πραγματείαν μάλιστα πάντων τιμῆσαι δοκεῖ Πυθαγόρας καὶ προαγαγεῖν ἐπὶ τὸ πρόσθεν ἀπαγαγὼν ἀπὸ τῆς τῶν ἐμπόρων χρείας. [Sidenote: The figures.] 47. Now one of the most remarkable statements that we have about Pythagoreanism is what we are told of Eurytos on the unimpeachable authority of Archytas. Eurytos was the disciple of Philolaos, and Aristoxenos expressly mentioned him along with Philolaos as having taught the last of the Pythagoreans, the men with whom he himself was personally acquainted. He therefore belongs to the beginning of the fourth century B.C., by which time the Pythagorean system was fully developed, and he was no eccentric enthusiast, but one of the foremost men in the school. We are told of him, then, that he used to give the number of all sorts of things, such as horses and men, and that he demonstrated these by arranging pebbles in a certain way. It is to be noted further that Aristotle compares his procedure to that of those who bring numbers into figures like the triangle and the square.

Apart from the story in Iamblichos (V. Pyth. 148) that Eurytos heard the voice of Philolaos from the grave after he had been many years dead, it is to be noticed that he is mentioned after him in the statement of Aristoxenos referred to (Diog. viii. 46; R. P. 62). Arist. Met. Ν, 5. 1092 b 8 (R. P. 76 a). Aristotle does not quote the authority of Archytas here, but the source of his statement is made quite clear by Theophr. Met. p. vi. a 19 (Usener), τοῦτο γὰρ (sc. τὸ μὴ μέχρι του προελθόντα παύεσθαι) τελέου καὶ φρονοῦντος, ὅπερ Ἀρχύτας ποτ’ ἔφη ποιεῖν Εὔρυτον διατιθέντα τινὰς ψήφους· λέγειν γὰρ ὡς ὅδε μὲν ἀνθρώπου ὁ ἀριθμός, ὅδε δὲ ἵππου, ὅδε δ’ ἄλλου τινὸς τυγχάνει.

Now these statements, and especially the remark of Aristotle last quoted, seem to imply the existence at this date, and earlier, of a numerical symbolism quite distinct from the alphabetical notation on the one hand and from the Euclidean representation of numbers by lines on the other. The former was inconvenient for arithmetical purposes, just because the zero was one of the few things the Greeks did not invent, and they were therefore unable to develop a really serviceable numerical symbolism based on position. The latter, as will appear shortly, is intimately bound up with that absorption of arithmetic by geometry, which is at least as old as Plato, but cannot be primitive. It seems rather that numbers were represented by dots arranged in symmetrical and easily recognised patterns, of which the marking of dice or dominoes gives us the best idea. And these markings are, in fact, the best proof that this is a genuinely primitive method of indicating numbers; for they are of unknown antiquity, and go back to the time when men could only count by arranging numbers in such patterns, each of which became, as it were, a fresh unit. This way of counting may well be as old as reckoning with the fingers, or even older.

Arithmetic is older than geometry, and was much more advanced in Egypt, though still in the form which the Greeks called λογιστική rather than as ἀριθμητική proper. Even Plato puts Arithmetic before Geometry in the Republic in deference to the tradition. His own theory of number, however, suggested the inversion of this order which we find carried out in Euclid. It is, therefore, very significant that we do not find any adequate account of what Aristotle can have meant by “those who bring numbers into figures like the triangle and the square” till we come to certain late writers who called themselves Pythagoreans, and revived the study of arithmetic as a science independent of geometry. These men not only abandoned the linear symbolism of Euclid, but also regarded the alphabetical notation, which they did use, as something conventional, and inadequate to represent the true nature of number. Nikomachos of Gerasa says expressly that the letters used to represent numbers are only significant by human usage and convention. The most natural way would be to represent linear or prime numbers by a row of units, polygonal numbers by units arranged so as to mark out the various plane figures, and solid numbers by units disposed in pyramids and so forth. He therefore gives us figures like this:—

α α α α α α α ααα α α α α α α α α α α α α ααα α α α α α Now it ought to be obvious that this is no innovation, but, like so many things in Neopythagoreanism, a reversion to primitive usage. Of course the employment of the letter alpha to represent the units is derived from the conventional notation; but otherwise we are clearly in presence of something which belongs to the very earliest stage of the science—something, in fact, which gives the only possible clue to the meaning of Aristotle’s remark, and to what we are told of the method of Eurytos. Nikomachos of Gerasa, Introd. Arithm. p. 83, 12, Hoche, Πρότερον δὲ ἐπιγνωστέον ὅτι ἕκαστον γράμμα ᾧ σημειούμεθα ἀριθμόν, οἷον τὸ ι, ᾧ τὸ δέκα, τὸ κ, ᾧ τὰ εἴκοσι, τὸ ω, ᾧ τὰ ὀκτακόσια, νόμῳ καὶ συνθήματι ἀνθρωπίνῳ, ἀλλ’ οὐ φύσει σημαντικόν, ἐστι τοῦ ἀριθμοῦ, κ.τ.λ. The same symbolism is used by Theo, Expositio, pp. 31 sqq. Cf. also Iambl. Introd. p. 56, 27, Pistelli, ἰστέον γὰρ ὡς τὸ παλαιὸν φυσικώτερον οἱ πρόσθεν ἐσημαίνοντο τὰς τοῦ ἀριθμοῦ ποσότητας, ἀλλ’ οὐχ ὥσπερ οἱ νῦν συμβολικῶς. [Sidenote: Triangular, square, and oblong numbers.]

48. This is still further confirmed by the tradition which represents the great revelation made by Pythagoras to mankind as having been precisely a figure of this kind, namely the tetraktys, by which the Pythagoreans used to swear, and we have no less an authority than Speusippos for holding that the whole theory which it implies was genuinely Pythagorean. In later days there were many kinds of tetraktys, but the original one, that by which the Pythagoreans swore, was the “tetraktys of the dekad.” It was a figure like this— and represented the number ten as the triangle of four. In other words, it showed at a glance that 1 + 2 + 3 + 4 = 10. Speusippos tells us of several properties which the Pythagoreans discovered in the dekad. It is, for instance, the first number that has in it an equal number of prime and composite numbers. How much of this goes back to Pythagoras himself, we cannot tell; but we are probably justified in referring to him the conclusion that it is “according to nature” that all Hellenes and barbarians count up to ten and then begin over again.

Cf. the formula Οὐ μὰ τὸν ἁμετέρᾳ γενεᾷ παραδόντα τετρακτύν, which is all the more likely to be old that it is put into the mouth of Pythagoras by the forger of the Χρυσᾶ ἔπη, thus making him swear by himself! See Diels, Arch. iii. p. 457. The Doric dialect shows, however, that it belongs to the later generations of the school. Speusippos wrote a work on the Pythagorean numbers, based chiefly on Philolaos, and a considerable fragment of it is preserved in the Theologumena Arithmetica. It will be found in Diels, Vorsokratiker, p. 235, 15, and is discussed by Tannery, Science hellène, pp. 374 sqq. For these see Theon, Expositio, pp. 93 sqq. Hiller. The τετρακτύς used by Plato in the Timaeus is the second described by Theon (Exp. p. 94, 10 sqq.). It is no doubt Pythagorean, but hardly as old as Pythagoras. It is obvious that the tetraktys may be indefinitely extended so as to exhibit the sums of the series of successive numbers in a graphic form, and these sums are accordingly called “triangular numbers.”

For similar reasons, the sums of the series of successive odd numbers are called “square numbers,” and those of successive even numbers “oblong.” If odd numbers are added to the unit in the form of gnomons, the result is always a similar figure, namely a square, while, if even numbers are added, we get a series of rectangles, as shown by the figure:— Square Numbers. Oblong Numbers. ─────────────┐ ───────────────┐ • • •  │ • • • • │ ───────┐ │ ───────────┐ │ • • │ • │ • • • │ • │ ──┐ │ │ ──────┐ │ │ • │ • │ • │ • • │ • │ • │ It is clear, then, that we are entitled to refer the study of sums of series to Pythagoras himself; but whether he went beyond the oblong, and studied pyramidal or cubic numbers, we cannot say.

Cf. Milhaud, Philosophes géomètres, pp. 115 sqq. Aristotle puts the matter thus (Phys. Γ, 4. 203 a 13): περιτιθεμένων γὰρ τῶν γνωμόνων περὶ τὸ ἓν καὶ χωρὶς ὁτὲ μὲν ἄλλο ἀεὶ γίγνεσθαι τὸ εἶδος, ὁτὲ δὲ ἕν. This is more clearly stated by Ps.-Plut. (Stob. i. p. 22, 16), Ἔτι δὲ τῇ μονάδι τῶν ἐφεξῆς περισσῶν περιτιθεμένων ὁ γινόμενος ἀεὶ τετράγωνός ἐστι· τῶν δὲ ἀρτίων ὁμοίως περιτιθεμένων ἑτερομήκεις καὶ ἄνισοι πάντες ἀποβαίνουσιν, ἴσως δὲ ἰσάκις οὐδείς. I cannot feel satisfied with any of the explanations which have been given of the words καὶ χωρίς in the Aristotelian passage (see Zeller, p. 351, n. 2), and I would therefore suggest ταῖς χώραις comparing Boutheros (Stob. i. p. 19, 9), who says, according to the MS. reading, Καὶ ὁ μὲν (ὁ περισσός), ὁπόταν γεννῶνται ἀνὰ λόγον καὶ πρὸς μονάδας, ταῖς αὑτοῦ χώραις καταλαμβάνει τοὺς ταῖς γραμμαῖς περιεχομένους (sc. ἀριθμούς). In the fragment referred to above (p. 113, n. 236), Speusippos speaks of four as the first pyramidal number; but this is taken from Philolaos, so we cannot safely ascribe it to Pythagoras. [Sidenote: Geometry and harmonics.]

