The scientific character of the early Greek cosmology.
XIII. It is necessary to say something as to the scientific worth of the philosophy we are about to study. We have just seen that the Eastern peoples were, at the time of which we write, considerably richer than the Greeks in accumulated facts, though these facts had certainly not been observed for any scientific purpose, and their possession never suggested a revision of the primitive view of the world. The Greeks, however, saw in them something that could be turned to account, and they were never as a people slow to act on the maxim,Chacun prend son bien partout où il le trouve. The most striking monument of this spirit which has come down to us is the work of Herodotos; and the visit of Solon to Croesus which he describes, however unhistorical it may be, gives a very lively and faithful picture of it. Croesus tells Solon that he has heard much of “his wisdom and his wanderings,” and how, from love of knowledge (φιλοσοφέων), he has travelled over much land for the purpose of seeing what was to be seen (θεωρίης εἵνεκεν). The words θεωρίη, φιλοσοφίη, and ἱστορίη are, in fact, the catchwords of the time, though they had, we must remember, a somewhat different meaning from that which they were afterwards made to bear at Athens.[42]The idea that underlies them all may, perhaps, be best rendered in English by the wordCuriosity; and it was just thisgreat gift of curiosity, and the desire to see all the wonderful things—pyramids, inundations, and so forth—that were to be seen, which enabled the Greeks to pick up and turn to their own use such scraps of knowledge as they could come by among the barbarians. No sooner did a Greek philosopher learn half a dozen geometrical propositions, and hear that the phenomena of the heavens recur in cycles, than he set to work to look for law everywhere in nature, and, with a splendid audacity, almost amounting to ὕβρις, to construct a system of the universe. We may smile, if we please, at the strange medley of childish fancy and true scientific insight which these Titanic efforts display, and sometimes we feel disposed to sympathise with the sages of the day who warned their more daring contemporaries “to think the thoughts befitting man’s estate” (ἀνθρώπινα φρονεῖν). But we shall do well to remember at the same time that even now it is just such hardy anticipations of experience that make scientific progress possible, and that nearly every one of the early inquirers whom we are about to study made some permanent addition to the store of positive knowledge, besides opening up new views of the world in every direction.
There is no justification either for the idea that Greek science was built up solely by more or less lucky guesswork, instead of by observation and experiment. The nature of our tradition, which mostly consists ofPlacita—that is, of what we call “results”—tends, no doubt, to create this impression. We are seldom told why any early philosopher held the views he did, and the appearance of a string of “opinions” suggests dogmatism. There are, however, certain exceptions to the general character of the tradition; and we mayreasonably suppose that, if the later Greeks had been interested in the matter, there would have been many more. We shall see that Anaximander made some remarkable discoveries in marine biology, which the researches of the nineteenth century have fully confirmed (§ 21), and even Xenophanes supported one of his theories by referring to the fossils and petrifactions of such widely separated places as Malta, Paros, and Syracuse (§ 59). This is enough to show that the theory, so commonly held by the earlier philosophers, that the earth had been originally in a moist state, was not mythological in origin, but was based on, or at any rate confirmed by, biological and palaeontological observations of a thoroughly modern and scientific type. It would surely be absurd to imagine that the men who could make these observations had not the curiosity or the ability to make many others of which the memory is lost. Indeed, the idea that the Greeks were not observers is almost ludicrously wrong, as is proved by two simple considerations. The anatomical accuracy of Greek sculpture bears witness to trained habits of observation, and those of the highest order, while the fixing of the seasons by the heliacal rising and setting of the stars shows a familiarity with celestial phenomena which is by no means common at the present day.[43]We know, then, that the Greeks could observe well in matters affecting agriculture, navigation, and the arts, and we know that they were curious about the world. Is it conceivable that they did not use their powers of observation to gratify that curiosity? It is true, of course, that they had not ourinstruments of precision; but a great deal can be discovered by the help of very simple apparatus. It is not to be supposed that Anaximander erected hisgnomonmerely that the Spartans might know the seasons.[44]
Nor is it true that the Greeks made no use of experiment. The rise of the experimental method dates from the time when the medical schools began to influence the development of philosophy, and accordingly we find that the first recorded experiment of a modern type is that of Empedokles with theklepsydra. We have his own account of this (fr.100), and we can see how it brought him to the verge of anticipating both Harvey and Torricelli. It is once more inconceivable that an inquisitive people should have applied the experimental method in a single case without extending it to the elucidation of other problems.