49. It is easy to see how this way of representing numbers would suggest problems of a geometrical nature. The dots which stand for the pebbles are regularly called “boundary-stones” (ὅροι, termini, “terms”), and the area which they occupy, or rather mark out, is the “field” (χώρα). This is evidently a very early way of speaking, and may therefore be referred to Pythagoras himself. Now it must have struck him that “fields” could be compared as well as numbers, and it is even likely that he knew the rough methods of doing this which were traditional in Egypt, though certainly these would fail to satisfy him. Once more the tradition is singularly helpful in suggesting the direction that his thoughts must have taken. He knew, of course, the use of the triangle 3, 4, 5 in constructing right angles. We have seen (p. 24) that it was familiar in the East from a very early date, and that Thales introduced it to the Hellenes, if they did not know it already. In later writers it is actually called the “Pythagorean triangle.” Now the Pythagorean proposition par excellence is just that, in a right-angled triangle, the square on the hypotenuse is equal to the squares on the other two sides, and the so-called Pythagorean triangle is the application of its converse to a particular case. The very name “hypotenuse” affords strong confirmation of the intimate connexion between the two things. It means literally “the cord stretching over against,” and this is surely just the rope of the “harpedonapt.” An early tradition says that Pythagoras sacrificed an ox when he discovered the proof of this proposition, and indeed it was the real foundation of scientific mathematics.

We have ὅροι of a series (ἔκθεσις), then of a proportion, and in later times of a syllogism. The signs :, ::, and ∴ are a survival of the original use. The term χώρα is often used by the later Pythagoreans, though Attic usage required χωρίον for a rectangle. The spaces between the γραμμαί of the abacus and the chess-board were also called χῶραι. In his commentary on Euclid i. 44, Proclus tells us on the authority of Eudemos that the παραβολή, ἔλλειψις, and ὑπερβολή of χωρία were Pythagorean inventions. For an account of these and the subsequent application of the terms in Conic Sections, see Milhaud, Philosophes géomètres, pp. 81 sqq. The verb ὑποτείνειν is, of course, used intransitively. The explanation suggested in the text seems to me much simpler than that of Max C. P. Schmidt (Kulturhistorische Beiträge, Heft i. pp. 64 sqq.). He explains the hypotenuse as the longest string in a triangular harp; but my view seems more in accordance with analogy. So ἡ κάθετος is, literally, a plumb-line. The statement comes from Eudemos; for it is found in Proclus’s commentary on Euclid i. 47. Whether historical or not, it is no Neopythagorean fancy. [Sidenote: Incommensurability.]

50. One great disappointment, however, awaited Pythagoras. It follows at once from the Pythagorean proposition that the square on the diagonal of a square is double the square on its side, and this ought surely to be capable of numerical expression. As a matter of fact, however, there is no square number which can be divided into two equal square numbers, and so the problem cannot be solved. In this sense, it is doubtless true that Pythagoras discovered the incommensurability of the diagonal and the side of a square, and the proof mentioned by Aristotle, namely, that, if they were commensurable, we should have to say that an even number was equal to an odd number, is distinctly Pythagorean in character. However that may be, it is certain that Pythagoras did not care to pursue the subject any further. He had, as it were, stumbled on the fact that the square root of two is a surd, but we know that it was left for Plato’s friends, Theodoros of Kyrene and Theaitetos, to give a complete theory of the matter. The fact is that the discovery of the Pythagorean proposition, by giving birth to geometry, had really superseded the old view of quantity as a sum of units; but it was not till Plato’s time that the full consequences of this were seen. For the present, the incommensurability of the diagonal and the square remained, as has been said, a “scandalous exception.” Our tradition says that Hippasos of Metapontion was drowned at sea for revealing this skeleton in the cupboard.

Arist. An. Pr. Α, 23. 41 a 26, ὅτι ἀσύμμετρος ἡ διάμετρος διὰ τὸ γίγνεσθαι τὰ περιττὰ ἴσα τοῖς ἀρτίοις συμμέτρου τεθείσης. The proofs given at the end of Euclid’s Tenth Book (vol. iii. pp. 408 sqq., Heiberg) turn on this very point. They are not Euclidean, and may be substantially Pythagorean. Cf. Milhaud, Philosophes géomètres, p. 94. Plato, Theaet. 147 d 3 sqq. How novel these consequences were, is shown by the fact that in Laws, 819 d 5, the Athenian Stranger says that he had only realised them late in life. This version of the tradition is mentioned in Iamblichos, V. Pyth. 247, and looks older than the other, which we shall come to later (§ 148). Hippasos is the enfant terrible of Pythagoreanism, and the traditions about him are full of instruction. [Sidenote: Proportion and harmony.]

51. These last considerations show that, while it is quite safe to attribute the substance of the First Book of Euclid to Pythagoras, the arithmetic of Books VII.-IX., and the “geometrical algebra” of Book II. are certainly not his. They operate with lines or with areas instead of with units, and the relations which they establish therefore hold good whether they are capable of numerical expression or not. That is doubtless why arithmetic is not treated in Euclid till after plane geometry, a complete inversion of the original order. For the same reason, the doctrine of proportion which we find in Euclid cannot be Pythagorean, and is indeed the work of Eudoxos. Yet it is clear that the early Pythagoreans, and probably Pythagoras himself, studied proportion in their own way, and that the three “medieties” in particular go back to the founder, especially as the most complicated of them, the “harmonic,” stands in close relation to his discovery of the octave. If we take the harmonic proportion 12 : 8 : 6, we find that 12 : 6 is the octave, 12 : 8 the fifth, and 8 : 6 the fourth, and it can hardly be doubted that it was Pythagoras himself who discovered these intervals. The stories which have come down to us about his observing the harmonic intervals in a smithy, and then weighing the hammers that produced them, or of his suspending weights corresponding to those of the hammers to equal strings, are, indeed, impossible and absurd; but it is sheer waste of time to rationalise them. For our purpose their absurdity is their chief merit. They are not stories which any Greek mathematician or musician could possibly have invented, but genuine popular tales bearing witness to the existence of a real tradition that Pythagoras was the author of this momentous discovery.

Plato (Tim. 36 a 3) defines the harmonic mean as τὴν ... ταὐτῷ μέρει τῶν ἄκρων αὐτῶν ὑπερέχουσαν καὶ ὑπερεχομένην. The harmonic mean of 12 and 6 is therefore 8; for 8 = 12 - 12/3 = 6 + 6/3. For these stories and a criticism of them, see Max C. P. Schmidt, Kulturhistorische Beiträge, i. pp. 78 sqq. The smith’s hammers belong to the region of Märchen, and it is not true either that the notes would be determined by the weight of the hammers, or that, if they were, the weights hung to equal strings would produce the notes. These inaccuracies were pointed out by Montucla (Martin, Études sur le Timée, i. p. 391). [Sidenote: Things are numbers.]

52. It was this too, no doubt, that led Pythagoras to say all things were numbers. We shall see that, at a later date, the Pythagoreans identified these numbers with geometrical figures; but the mere fact that they called them “numbers,” when taken in connexion with what we are told about the method of Eurytos, is sufficient to show this was not the original sense of the doctrine. It is enough to suppose that Pythagoras reasoned somewhat as follows. If musical sounds can be reduced to numbers, why should not everything else? There are many likenesses to number in things, and it may well be that a lucky experiment, like that by which the octave was discovered, will reveal their true numerical nature. The Neopythagorean writers, going back in this as in other matters to the earliest tradition of the school, indulge their fancy in tracing out analogies between things and numbers in endless variety; but we are fortunately dispensed from following them in these vagaries. Aristotle tells us distinctly that the Pythagoreans explained only a few things by means of numbers, which means that Pythagoras himself left no developed doctrine on the subject, while the Pythagoreans of the fifth century did not care to add anything of the sort to the school tradition. Aristotle does imply, however, that, according to them the “right time” (καιρός) was seven, justice was four, and marriage three. These identifications, with a few others like them, we may safely refer to Pythagoras or his immediate successors; but we must not attach much importance to them. They are mere sports of the analogical fancy. If we wish to understand the cosmology of Pythagoras, we must start, not from them, but from any statements we can find that present points of contact with the teaching of the Milesian school. These, we may fairly infer, belong to the system in its most primitive form.

Arist. Met. Μ, 4. 1078 b 21 (R. P. 78); Zeller, p. 390, n. 2. The Theologumena Arithmetica, wrongly attributed to Nikomachos of Gerasa, is full of fanciful doctrine on this subject (R. P. 78 a). Alexander in Met. p. 38, 8, gives a few definitions which may be old (R. P. 78 c). [Sidenote: Cosmology.] 53. Now the most striking statement of this kind is one of Aristotle’s. The Pythagoreans held, he tells us, that there was “boundless breath” outside the heavens, and that it was inhaled by the world. In substance, this is the doctrine of Anaximenes, and it becomes practically certain that it was that of Pythagoras, when we find that Xenophanes denied it. We may infer, then, that the further development of the idea is also due to Pythagoras himself. We are told that, after the first unit had been formed—however that may have taken place—the nearest part of the Boundless was first drawn in and limited; and further, that it is just the Boundless thus inhaled that keeps the units separate from each other. It represents the interval between them. This is a very primitive way of describing the nature of discrete quantity. Arist. Phys. Δ, 6. 213 b 22 (R. P. 75).

Diog. ix. 19 (R. P. 103 c). It is true that Diogenes is here drawing from a biographical rather than a doxographical source (Dox. p. 168), but this touch can hardly be an invention. Arist. Met. Μ, 3. 1091 a 13 (R. P. 74). Arist. Phys. Δ, 6. 213 b 23 (R. P. 75 a). The words διορίζει τὰς φύσεις have caused unnecessary difficulty, because they have been supposed to attribute the function of limiting to the ἄπειρον. Aristotle makes it quite clear that his meaning is that stated in the text. Cf. especially the words χωρισμοῦ τινος τῶν ἐφεξῆς καὶ διορίσεως. The term διωρισμένον is the proper antithesis to συνεχές. In his work on the Pythagorean philosophy, Aristotle used instead the phrase διορίζει τὰς χώρας (Stob. i. p. 156, 8; R. P. 75), which is also quite intelligible if we remember what the Pythagoreans meant by χώρα (cf. p. 115, n. 240).

In the passages of Aristotle just referred to, the Boundless is also spoken of as the void or empty. This identification of air and the void is a confusion which we have already met with in Anaximenes, and it need not surprise us to find it here too. We find also, as we might expect, distinct traces of the other confusion, that of air and vapour. It seems certain, in fact, that Pythagoras identified the Limit with fire, and the Boundless with darkness. We are told by Aristotle that Hippasos made Fire the first principle, and we shall see that Parmenides, in discussing the opinions of his contemporaries, attributes to them the view that there were two primary “forms,” Fire and Night. We also find that Light and Darkness appear in the Pythagorean table of opposites under the heads of the Limit and the Unlimited respectively. The identification of breath with darkness here implied is a strong proof of the primitive character of the doctrine; for in the sixth century darkness was supposed to be a sort of vapour, while in the fifth, its true nature was well known. Plato, with his usual historical tact, makes the Pythagorean Timaios describe mist and darkness as condensed air. We must think, then, of a “field” of darkness or breath marked out by luminous units, an imagination which the starry heavens would naturally suggest. It is even probable that we should ascribe to Pythagoras the Milesian view of a plurality of worlds, though it would not have been natural for him to speak of an infinite number. We know, at least, that Petron, one of the early Pythagoreans, said there were just a hundred and eighty-three worlds arranged in a triangle; and Plato makes Timaios admit, when laying down that there is only one world, that something might be urged in favour of the view that there are five, as there are five regular solids.

Cf. Arist. Phys. Δ, 6. 213 a 27, οἱ δ’ ἄνθρωποι ... φασὶν ἐν ᾦ ὅλως μηδέν ἐστι, τοῦτ’ εἶναι κενόν, διὸ τὸ πλῆρες ἀέρος κενὸν εἶναι; de Part. An. Β, 10. 656 b 15, τὸ γὰρ κενὸν καλούμενον ἀέρος πλῆρές ἐστι; de An. Β, 10 419 b 34, δοκεῖ γὰρ εἶναι κενὸν ὁ ἀήρ. Arist. Met. Α, 3. 984 a 7 (R. P. 56 c). See Chap. IV. § 91. Arist. Met. Α, 5. 986 a 25 (R. P. 66). Plato, Tim. 58 d 2. This is quoted by Plutarch, de def. orac. 422 b, d, from Phanias of Eresos, who gave it on the authority of Hippys of Rhegion. If we may follow Wilamowitz (Hermes, xix. p. 444) in supposing that this really means Hippasos of Metapontion (and it was in Rhegion that the Pythagoreans took refuge), this is a very valuable piece of evidence. Plato, Tim. 55 c 7 sqq. [Sidenote: The heavenly bodies.]

54. Anaximander had regarded the heavenly bodies as wheels of “air” filled with fire which escapes through certain openings (§ 19), and there is evidence that Pythagoras adopted the same view. We have seen that Anaximander only assumed the existence of three such wheels, and held that the wheel of the sun was the lowest. It is extremely probable that Pythagoras identified the intervals between these rings with the three musical intervals which he had discovered, the fourth, the fifth, and the octave. That would be the most natural beginning for the later doctrine of the “harmony of the spheres,” though that expression would be doubly misleading if applied to any theory we can properly ascribe to Pythagoras himself. The word ἁρμονία does not mean harmony, and the “spheres” are an anachronism. We are still at the stage when wheels or rings were considered sufficient to account for the motions of the heavenly bodies. It is also to be observed that sun, moon, planets, and fixed stars must all be regarded as moving in the same direction from east to west. Pythagoras certainly did not ascribe to the planets an orbital motion of their own from west to east. The old idea was rather that they were left behind more or less every day. As compared with the fixed stars, Saturn is left behind least of all, and the Moon most; so, instead of saying that the Moon took a shorter time than Saturn to complete its path through the signs of the Zodiac, men said Saturn travelled quicker than the Moon, because it more nearly succeeds in keeping up with the signs. Instead of holding that Saturn takes thirty years to complete its revolution, they said it took the fixed stars thirty years to pass Saturn, and only twenty-nine days and a half to pass the Moon. This is one of the most important points to bear in mind regarding the planetary systems of the Greeks, and we shall return to it again.

This will be found in Chap. IV. § 93. For a clear statement of this view (which was still that of Demokritos), see Lucretius, v. 621 sqq. The view that the planets had an orbital motion from west to east is attributed by Aetios, ii. 16, 3, to Alkmaion (§ 96), which certainly implies that Pythagoras did not hold it. As we shall see (§ 152), it is far from clear that any of the Pythagoreans did. It seems rather to be Plato’s discovery.

The account just given of the views of Pythagoras is, no doubt, conjectural and incomplete. We have simply assigned to him those portions of the Pythagorean system which appear to be the oldest, and it has not even been possible at this stage to cite fully the evidence on which our discussion is based. It will only appear in its true light when we have examined the second part of the poem of Parmenides and the system of the later Pythagoreans. For reasons which will then be apparent, I do not venture to ascribe to Pythagoras himself the theory of the earth’s revolution round the central fire. It seems safest to suppose that he still adhered to the geocentric hypothesis of Anaximander. In spite of this, however, it will be clear that he opened a new period in the development of Greek science, and it was certainly to his school that its greatest discoveries were directly or indirectly due. When Plato deliberately attributes some of his own most important discoveries to the Pythagoreans, he was acknowledging in a characteristic way the debt he owed them. See Chap. IV. §§ 92-93, and Chap. VII. §§ 150-152. II. XENOPHANES OF KOLOPHON [Sidenote: Life.]

55. We have seen how Pythagoras identified himself with the religious movement of his time; we have now to consider a very different manifestation of the reaction against that view of the gods which the poets had made familiar to every one. Xenophanes denied the anthropomorphic gods altogether, but was quite unaffected by the revival of more primitive ideas that was going on all round him. We still have a fragment of an elegy in which he ridiculed Pythagoras and the doctrine of transmigration. “Once, they say, he was passing by when a dog was being ill-treated. ‘Stop!’ he said, ‘don’t hit it! It is the soul of a friend! I knew it when I heard its voice.’” We are also told that he opposed the views of Thales and Pythagoras, and attacked Epimenides, which is likely enough, though no fragments of the kind have come down to us. His chief importance lies in the fact that he was the author of the quarrel between philosophy and poetry which culminated in Plato’s Republic. See fr. 7 (= 18 Karst.), ap. Diog. viii. 36 (R. P. 88).

Diog. ix. 18 (R. P. 97). We know that Xenophanes referred to the prediction of an eclipse by Thales (Chap. I. p. 41, n. 62). We shall see that his own view of the sun was hardly consistent with the possibility of such a prediction, so it may have been in connexion with this that he opposed him.

It is not easy to determine the date of Xenophanes. Timaios said he was a contemporary of Hieron and Epicharmos, and he certainly seems to have played a part in the anecdotical romance of Hieron’s court which amused the Greeks of the fourth century much as that of Croesus and the Seven Wise Men amused those of the fifth. As Hieron reigned from 478 to 467 B.C., that would make it impossible to date the birth of Xenophanes much earlier than 570 B.C., even if we suppose him to have lived till the age of a hundred. On the other hand, both Sextus and Clement say that Apollodoros gave Ol. XL. (620-616 B.C.) as the date of his birth, and the former adds that his days were prolonged till the time of Dareios and Cyrus. Again, Diogenes, whose information on such matters mostly comes from Apollodoros, says that he flourished in Ol. LX. (540-537 B.C.), and Diels holds that Apollodoros really said so. However that may be, it is evident that the date 540 B.C. is based on the assumption that he went to Elea in the year of its foundation, and is, therefore, a mere combination.