Of course the great difficulty for us is the geocentric hypothesis from which science inevitably started, though only to outgrow it in a surprisingly short time. So long as the earth is supposed to be in the centre of the world, meteorology, in the later sense of the word, is necessarily identified with astronomy. It is difficult for us to feel at home in this point of view, and indeed we have no suitable word to express what the Greeks at first called an οὐρανός. It will be convenient to use the word “world” for it; but then we must remember that it does not refer solely, or even chiefly,to the earth. The later word κόσμος bears witness to the growth of scientific ideas. It meant at first the marshalling of an army, and next the ordered constitution of a state. It was transferred from this to the world because in early days the regularity and constancy of human life was far more clearly seen than the uniformity of nature. Man lived in a charmed circle of law and custom, but the world around him still seemed lawless. That, too, is why, when the regular course of nature was first realised, no better word for it could be found than δίκη. It is the same metaphor which still lives on in the expression “natural law.”[45]
The science of the sixth century was mainly concerned, then, with those parts of the world that are “aloft” (τὰ μετέωρα), and these include, along with the heavenly bodies, such things as clouds, rainbows, and lightning. That is how the heavenly bodies came sometimes to be explained as ignited clouds, an idea which seems astonishing to us. But we must bear in mind that science inevitably and rightly began with the most obvious hypothesis, and that it was only the thorough working out of this that could show its inadequacy. It is just because the Greeks were the first people to take the geocentric hypothesis seriously that they were able to go beyond it. Of course the pioneers of Greek thought had no clear idea of the nature of scientific hypothesis, and supposed themselves to be dealing with ultimate reality. That was inevitable before the rise of Logic. At the sametime, a sure instinct guided them to the right method, and we can see how it was the effort to “save appearances”[46]that really operated from the first. It is, therefore, to those men that we owe the conception of an exact science which should ultimately take in the whole world as its object. They fancied—absurdly enough, no doubt—that they could work out this science at once. We sometimes make the same mistake nowadays; and it can no more rob the Greeks of the honour of having been the first to see the true, though perhaps unattainable, end of all science than it can rob our own scientific men of the honour of having brought that end nearer than it was. It is still knowledge of the kind foreseen and attempted by the Greeks that they are in search of.
Schools of philosophy.
XIV. Theophrastos, the first writer to treat the history of Greek philosophy in a systematic way,[47]represented the early cosmologists as standing to one another in the relation of master and scholar, and as members of regular societies. This has been regarded by many modern writers as an anachronism, and some have even denied the existence of “schools” of philosophy altogether. Such a reaction against the older view was quite justified in so far as it was directed against arbitrary classifications like the “Ionic” and “Italian” schools, which are derived through Laertios Diogenes from the Alexandrian writers of “Successions.” But the express statements of Theophrastos are notto be so lightly set aside. As this point is of great importance, it will be necessary to elucidate it still further before we enter upon our story.
The modern view really rests upon a mistaken idea of the way in which civilisation develops. In almost every department of life, we find that the corporation at first is everything and the individual nothing. The peoples of the East hardly got beyond this stage at all; their science, such as it is, is anonymous, the inherited property of a caste or guild, and we still see clearly in some cases that it was once the same among the Hellenes. Medicine, for instance, was originally the “mystery” of the Asklepiads, and it is to be supposed that all craftsmen (δημιουργοί), amongst whom Homer classes the bards (ἀοιδοί), were at first organised in a similar way. What distinguished the Hellenes from other peoples was that at a comparatively early date these crafts came under the influence of outstanding individuals, who gave them a fresh direction and a new impulse. It is doubtless in some such way that we should understand the relation of Homer to the Homeridai. The Asklepiads at a later date produced Hippokrates, and if we knew more of such guilds as the Daidalids, it is likely we should find something of the same kind. But this does not destroy the corporate character of the craft; indeed, it rather intensifies it. The guild becomes what we call a “school,” and the disciple takes the place of the apprentice. That is a vital change. A close guild with none but official heads is essentially conservative, while a band of disciples attached to a master they revere is the greatest progressive force the world knows.