Timaios ap. Clem. Strom. i. p. 533 (R. P. 95). There is only one anecdote which actually represents Xenophanes in conversation with Hieron (Plut. Reg. apophth. 175 e), but it is natural to understand Arist. Met. Γ, 5. 1010 a 4 as an allusion to a remark made by Epicharmos to him. Aristotle has more than one anecdote about Xenophanes, and it seems most likely that he derived them from the romance of which Xenophon’s Strom. is an echo. Clem., loc. cit.; Sext. Strom. i. 257. The mention of Cyrus is confirmed by Hipp. Strom. i. 94. Diels thinks that Dareios was mentioned first for metrical reasons; but no one has satisfactorily explained why Cyrus should be mentioned at all, unless the early date was intended. On the whole subject, see Jacoby, pp. 204 sqq., who is certainly wrong in supposing that ἄχρι τῶν Δαρείου καὶ Κύρου χρόνων can mean “during the times of Dareios and Cyrus.” Strom. xxxi. p. 22. He assumes an early corruption of N into M. As Apollodoros gave the Athenian archon, and not the Olympiad, we might with more probability suppose a confusion due to two archons having the same name.

As Elea was founded by the Phokaians six years after they left Phokaia (Herod. i. 164 sqq.) its date is just 540-39 B.C. Cf. the way in which Apollodoros dated Empedokles by the era of Thourioi (§ 98). What we do know for certain is that Xenophanes had led a wandering life from the age of twenty-five, and that he was still alive and making poetry at the age of ninety-two. He says himself (fr. 8 = 24 Karst.; R. P. 97):— There are by this time threescore years and seven that have tossed my careworn soul up and down the land of Hellas; and there were then five-and-twenty years from my birth, if I can say aught truly about these matters. Bergk (Litteraturgesch. ii. p. 418, n. 23) took φροντίς here to mean the literary work of Xenophanes, but it is surely an anachronism to suppose that at this date it could be used like the Latin cura. It is tempting to suppose that in this passage Xenophanes was referring to the conquest of Ionia by Harpagos, and that he is, in fact, answering the question asked in another poem (fr. 22 = 17 Karst.; R. P. 95 a):—

This is the sort of thing we should say by the fireside in the winter-time, as we lie on soft couches after a good meal, drinking sweet wine and crunching chickpeas: “Of what country are you, and how old are you, good sir? And how old were you when the Mede appeared?” It was certainly another poem; for it is in hexameters while the preceding fragment is in elegiacs. We cannot, however, be sure of this, and we must be content with what is, after all, for our purpose the main fact, namely, that he refers to Pythagoras in the past tense, and is in turn so referred to by Herakleitos. Xenophanes, fr. 7 (above, p. 124, n. 265); Herakleitos, frs. 16, 17 (below, p. 147).

Theophrastos said that Xenophanes had “heard” Anaximander, and we shall see that he was certainly acquainted with the Ionian cosmology. When driven from his native city, he lived in Sicily, chiefly, we are told, at Zankle and Katana. Like Archilochos before him, he unburdened his soul in elegies and satires, which he recited at the banquets where, we may suppose, the refugees tried to keep up the usages of good Ionian society. The statement that he was a rhapsode has no foundation at all. The singer of elegies was no professional like the rhapsode, but the social equal of his listeners. In his ninety-second year he was still, we have seen, leading a wandering life, which is hardly consistent with the statement that he settled at Elea and founded a school there, especially if we are to think of him as spending his last days at Hieron’s court. It is quite probable that he visited Elea, and it is just possible that he wrote a poem of two thousand hexameters on the foundation of that city, which was naturally a subject of interest to all the Ionic émigrés. But it is very remarkable that no ancient writer expressly says that he ever was at Elea, and the only thing besides the doubtful poem referred to which connects him with it is a single anecdote of Aristotle’s as to the answer he gave the Eleates when they asked whether they should sacrifice to Leukothea and lament her or not. “If you think her a goddess,” he said, “do not lament her; if not, do not sacrifice to her.” That is absolutely all, and it is only an apophthegm. It is strange there should be no more if Xenophanes had really found a home at last in the Phokaian colony.

Diog. ix. 21 (R. P. 96 a). Diog. ix. 18 (R. P. 96). The use of the old name Zankle, instead of the later Messene, points to an early source for this statement—probably the elegies of Xenophanes himself. Diog. ix. 18 (R. P. 97) says αὐτὸς ἐρραψῴδει τὰ ἑαυτοῦ, which is a very different thing. Nothing is said anywhere of his reciting Homer, and the word ῥαψῳδεῖν is used quite loosely for “to recite.” Gomperz’s imaginative picture (Greek Thinkers, vol. i. p. 155) has no further support than this single word. Nor is there any trace of Homeric influence in the fragments. They are in the usual elegiac style. The statement is justly suspected by Hiller (Rh. Mus. xxxiii. p. 529) to come from Lobon of Argos, who provided the Seven Wise Men, Epimenides, etc., with stichometric notices, all duly recorded in Diogenes. Even if true, however, it proves nothing. Arist. Rhet. Β, 26. 1400 b 5 (R. P. 98 a). Anecdotes like this are really anonymous. Plutarch transfers the story to Egypt (P. Ph. Fr. p. 22, § 13), and others tell it of Herakleitos. It is hardly safe to build on such a foundation. [Sidenote: Poems.]

56. According to a notice preserved in Diogenes, Xenophanes wrote in hexameters and also composed elegies and iambics against Homer and Hesiod. No good authority says anything about his having written a philosophical poem. Simplicius tells us he had never met with the verses about the earth stretching infinitely downwards (fr. 28), and this means that the Academy possessed no copy of such a poem, which would be very strange if it had ever existed. Simplicius was able to find the complete works of much smaller men. Nor does internal evidence lend any support to the view that he wrote a philosophical poem. Diels refers about twenty-eight lines to it, but they would all come in quite as naturally in his attacks on Homer and Hesiod, as I have endeavoured to show. It is also significant that a considerable number of them are derived from commentators on Homer. It seems probable, then, that Xenophanes expressed his theological and philosophical views incidentally in his satires. That would be quite in the manner of the time, as we can see from the remains of Epicharmos. Diog. ix. 18 (R. P. 97). The word ἐπικόπτων is a reminiscence of Timon, fr. 60; Diels, Ξεινοφάνης ὑπάτυφος Ὁμηραπάτης ἐπικόπτης.

The oldest reference to a poem Περὶ φύσεως is in the Geneva scholium on Il. xxi. 196 (quoting fr. 30), and this goes back to Krates of Mallos. We must remember, however, that such titles are of later date than Xenophanes, and he had been given a place among philosophers long before the time of Krates. All we can say, therefore, is that the Pergamene librarians gave the title Περὶ φύσεως to some poem of Xenophanes. Simpl. de Caelo, p. 522, 7 (R. P. 97 b). It is true that two of our fragments (25 and 26) are preserved by Simplicius, but he got them from Alexander. Probably they were quoted by Theophrastos; for it is plain that Alexander had no first-hand knowledge of Xenophanes either. If he had, he would not have been taken in by M.X.G. (See p. 138, n. 305.) Three fragments (27, 31, 33) come from the Homeric Allegories, two (30, 32) are from Homeric scholia.

The satires themselves are called Silloi by late writers, and this name may go back to Xenophanes himself. It is also possible, however, that it originates in the fact that Timon of Phleious, the “sillographer” (c. 259 B.C.), put much of his satire upon philosophers into the mouth of Xenophanes. Only one iambic line has been preserved, and that is immediately followed by a hexameter (fr. 14 = 5 Karst.). This suggests that Xenophanes inserted iambic lines among his hexameters in the manner of the Margites, which would be a very natural thing for him to do. Cf. Wilamowitz, Progr. Gryphiswald. 1880. [Sidenote: The fragments.] 57. I give all the fragments of any importance according to the text and arrangement of Diels. ELEGIES

Now is the floor clean, and the hands and cups of all; one sets twisted garlands on our heads, another hands us fragrant ointment on a salver. The mixing bowls stand ready, full of gladness, and there is more wine at hand that promises never to leave us in the lurch, soft and smelling of flowers in the jars. In the midst the frankincense sends up its holy smoke, and there is cold water, sweet and clean. Brown loaves are set before us and a lordly table laden with cheese and rich honey. The altar in the midst is clustered round with flowers; song and revel fill the halls.

But first it is meet that men should hymn the god with joyful song, with holy tales and pure words; then after libation and prayer made that we may have strength to do right—for that is in truth the better way—no sin is it to drink as much as a man can take and get home without an attendant, so he be not stricken in years. And above all men is he to be praised who after drinking gives goodly proof of himself in the trial of skill, as memory and voice will serve him. Let him not sing of Titans and Giants—those fictions of the men of old—nor of turbulent civil broils in which is no good thing at all; but ever give heedful reverence to the gods.

What if a man win victory in swiftness of foot, or in the pentathlon, at Olympia, where is the precinct of Zeus by Pisa’s springs, or in wrestling,—what if by cruel boxing or that fearful sport men call pankration he become more glorious in the citizens’ eyes, and win a place of honour in the sight of all at the games, his food at the public cost from the State, and a gift to be an heirloom for him,—what if he conquer in the chariot-race,—he will not deserve all this for his portion so much as I do. Far better is our art than the strength of men and of horses! These are but thoughtless judgments, nor is it fitting to set strength before our art. Even if there arise a mighty boxer among a people, or one great in the pentathlon or at wrestling, or one excelling in swiftness of foot—and that stands in honour before all tasks of men at the games—the city would be none the better governed for that. It is but little joy a city gets of it if a man conquer at the games by Pisa’s banks; it is not this that makes fat the store-houses of a city.