It is certain that the later Athenian schools wereorganised corporations, the oldest of which, the Academy, maintained its existence as such for some nine hundred years, and the only question we have to decide is whether this was an innovation made in the fourth centuryB.C., or rather the continuance of an old tradition. As it happens, we have the authority of Plato for speaking of the chief early systems as handed down in schools. He makes Sokrates speak of “the men of Ephesos,” the Herakleiteans, as forming a strong body in his own day,[48]and the stranger of theSophistand theStatesmanspeaks of his school as still in existence at Elea.[49]We also hear of “Anaxagoreans,”[50]and no one, of course, can doubt that the Pythagoreans were a society. In fact, there is hardly any school but that of Miletos for which we have not external evidence of the strongest kind; and even as regards it, we have the significant fact that Theophrastos speaks of philosophers of a later date as having been “associates of the philosophy of Anaximenes.”[51]We shall see too in the first chapter that the internal evidence in favour of the existence of a Milesian school is very strong indeed. It is from this point of view, then, that we shall now proceed to consider the men who created Hellenic science.
1. It will be observed that Demokritos falls outside the period thus limited. The common practice of treating this younger contemporary of Sokrates along with the “pre-Socratic philosophers” obscures the true course of historical development. Demokritos comes after Protagoras, and his theory is already conditioned by the epistemological problem. (See Brochard,“Protagoras et Démocrite,”Arch.ii. p. 368.) He has also a regular theory of conduct (E. Meyer,Gesch. des Alterth.iv. § 514 n.).
1. It will be observed that Demokritos falls outside the period thus limited. The common practice of treating this younger contemporary of Sokrates along with the “pre-Socratic philosophers” obscures the true course of historical development. Demokritos comes after Protagoras, and his theory is already conditioned by the epistemological problem. (See Brochard,“Protagoras et Démocrite,”Arch.ii. p. 368.) He has also a regular theory of conduct (E. Meyer,Gesch. des Alterth.iv. § 514 n.).
2. See E. Meyer,Gesch. des Alterth.ii. § 64; Menzies,History of Religion, pp. 272-276.
2. See E. Meyer,Gesch. des Alterth.ii. § 64; Menzies,History of Religion, pp. 272-276.
3. On all this, see especially Rohde,Psyche, pp. 14 sqq.
3. On all this, see especially Rohde,Psyche, pp. 14 sqq.
4. Hes.Theog.27. They are the same Muses who inspired Homer, which means, in our language, that Hesiod wrote in hexameters and used the Epic dialect. The new literarygenrehas not yet found its appropriate vehicle, which is elegy.
4. Hes.Theog.27. They are the same Muses who inspired Homer, which means, in our language, that Hesiod wrote in hexameters and used the Epic dialect. The new literarygenrehas not yet found its appropriate vehicle, which is elegy.
5. There is great historical insight here. It was Hesiod, not our modern historians, who first pointed out that the “Greek Middle Ages” were a break in the normal development.
5. There is great historical insight here. It was Hesiod, not our modern historians, who first pointed out that the “Greek Middle Ages” were a break in the normal development.
6. Herod. ii. 53.
6. Herod. ii. 53.
7. The word χάος certainly means the “gape” or “yawn,” the Orphic χάσμα πελώριον. Grimm compared it with the ScandinavianGinnunga-Gap.
7. The word χάος certainly means the “gape” or “yawn,” the Orphic χάσμα πελώριον. Grimm compared it with the ScandinavianGinnunga-Gap.
8. Quoted from Taylor’sNew Zealand, pp. 110-112, by Mr. Andrew Lang, inMyth, Ritual, and Religion, vol. ii. p. 52 (2nd ed.).
8. Quoted from Taylor’sNew Zealand, pp. 110-112, by Mr. Andrew Lang, inMyth, Ritual, and Religion, vol. ii. p. 52 (2nd ed.).
9. For the remains of Pherekydes, see Diels,Vorsokratiker, pp. 506 sqq. (1st ed.), and the interesting account in Gomperz,Greek Thinkers, vol. i. pp. 85 sqq.
9. For the remains of Pherekydes, see Diels,Vorsokratiker, pp. 506 sqq. (1st ed.), and the interesting account in Gomperz,Greek Thinkers, vol. i. pp. 85 sqq.
10. This was the view of Lobeck with regard to the so-called “Rhapsodic Theogony” described by Damaskios, and was revived by Otto Kern (De Orphei Epimenidis Pherecydis Theogoniis, 1888). Its savage character is the best proof of its antiquity. Cf. Lang,Myth, Ritual, and Religion, vol. i. chap. x.