They learnt dainty and unprofitable ways from the Lydians, so long as they were free from hateful tyranny; they went to the market-place with cloaks of purple dye, not less than a thousand of them all told, vainglorious and proud of their comely tresses, reeking with fragrance from cunning salves. SATIRES Since all at first have learnt according to Homer.... Homer and Hesiod have ascribed to the gods all things that are a shame and a disgrace among mortals, stealings and adulteries and deceivings of one another. R. P. 99. They have uttered many, many lawless deeds of the gods, stealings and adulteries and deceivings of one another. R. P. ib. But mortals deem that the gods are begotten as they are, and have clothes like theirs, and voice and form. R. P. 100. Yes, and if oxen and horses or lions had hands, and could paint with their hands, and produce works of art as men do, horses would paint the forms of the gods like horses, and oxen like oxen, and make their bodies in the image of their several kinds. R. P. ib. The Ethiopians make their gods black and snub-nosed; the Thracians say theirs have blue eyes and red hair. R. P. 100 b.

The gods have not revealed all things to men from the beginning, but by seeking they find in time what is better. R. P. 104 b. One god, the greatest among gods and men, neither in form like unto mortals nor in thought.... R. P. 100. He sees all over, thinks all over, and hears all over. R. P. 102. But without toil he swayeth all things by the thought of his mind. R. P. 108 b. And he abideth ever in the selfsame place, moving not at all; nor doth it befit him to go about now hither now thither. R. P. 110 a. All things come from the earth, and in earth all things end. R. P. 103 a. This limit of the earth above is seen at our feet in contact with the air; below it reaches down without a limit. R. P. 103. All things are earth and water that come into being and grow. R. P. 103. The sea is the source of water and the source of wind; for neither in the clouds (would there be any blasts of wind blowing forth) from within without the mighty sea, nor rivers’ streams nor rain-water from the sky. The mighty sea is father of clouds and of winds and of rivers. R. P. 103.

The sun swinging over the earth and warming it.... She that they call Iris is a cloud likewise, purple, scarlet and green to behold. R. P. 103. For we all are born of earth and water. R. P. ib. There never was nor will be a man who has certain knowledge about the gods and about all the things I speak of. Even if he should chance to say the complete truth, yet he himself knows not that it is so. But all may have their fancy. R. P. 104. Let these be taken as fancies something like the truth. R. P. 104 a. All of them that are visible for mortals to behold. And in some caves water drips.... If god had not made brown honey, men would think figs far sweeter than they do. I formerly, with Zeller, preferred Theodoret’s reading αἴσθησιν, but both Clement and Eusebios have ἐσθῆτα, and Theodoret is entirely dependent on them. Reading ἠέρι for καὶ ῥεῖ with Diels. This fragment has been recovered in its entirety from the Geneva scholia on Homer (see Arch. iv. p. 652). The words in brackets are added by Diels. See also Praechter, “Zu Xenophanes” (Philol. xviii. p. 308).

The word is ὑπεριέμενος. This is quoted from the Allegories as an explanation of the name Hyperion, and doubtless Xenophanes so meant it. Reading δεδοξάσθω with Wilamowitz. As Diels suggests, this probably refers to the stars, which Xenophanes held to be clouds. [Sidenote: The heavenly bodies.] 58. The intention of one of these fragments (fr. 32) is perfectly clear. “Iris too” is a cloud, and we may infer that the same thing had just been said of the sun, moon, and stars; for the doxographers tell us that these were all explained as “clouds ignited by motion.” To the same context clearly belongs the explanation of the St. Elmo’s fire which Aetios has preserved. “The things like stars which appear on ships,” we are told, “which some call the Dioskouroi, are little clouds made luminous by motion.” In the doxographers this explanation is repeated with trifling variations under the head of moon, stars, comets, lightning, shooting stars, and so forth, which gives the appearance of a systematic cosmology. But the system is due to the arrangement of the work of Theophrastos, and not to Xenophanes; for it is obvious that a very few hexameters added to those we possess would amply account for the whole doxography.

Cf. Diels ad loc. (P. Ph. Fr. p. 44), “ut Sol et cetera astra, quae cum in nebulas evanescerent, deorum simul opinio casura erat.” Cf. Arch. x. p. 533. Aet. ii. 18, 1 (Dox. p. 347), Ξενοφάνης τοὺς ἐπὶ τῶν πλοίων φαινομένους οἷον ἀστέρας, οὓς καὶ Διοσκούρους καλοῦσί τινες, νεφέλια εἶναι κατὰ τὴν ποιὰν κίνησιν παραλάμποντα.

What we hear of the sun presents some difficulties. We are told, on the one hand, that it too was an ignited cloud; but this can hardly be right. The evaporation of the sea from which clouds arise is distinctly said to be due to the sun’s heat. Theophrastos stated that the sun, according to Xenophanes, was a collection of sparks from the moist exhalation; but even this leaves the exhalation itself unexplained. That, however, matters little, if the chief aim of Xenophanes was to discredit the anthropomorphic gods, rather than to give a scientific theory of the heavenly bodies. The important thing is that Helios too is a temporary phenomenon. The sun does not go round the earth, as Anaximander taught, but straight on, and the appearance of a circular path is solely due to its increasing distance. So it is not the same sun that rises next morning, but a new one altogether; while the old one “tumbles into a hole” when it comes to certain uninhabited regions of the earth. Besides that, there are many suns and moons, one of each for every region of the earth. It is obvious that things of that kind cannot be gods. The passages from Aetios are collected in P. Ph. Fr. pp. 32 sqq. (Vors. p. 42).

Aet. ii. 20, 3 (Dox. p. 348), Ξενοφάνης ἐκ νεφῶν πεπυρωμένων εἶναι τὸν ἥλιον. Θεόφραστος ἐν τοῖς Φυσικοῖς γέγραφεν ἐκ πυριδίων μὲν τῶν συναθροιζομένων ἐκ τῆς ὑγρᾶς ἀναθυμιάσεως, συναθροιζόντων δὲ τὸν ἥλιον. Aet. ii. 24, 9 (Dox. p. 355). πολλοὺς εἶναι ἡλίους καὶ σελήνας κατὰ κλίματα τῆς γῆς καὶ ἀποτομὰς καὶ ζώνας, κατὰ δέ τινα καιρὸν ἐμπίπτειν τὸν δίσκον εἴς τινα ἀποτομὴν τῆς γῆς οὐκ οἰκουμένην ὑφ’ ἡμῶν καὶ οὕτως ὥσπερ κενεμβατοῦντα ἔκλειψιν ὑποφαίνειν· ὁ δ’ αὐτὸς τὸν ἥλιον εἰς ἄπειρον μὲν προιέναι, δοκεῖν δὲ κυκλεῖσθαι διὰ τὴν ἀπόστασιν. It is clear that in this notice ἔκλειψινἕκλειψιν has been erroneously substituted for δύσιν, as it has also in Aet. ii. 24, 4 (Dox. p. 354).

The vigorous expression “tumbling into a hole” seems clearly to come from the verses of Xenophanes himself, and there are others of a similar kind, which we must suppose were quoted by Theophrastos. The stars go out in the daytime, but glow again at night “like charcoal embers.” The sun is of some use in producing the world and the living creatures in it, but the moon “does no work in the boat.” Such expressions can only be meant to make the heavenly bodies appear ridiculous, and it will therefore be well to ask whether the other supposed cosmological fragments can be interpreted on the same principle. That this is the meaning of ὥσπερ κενεμβατοῦντα appears sufficiently from the passages referred to in Liddell and Scott. Aet. ii. 13, 14 (Dox. p. 343), ἀναζωπυρεῖν νύκτωρ καθάπερ τοὺς ἄνθρακας. Aet. ii. 30, 8 (Dox. p. 362), τὸν μὲν ἥλιον χρήσιμον εἶναι πρὸς τὴν τοῦ κόσμου καὶ τὴν τῶν ἐν αὐτῷ ζῴων γένεσίν τε καὶ διοίκησιν, τὴν δὲ σελήνην παρέλκειν, The verb παρέλκειν means “to cork.” Cf. Aristophanes, Pax, 1306. [Sidenote: Earth and water.] 59. In fr. 29 Xenophanes says that “all things are earth and water,” and Hippolytos has preserved the account given by Theophrastos of the context in which this occurred. It was as follows:—

Xenophanes said that a mixture of the earth with the sea is taking place, and that it is being gradually dissolved by the moisture. He says that he has the following proofs of this. Shells are found in midland districts and on hills, and he says that in the quarries at Syracuse has been found the imprint of a fish and of seaweed, at Paros the form of an anchovy in the depth of the stone, and at Malta flat impressions of all marine animals. These, he says, were produced when all things were formerly mud, and the outlines were dried in the mud. All human beings are destroyed when the earth has been carried down into the sea and turned to mud. This change takes place for all the worlds.—Hipp. Ref. i. 14 (R. P. 103 a).

This is, of course, the theory of Anaximander, and we may perhaps credit him rather than Xenophanes with the observations of fossils. Most remarkable of all, however, is the statement that this change applies to “all the worlds.” It really seems impossible to doubt that Theophrastos attributed a belief in “innumerable worlds” to Xenophanes. As we have seen already, Aetios includes him in his list of those who held this doctrine, and Diogenes ascribes it to him also. In this place, Hippolytos seems to take it for granted. We shall also find, however, that in another connexion he said the World or God was one. If our interpretation of him is correct, there is no difficulty here. The main point is that, so far from being a primeval goddess, and “a sure seat for all things ever,” Gaia too is a passing appearance. That belongs to the attack upon Hesiod, and, if in this connexion Xenophanes spoke, with Anaximander, of “innumerable worlds,” while elsewhere he said that God or the World was one, that is probably connected with a still better attested contradiction which we have now to examine.