10. This was the view of Lobeck with regard to the so-called “Rhapsodic Theogony” described by Damaskios, and was revived by Otto Kern (De Orphei Epimenidis Pherecydis Theogoniis, 1888). Its savage character is the best proof of its antiquity. Cf. Lang,Myth, Ritual, and Religion, vol. i. chap. x.
11. Arist.Met.Ν, 4. 1091 b 8.
11. Arist.Met.Ν, 4. 1091 b 8.
12. Simonides, fr. 85, 2 Bergk.Il.vi. 146.
12. Simonides, fr. 85, 2 Bergk.Il.vi. 146.
13. On Adonis-Thammuz, Lityerses, Linos, and Osiris, see Frazer,Golden Bough, vol. i. pp. 278 sqq.
13. On Adonis-Thammuz, Lityerses, Linos, and Osiris, see Frazer,Golden Bough, vol. i. pp. 278 sqq.
14. The Epic phrase ἀθάνατος καὶ ἀγήρως seems to have suggested this. Anaximander applied both epithets to the primary substance (R. P. 17 and 17 a). Euripides, in describing the blessedness of the scientific life (fr. inc. 910), says ἀθανάτου ... φύσεως κόσμον ἀγήρω (R. P. 148 c fin.).
14. The Epic phrase ἀθάνατος καὶ ἀγήρως seems to have suggested this. Anaximander applied both epithets to the primary substance (R. P. 17 and 17 a). Euripides, in describing the blessedness of the scientific life (fr. inc. 910), says ἀθανάτου ... φύσεως κόσμον ἀγήρω (R. P. 148 c fin.).
15. I do not mean to imply that the philosophers used this title themselves; for early prose writings had no titles. The writer mentioned his name and the subject of his work in the first sentence, as Herodotos, for instance, does.
15. I do not mean to imply that the philosophers used this title themselves; for early prose writings had no titles. The writer mentioned his name and the subject of his work in the first sentence, as Herodotos, for instance, does.
16. Plato,Laws, 892 c 2, φύσιν βούλονται λέγειν γένεσιν (i.e.τὸ ἐξ οὗ γίγνεται) τὴν περὶ τὰ πρῶτα (i.e.τὴν τῶν πρώτων). Arist.Phys.Β, 1. 193 a 21, διόπερ οἱ μὲν πῦρ, οἱ δὲ γῆν, οἱ δ’ ἀέρα φασίν, οἱ δὲ ὗδωρ, οἱ δ’ ἔνια τούτων, οἱ δὲ πάντα ταῦτα τὴν φύσιν εἶναι τὴν τῶν ὄντων.
16. Plato,Laws, 892 c 2, φύσιν βούλονται λέγειν γένεσιν (i.e.τὸ ἐξ οὗ γίγνεται) τὴν περὶ τὰ πρῶτα (i.e.τὴν τῶν πρώτων). Arist.Phys.Β, 1. 193 a 21, διόπερ οἱ μὲν πῦρ, οἱ δὲ γῆν, οἱ δ’ ἀέρα φασίν, οἱ δὲ ὗδωρ, οἱ δ’ ἔνια τούτων, οἱ δὲ πάντα ταῦτα τὴν φύσιν εἶναι τὴν τῶν ὄντων.
17. Zeller, p. 217, n. 2 (Eng. trans. p. 248, n. 2). See below, Chap. I. p. 57,n.105.
17. Zeller, p. 217, n. 2 (Eng. trans. p. 248, n. 2). See below, Chap. I. p. 57,n.105.
18. We have the authority of Plato for giving them this name. Cf.Phd.96 a 7, ταύτης τῆς σοφίας ἣν δὴ καλοῦσι περὶ φύσεως ἱστορίαν. So, in the fragment of Euripides referred to on p. 12,n.14, the man who discerns “the ageless order of immortal φύσις” is referred to as ὅστις τῆς ἱστορίας ἔσχε μάθησιν.
18. We have the authority of Plato for giving them this name. Cf.Phd.96 a 7, ταύτης τῆς σοφίας ἣν δὴ καλοῦσι περὶ φύσεως ἱστορίαν. So, in the fragment of Euripides referred to on p. 12,n.14, the man who discerns “the ageless order of immortal φύσις” is referred to as ὅστις τῆς ἱστορίας ἔσχε μάθησιν.