There is an interesting note on these in Gomperz’s Greek Thinkers (Eng. trans. i. p. 551). I have translated his conjecture φυκῶν instead of the MS. φωκῶν, as this is said to involve a palæontological impossibility, and impressions of fucoids are found, not indeed in the quarries of Syracuse, but near them. It is said also that there are no fossils in Paros, so the anchovy must have been an imaginary one. Aet. ii. 1, 2 (Dox., p. 327); Diog. ix. 19 (R. P. 103 c). It is true, of course, that this passage of Diogenes comes from the biographical compendium (Dox. p. 168); but, for all that, it is a serious matter to deny the Theophrastean origin of a statement found in Aetios, Hippolytos, and Diogenes. [Sidenote: Finite or infinite?]

60. Aristotle tried without success to discover from the poems of Xenophanes whether he regarded the world as finite or infinite. “He made no clear pronouncement on the subject,” he tells us. Theophrastos, on the other hand, decided that he regarded it as spherical and finite because he said it was “equal every way.” This, however, leads to very serious difficulties. We have seen already that Xenophanes said the sun went right on to infinity, and this agrees with his view of the earth as an infinitely extended plain. Still more difficult to reconcile with the idea of a spherical and finite world is the statement of fr. 28 that, while the earth has an upper limit which we see, it has no limit below. This is attested by Aristotle, who speaks of the earth being “infinitely rooted,” and adds that Empedokles criticised Xenophanes for holding this view. It further appears from the fragment of Empedokles quoted by Aristotle that Xenophanes said the vast Air extended infinitely upwards. We are therefore bound to try to find room for an infinite earth and an infinite air in a spherical and finite world! That comes of trying to find science in satire. If, on the other hand, we regard these statements from the same point of view as those about the heavenly bodies, we shall at once see what they most probably mean. The story of Ouranos and Gaia was always the chief scandal of the Theogony, and the infinite air gets rid of Ouranos altogether. As to the earth stretching infinitely downwards, that gets rid of Tartaros, which Homer described as situated at the bottommost limit of earth and sea, as far beneath Hades as heaven is above the earth. This is pure conjecture, of course; but, if it is even possible, we are entitled to disbelieve that such startling contradictions occurred in a cosmological poem.

Arist. Met. Α, 5. 986 b 23 (R. P. 101), οὐδὲν διεσαφήνισεν. This is given as an inference by Simpl. Phys. p. 23, 18 (R. P. 108 b), διὰ τὸ πανταχόθεν ὅμοιον. It does not merely come from M.X.G. (R. P. 108), πάντῃ δ’ ὅμοιον ὄντα σφαιροειδῆ εἶναι. Hippolytos has it too (Ref. i. 14; R. P. 102 a), so it goes back to Theophrastos. Timon of Phleious understood Xenophanes in the same way; for he makes him call the One ἴσον ἁπάντῃ (fr. 60, Diels = 40 Wachsm.; R. P. 102 a). Arist. de Caelo, Β, 13. 294 a 21 (R. P. 103 b). I take δαψιλός as an attribute and ἀπείρονα as predicate to both subjects. Il. viii. 13-16, 478-481, especially the words οὐδ’ εἴ κε τὰ νείατα πείραθ’ ἵκηαι | γαίης καὶ πόντοιο κ.τ.λ. Iliad viii. must have seemed a particularly bad book to Xenophanes.

A more subtle explanation of the difficulty commended itself to the late Peripatetic who wrote an account of the Eleatic school, part of which is still extant in the Aristotelian corpus, and is generally known now as the treatise on Melissos, Xenophanes, and Gorgias. He said that Xenophanes declared the world to be neither finite nor infinite, and he composed a series of arguments in support of this thesis, to which he added another like it, namely, that the world is neither in motion nor at rest. This has introduced endless confusion into our sources. Alexander used this treatise as well as the great work of Theophrastos, and Simplicius supposed the quotations from it to be from Theophrastos too. Having no copy of the poems he was completely baffled, and until recently all accounts of Xenophanes were vitiated by the same confusion. It may even be suggested that, but for this, we should have heard very little of the “philosophy of Xenophanes,” a way of speaking which is in the main a survival from the days before this scholastic exercise was recognised as having no authority.

In Bekker’s edition this treatise bears the title Περὶ Ξενοφάνους, περὶ Ζήνωνος, περὶ Γοργίου, but the best MS. gives as the titles of its three sections: (1) Περὶ Ζήνωνος, (2) Περὶ Ξενοφάνους, (3) Περὶ Γοργίου. The first section, however, plainly refers to Melissos, so the whole treatise is now entitled De Melisso, Xenophane, Gorgia (M.X.G.). It has been edited by Apelt in the Teubner Series, and more recently by Diels (Abh. der k. Preuss. Akad. 1900), who has also given the section dealing with Xenophanes in P. Ph. Fr. pp. 24-29 (Vors. pp. 36 sqq.). He has now withdrawn the view maintained in Dox. p. 108 that the work belongs to the third century B.C., and holds that it was a Peripatetico eclectico (i.e. sceptica, platonica, stoica admiscente) circa Christi natalem conscriptum. If that is so, there is no reason to doubt, as I formerly did, that the second section is really meant to deal with Xenophanes. The writer would have no first-hand knowledge of his poems, and the order in which the philosophers are discussed is that of the passage in the Metaphysics which suggested the whole thing. It is possible that a section on Parmenides preceded what we now have. [Sidenote: God and the world.]

61. In the passage of the Metaphysics just referred to, Aristotle speaks of Xenophanes as “the first partisan of the One,” and the context shows that he means to suggest he was the first of the Eleatics. We have seen already that the certain facts of his life make it very unlikely that he settled at Elea and founded a school there, and it is probable that, as usual in such cases, Aristotle is simply reproducing certain statements of Plato. At any rate, Plato had spoken of the Eleatics as the “partisans of the Whole,” and he had also spoken of the school as “starting with Xenophanes and even earlier.” The last words, however, show clearly enough what he meant. Just as he called the Herakleiteans “followers of Homer and still more ancient teachers,” so he attached the Eleatic school to Xenophanes and still earlier authorities. We have seen in other instances how these playful and ironical remarks of Plato were taken seriously by his successors, and we need not let this fresh instance of the same thing influence our general view of Xenophanes unduly.

Met. Α, 5. 986 b 21 (R. P. 101), πρῶτος τούτων ἑνίσας. The verb ἑνίζειν occurs nowhere else, but is plainly formed on the analogy of μηδίζειν, φιλιππίζειν, and the like. It is not likely that it means “to unify.” Aristotle could easily have said ἑνώσας if he had meant that. Tht. 181 a 6, τοῦ ὅλου στασιῶται. The noun στασιῶτης has no other meaning than “partisan.” There is no verb στασιοῦν “to make stationary,” and such a formation would be against all analogy. The derivation στασιώτας ... ἀπὸ τῆς στάσεως appears first in Sext. Math. x. 46, from which passage we may infer that Aristotle used the word, not that he gave the derivation. Soph. 242 d 5 (R. P. 101 b). If the passage implies that Xenophanes settled at Elea, it equally implies this of his predecessors. But Elea was not founded till Xenophanes was in the prime of life. Tht. 179 e 3, τῶν Ἡρακλειτείων ἤ, ὥσπερ σὺ λέγεις Ὁμηρείων καὶ ἔτι παλαιοτέρων. In this passage, Homer stands to the Herakleiteans in exactly the same relation as Xenophanes does to the Eleatics in the Sophist.

Aristotle goes on to tell us that Xenophanes, “referring to the whole world, said the One was god.” This clearly alludes to frs. 23-26, where all human attributes are denied of a god who is said to be one and “the greatest among gods and men.” It may be added that these verses gain very much in point if we may think of them as closely connected with frs. 11-16, instead of referring the one set of verses to the Satires and the other to a cosmological poem. It was probably in the same context that Xenophanes called the world or god “equal every way” and denied that it breathed. The statement that, there is no mastership among the gods also goes very well with fr. 26. A god has no wants, nor is it fitting for one god to be the servant of others, like Iris and Hermes in Homer. Met. 981 b 24. The words cannot mean “gazing up at the whole heavens,” or anything of that sort. They are taken as I take them by Bonitz (im Hinblicke auf den ganzen Himmel) and Zeller (im Hinblick auf das Weltganze). The word ἀποβλέπειν had become much too colourless to bear the other meaning, and οὐρανός, as we know, means what was later called κόσμος.

See above, p. 137, n. 301. Diog. ix. 19 (R. P. 103 c), ὅλον δ’ ὁρᾶν καὶ ὅλον ἀκούειν, μὴ μέντοι ἀναπνεῖν. See above, p. 120, n. 252. [Plut.] Strom. fr. 4, ἀποφαίνεται δὲ καὶ περὶ θεῶν ὡς οὐδεμιᾶς ἡγεμονίας ἐν αὐτοῖς οὔσης· οὐ γὰρ ὅσιον δεσπόζεσθαί τινα τῶν θεῶν, ἐπιδεῖσθαί τε μηδενὸς αὐτῶν μηδένα μηδ’ ὅλως, ἀκούειν δὲ καὶ ὁρᾶν καθόλου καὶ μὴ κατὰ μέρος. [Sidenote: Monotheism or polytheism.]

62. That this “god” is just the world, Aristotle tells us, and the use of the word θεός is quite in accordance with Anaximander’s. Xenophanes regarded it as sentient, though without any special organs of sense, and it sways all things by the thought of its mind. He also calls it “one god,” and, if that is monotheism, then Xenophanes was a monotheist, though this is surely not how the word is generally understood. The fact is that the expression “one god” wakens all sorts of associations in our mind which did not exist at all for the Greeks of this time. His contemporaries would have been more likely to call Xenophanes an atheist than anything else. As Eduard Meyer excellently says: “In Greece the question of one god or gods many hardly plays any part. Whether the divine power is thought of as a unity or a plurality, is irrelevant in comparison with the question whether it exists at all, and how its nature and its relation to the world is to be understood.” Gesch. des Alterth. ii. § 466.

On the other hand, it is wrong to say with Freudenthal that Xenophanes was in any sense a polytheist. That he should use the language of polytheism in his elegies is only what we should expect, and the other references to “gods” can be best explained as incidental to his attack on the anthropomorphic gods of Homer and Hesiod. In one case, Freudenthal has pressed a proverbial way of speaking too hard. Least of all can we admit that Xenophanes allowed the existence of subordinate or departmental gods; for it was just the existence of such that he was chiefly concerned to deny. At the same time, I cannot help thinking that Freudenthal was more nearly right than Wilamowitz, who says that Xenophanes “upheld the only real monotheism that has ever existed upon earth.” Diels, I fancy, comes nearer the mark, when he calls it a “somewhat narrow pantheism.” But all these views would have surprised Xenophanes himself about equally. He was really Goethe’s Weltkind, with prophets to right and left of him, and he would have smiled if he had known that one day he was to be regarded as a theologian. Freudenthal, Die Theologie des Xenophanes.

Xenophanes calls his god “greatest among gods and men,” but this is simply a case of “polar expression,” to which parallels will be found in Wilamowitz’s note to the Herakles, v. 1106. Cf. especially the statement of Herakleitos (fr. 20) that “no one of gods or men” made the world. Griechische Literatur, p. 38. Parmenides Lehrgedicht, p. 9.

HERAKLEITOS OF EPHESOS [Sidenote: Life of Herakleitos.]

63. Herakleitos of Ephesos, son of Blyson, is said to have “flourished” in Ol. LXIX. (504/3-501/0 B.C.); that is to say, just in the middle of the reign of Dareios, with whom several traditions connected him. We shall see that Parmenides was assigned to the same Olympiad, though for another reason (§ 84). It is more important, however, for our purpose to notice that, while Herakleitos refers to Pythagoras and Xenophanes by name and in the past tense (fr. 16), he is in turn referred to by Parmenides (fr. 6). These references are sufficient to mark his proper place in the history of philosophy. Zeller holds, indeed, that he cannot have published his work till after 478 B.C., on the ground that the expulsion of his friend Hermodoros, alluded to in fr. 114, could not have taken place before the downfall of Persian rule. If that were so, it might be hard to see how Parmenides could have known the views of Herakleitos; but there is surely no difficulty in supposing that the Ephesians may have sent one of their foremost citizens into banishment at a time when they were still paying tribute to the Great King. The Persians never took their internal self-government from the Ionian cities, and the spurious Letters of Herakleitos show the accepted view was that the expulsion of Hermodoros took place during the reign of Dareios.

Diog. ix. 1 (R. P. 29), no doubt from Apollodoros through some intermediate authority. Jacoby, pp. 227 sqq. Bernays, Die Heraklitischen Briefe, pp. 13 sqq. Bernays, op. cit. pp. 20 sqq. Sotion said that Herakleitos was a disciple of Xenophanes, which is not probable; for Xenophanes seems to have left Ionia for ever before Herakleitos was born. More likely he was not a disciple of any one; but it is clear, at the same time, that he was acquainted both with the Milesian cosmology and with the poems of Xenophanes. He also knew something of the theories taught by Pythagoras (fr. 17). Sotion ap. Diog. ix. 5 (R. P. 29 c). Of the life of Herakleitos we really know nothing, except, perhaps, that he belonged to the ancient royal house and resigned the nominal position of Basileus in favour of his brother. The origin of the other statements bearing on it is quite transparent. Diog. ix. 6 (R. P. 31).

See Patin, Heraklits Einheitslehre, pp. 3 sqq. Herakleitos said (fr. 68) that it was death to souls to become water; and we are told accordingly that he died of dropsy. He said (fr. 114) that the Ephesians should leave their city to their children, and (fr. 79) that Time was a child playing draughts. We are therefore told that he refused to take any part in public life, and went to play with the children in the temple of Artemis. He said (fr. 85) that corpses were more fit to be cast out than dung; and we are told that he covered himself with dung when attacked with dropsy. Lastly, he is said to have argued at great length with his doctors because of fr. 58. For these tales see Diog. ix. 3-5, and compare the stories about Empedokles discussed in Chap. V. § 100. [Sidenote: His book.]

64. We do not know the title of the work of Herakleitos—if, indeed, it had one at all—and it is not very easy to form a clear idea of its contents. We are told that it was divided into three discourses: one dealing with the universe, one political, and one theological. It is not likely that this division is due to Herakleitos himself; all we can infer from the statement is that the work fell naturally into these three parts when the Stoic commentators took their editions of it in hand. The variety of titles enumerated in Diog. ix. 12 (R. P. 30 b) seems to show that none was authentically known. That of “Muses” comes from Plato, Soph. 242 d 7. The others are mere “mottoes” (Schuster) prefixed by Stoic editors, and intended to emphasise their view that the subject of the work was ethical or political (Diog. ix. 15; R. P. 30 c). Diog. ix. 5 (R. P. 30). Bywater has followed this hint in his arrangement of the fragments. The three sections are 1-90, 91-97, 98-130.

The style of Herakleitos is proverbially obscure, and, at a later date, got him the nickname of “the Dark.” Now the fragments about the Delphic god and the Sibyl (frs. 11 and 12) seem to show that he was quite conscious of writing an oracular style, and we have to ask why he did so. In the first place, it was the manner of the time. The stirring events of the age, and the influence of the religious revival, gave something of a prophetic tone to all the leaders of thought. Pindar and Aischylos have it too. They all feel that they are in some measure inspired. It is also the age of great individualities, who are apt to be solitary and disdainful. Herakleitos at least was so. If men cared to dig for the gold they might find it (fr. 8); if not, they must be content with straw (fr. 51). This seems to have been the view taken by Theophrastos, who said that the headstrong temperament of Herakleitos sometimes led him into incompleteness and inconsistencies of statement. But that is a very different thing from studied obscurity and the disciplina arcani sometimes attributed to him; if Herakleitos does not go out of his way to make his meaning clear, neither does he hide it (fr. 11).

R. P. 30 a. The epithet ὁ σκοτεινός is of late date, but Timon of Phleious already called him αἰνικτής (fr. 43, Diels). See the valuable observations of Diels in the Introduction to his Herakleitos von Ephesos, pp. iv. sqq. Cf. Diog. ix. 6 (R. P. 31). [Sidenote: The fragments.] 65. I give a version of the fragments according to the arrangement of Mr. Bywater’s exemplary edition. (1) It is wise to hearken, not to me, but to my Word, and to confess that all things are one. R. P. 40. (2) Though this Word is true evermore, yet men are as unable to understand it when they hear it for the first time as before they have heard it at all. For, though all things come to pass in accordance with this Word, men seem as if they had no experience of them, when they make trial of words and deeds such as I set forth, dividing each thing according to its nature and showing how it truly is. But other men know not what they are doing when awake, even as they forget what they do in sleep. R. P. 32. (3) Fools when they do hear are like the deaf: of them does the saying bear witness that they are absent when present. R. P. 31 a.

(4) Eyes and ears are bad witnesses to men if they have souls that understand not their language. R. P. 42. (5) The many do not take heed of such things as those they meet with, nor do they mark them when they are taught, though they think they do. (6) Knowing not how to listen nor how to speak. (7) If you do not expect the unexpected, you will not find it; for it is hard to be sought out and difficult. (8) Those who seek for gold dig up much earth and find a little. R. P. 44 b. (10) Nature loves to hide. R. P. 34 f. (11) The lord whose is the oracle at Delphoi neither utters nor hides his meaning, but shows it by a sign. R. P. 30 a. (12) And the Sibyl, with raving lips uttering things mirthless, unbedizened, and unperfumed, reaches over a thousand years with her voice, thanks to the god in her. R. P. 30 a. (13) The things that can be seen, heard, and learned are what I prize the most. R. P. 42. (14) ... bringing untrustworthy witnesses in support of disputed points. (15) The eyes are more exact witnesses than the ears. R. P. 42 c.

(16) The learning of many things teacheth not understanding, else would it have taught Hesiod and Pythagoras, and again Xenophanes and Hekataios. R. P. 31. (17) Pythagoras, son of Mnesarchos, practised inquiry beyond all other men, and choosing out these writings, claimed for his own wisdom what was but a knowledge of many things and an art of mischief. R. P. 31 a. (18) Of all whose discourses I have heard, there is not one who attains to understanding that wisdom is apart from all. R. P. 32 b. (19) Wisdom is one thing. It is to know the thought by which all things are steered through all things. R. P. 40. (20) This world, which is the same for all, no one of gods or men has made; but it was ever, is now, and ever shall be an ever-living Fire, with measures kindling, and measures going out. R. P. 35. (21) The transformations of Fire are, first of all, sea; and half of the sea is earth, half whirlwind. ... R. P. 35 b. (22) All things are an exchange for Fire, and Fire for all things, even as wares for gold and gold for wares. R. P. 35.

(23) It becomes liquid sea, and is measured by the same tale as before it became earth. R. P. 39. (24) Fire is want and surfeit. R. P. 36 a. (25) Fire lives the death of air, and air lives the death of fire; water lives the death of earth, earth that of water. R. P. 37. (26) Fire in its advance will judge and convict all things. R. P. 36 a. (27) How can one hide from that which never sets? (28) It is the thunderbolt that steers the course of all things. R. P. 35 b. (29) The sun will not overstep his measures; if he does, the Erinyes, the handmaids of Justice, will find him out. R. P. 39. (30) The limit of East and West is the Bear; and opposite the Bear is the boundary of bright Zeus. (31) If there were no sun it would be night, for all the other stars could do. (32) The sun is new every day. (33) See above, Chap. I. p. 41, n. 62. (34) ... the seasons that bring all things. (35) Hesiod is most men’s teacher. Men think he knew very many things, a man who did not know day or night! They are one. R. P. 39 b.

(36) God is day and night, winter and summer, war and peace, surfeit and hunger; but he takes various shapes, just as fire, when it is mingled with spices, is named according to the savour of each. R. P. 39 b. (37) If all things were turned to smoke, the nostrils would distinguish them. (38) Souls smell in Hades. R. P. 46 d. (39) Cold things become warm, and what is warm cools; what is wet dries, and the parched is moisted. (40) It scatters and it gathers; it advances and retires. (41, 42) You cannot step twice into the same rivers; for fresh waters are ever flowing in upon you. R. P. 33. (43) Homer was wrong in saying: “Would that strife might perish from among gods and men!” He did not see that he was praying for the destruction of the universe; for, if his prayer were heard, all things would pass away.... R. P. 34 d. (44) War is the father of all and the king of all; and some he has made gods and some men, some bond and some free. R. P. 34. (45) Men do not know how what is at variance agrees with itself. It is an attunement of opposite tensions, like that of the bow and the lyre. R. P. 34.

(46) It is the opposite which is good for us. (47) The hidden attunement is better than the open. R. P. 34. (48) Let us not conjecture at random about the greatest things. (49) Men that love wisdom must be acquainted with very many things indeed. (50) The straight and the crooked path of the fuller’s comb is one and the same. (51) Asses would rather have straw than gold. R. P. 31 a. (51_a_) Oxen are happy when they find bitter vetches to eat. R. P. 48 b. (52) The sea is the purest and the impurest water. Fish can drink it, and it is good for them; to men it is undrinkable and destructive. R. P. 47 c. (53) Swine wash in the mire, and barnyard fowls in dust. (54) ... to delight in the mire. (55) Every beast is driven to pasture with blows. (56) Same as 45. (57) Good and ill are one. R. P. 47 c. (58) Physicians who cut, burn, stab, and rack the sick, demand a fee for it which they do not deserve to get. R. P. 47 c.

(59) Couples are things whole and things not whole, what is drawn together and what is drawn asunder, the harmonious and the discordant. The one is made up of all things, and all things issue from the one. (60) Men would not have known the name of justice if these things were not. (61) To God all things are fair and good and right, but men hold some things wrong and some right. R. P. 45. (62) We must know that war is common to all and strife is justice, and that all things come into being and pass away (?) through strife. (64) All the things we see when awake are death, even as all we see in slumber are sleep. R. P. 42 c. (65) The wise is one only. It is unwilling and willing to be called by the name of Zeus. R. P. 40. (66) The bow (βιός) is called life (βίος), but its work is death. R. P. 49 a. (67) Mortals are immortals and immortals are mortals, the one living the others’ death and dying the others’ life. R. P. 46. (68) For it is death to souls to become water, and death to water to become earth. But water comes from earth; and from water, soul. R. P. 38.

(69) The way up and the way down is one and the same. R. P. 36 d. (70) In the circumference of a circle the beginning and end are common. (71) You will not find the boundaries of soul by travelling in any direction, so deep is the measure of it. R. P. 41 d. (72) It is pleasure to souls to become moist. R. P. 46 c. (73) A man, when he gets drunk, is led by a beardless lad, tripping, knowing not where he steps, having his soul moist. R. P. 42. (74-76) The dry soul is the wisest and best. R. P. 42. (77) Man is kindled and put out like a light in the night-time. (78) And it is the same thing in us that is quick and dead, awake and asleep, young and old; the former are shifted and become the latter, and the latter in turn are shifted and become the former. R. P. 47. (79) Time is a child playing draughts, the kingly power is a child’s. R. P. 40 a. (80) I have sought for myself. R. P. 48. (81) We step and do not step into the same rivers; we are and are not. R. P. 33 a.

(82) It is a weariness to labour for the same masters and be ruled by them. (83) It rests by changing. (84) Even the posset separates if it is not stirred. (85) Corpses are more fit to be cast out than dung. (86) When they are born, they wish to live and to meet with their dooms—or rather to rest—and they leave children behind them to meet with their dooms in turn. (87-89) A man may be a grandfather in thirty years. (90) Those who are asleep are fellow-workers.... (91_a_) Thought is common to all. (91_b_) Those who speak with understanding must hold fast to what is common to all as a city holds fast to its law, and even more strongly. For all human laws are fed by the one divine law. It prevails as much as it will, and suffices for all things with something to spare. R. P. 43. (92) So we must follow the common, yet the many live as if they had a wisdom of their own. R. P. 44. (93) They are estranged from that with which they have most constant intercourse. R. P. 32 b. (94) It is not meet to act and speak like men asleep.

(95) The waking have one common world, but the sleeping turn aside each into a world of his own. (96) The way of man has no wisdom, but that of God has. R. P. 45. (97) Man is called a baby by God, even as a child by a man. R. P. 45. (98, 99) The wisest man is an ape compared to God, just as the most beautiful ape is ugly compared to man. (100) The people must fight for its law as for its walls. R. P. 43 b. (101) Greater deaths win greater portions. R. P. 49 a. (102) Gods and men honour those who are slain in battle. R. P. 49 a. (103) Wantonness needs putting out, even more than a house on fire. R. P. 49 a. (104) It is not good for men to get all they wish to get. It is sickness that makes health pleasant; evil, good; hunger, plenty; weariness, rest. R. P. 48 b. (105-107) It is hard to fight with one’s heart’s desire. Whatever it wishes to get, it purchases at the cost of soul. R. P. 49 a. (108, 109) It is best to hide folly; but it is hard in times of relaxation, over our cups.

(110) And it is law, too, to obey the counsel of one. R. P. 49 a. (111) For what thought or wisdom have they? They follow the poets and take the crowd as their teacher, knowing not that there are many bad and few good. For even the best of them choose one thing above all others, immortal glory among mortals, while most of them are glutted like beasts. R. P. 31 a. (112) In Priene lived Bias, son of Teutamas, who is of more account than the rest. (He said, “Most men are bad.”) (113) One is ten thousand to me, if he be the best. R. P. 31 a. (114) The Ephesians would do well to hang themselves, every grown man of them, and leave the city to beardless lads; for they have cast out Hermodoros, the best man among them, saying, “We will have none who is best among us; if there be any such, let him be so elsewhere and among others.” R. P. 29 b. (115) Dogs bark at every one they do not know. R. P. 31 a. (116) ... (The wise man) is not known because of men’s want of belief. (117) The fool is fluttered at every word. R. P. 44 b.

(118) The most esteemed of them knows but fancies; yet of a truth justice shall overtake the artificers of lies and the false witnesses. (119) Homer should be turned out of the lists and whipped, and Archilochos likewise. R. P. 31. (120) One day is like any other. (121) Man’s character is his fate. (122) There awaits men when they die such things as they look not for nor dream of. R. P. 46 d. (123) ... that they rise up and become the wakeful guardians of the quick and dead. R. P. 46 d. (124) Night-walkers, Magians, priests of Bakchos and priestesses of the wine-vat, mystery-mongers.... (125) The mysteries practised among men are unholy mysteries. R. P. 48. (126) And they pray to these images, as if one were to talk with a man’s house, knowing not what gods or heroes are. R. P. 49 a. (127) For if it were not to Dionysos that they made a procession and sang the shameful phallic hymn, they would be acting most shamelessly. But Hades is the same as Dionysos in whose honour they go mad and keep the feast of the wine-vat. R. P. 49.

(129, 130) They vainly purify themselves by defiling themselves with blood, just as if one who had stepped into the mud were to wash his feet in mud. Any man who marked him doing thus, would deem him mad. R. P. 49 a. In his edition, Diels has given up all attempt to arrange the fragments according to subject, and this makes his text unsuitable for our purpose. I think, too, that he overestimates the difficulty of an approximate arrangement, and makes too much of the view that the style of Herakleitos was “aphoristic.” That it was so, is an important and valuable remark; but it does not follow that Herakleitos wrote like Nietzsche. For a Greek, however prophetic in his tone, there must always be a distinction between an aphoristic and an incoherent style. See the excellent remarks of Lortzing in Berl. Phil. Wochenschr. 1896, pp. 1 sqq. Both Bywater and Diels accept Bergk’s λόγου for δόγματος and Miller’s εἶναι for εἰδέναι. Cf. Philo, leg. all. iii. c, quoted in Bywater’s note.