19. Herod. i. 163.
19. Herod. i. 163.
20. All he can say is that the worship of Dionysos and the doctrine of transmigration came from Egypt (ii. 49, 123). We shall see that both these statements are incorrect, and in any case they do not imply anything directly as to philosophy.
20. All he can say is that the worship of Dionysos and the doctrine of transmigration came from Egypt (ii. 49, 123). We shall see that both these statements are incorrect, and in any case they do not imply anything directly as to philosophy.
21. InRep.435 e, after saying that τὸ θυμοειδές is characteristic of the Thracians and Scythians, and τὸ φιλομαθές of the Hellenes, he refers us to Phoenicia and Egypt for τὸ φιλοχρήματον. In theLaws, where the Egyptians are so strongly commended for their conservatism in matters of art, he says (747 b 6) that arithmetical studies are valuable only if we remove all ἀνελευθερία and φιλοχρηματία from the souls of the learners. Otherwise, we produce πανουργία instead of σοφία, as we can see that the Phoenicians, the Egyptians, and many other peoples do.
21. InRep.435 e, after saying that τὸ θυμοειδές is characteristic of the Thracians and Scythians, and τὸ φιλομαθές of the Hellenes, he refers us to Phoenicia and Egypt for τὸ φιλοχρήματον. In theLaws, where the Egyptians are so strongly commended for their conservatism in matters of art, he says (747 b 6) that arithmetical studies are valuable only if we remove all ἀνελευθερία and φιλοχρηματία from the souls of the learners. Otherwise, we produce πανουργία instead of σοφία, as we can see that the Phoenicians, the Egyptians, and many other peoples do.
22. Arist.Met.Α, 1. 981 b 23.
22. Arist.Met.Α, 1. 981 b 23.
23. See Zeller, p. 3, n. 2. Philo applies the term πάτριος φιλοσοφία to the theology of the Essenes and Therapeutai.
23. See Zeller, p. 3, n. 2. Philo applies the term πάτριος φιλοσοφία to the theology of the Essenes and Therapeutai.
24. On this, see Lang,Myth, Ritual, and Religion, vol. ii. p. 135.
24. On this, see Lang,Myth, Ritual, and Religion, vol. ii. p. 135.
25. Noumenios, fr. 13 (R. P. 624), Τί γάρ ἐστι Πλάτων ἢ Μωυσῆς ἀττικίζων;
25. Noumenios, fr. 13 (R. P. 624), Τί γάρ ἐστι Πλάτων ἢ Μωυσῆς ἀττικίζων;
26. Clement (Strom.i. p. 8, 5, Stählin) calls Plato ὁ ἐξ Ἑβραίων φιλόσοφος.
26. Clement (Strom.i. p. 8, 5, Stählin) calls Plato ὁ ἐξ Ἑβραίων φιλόσοφος.
27. We learn from Strabo (xvi. p. 757) that it was Poseidonios who introduced Mochos of Sidon into the history of philosophy. He attributes the atomic theory to him. His identification with Moses, however, is a latertour de force. Philon of Byblos published what purported to be a translation of an ancient Phoenician history by Sanchuniathon, which was used by Porphyry and afterwards by Eusebios. How familiar all this became, is shown by the speech of the stranger in theVicar of Wakefield, chap. xiv.
27. We learn from Strabo (xvi. p. 757) that it was Poseidonios who introduced Mochos of Sidon into the history of philosophy. He attributes the atomic theory to him. His identification with Moses, however, is a latertour de force. Philon of Byblos published what purported to be a translation of an ancient Phoenician history by Sanchuniathon, which was used by Porphyry and afterwards by Eusebios. How familiar all this became, is shown by the speech of the stranger in theVicar of Wakefield, chap. xiv.
28. Herod. ii. 143; Plato,Tim.22 b 3.
28. Herod. ii. 143; Plato,Tim.22 b 3.
29. Gomperz’s “native bride,” who discusses the wisdom of her people with her Greek lord (Greek Thinkers, vol. i. p. 95), does not convince me either. She would probably teach her maids the rites of strange goddesses; but she would not be likely to talk theology with her husband, and still less philosophy or science. The use of Babylonian as an international language will account for the fact that the Egyptians knew something of Babylonian astronomy; but it does not help us to explain how the Greeks could communicate with the Egyptians. It is plain that the Greeks did not even know of this international language; for it is just the sort of thing they would have recorded with interest if they had. In early days, they may have met with it in Cyprus, but that was apparently forgotten.
29. Gomperz’s “native bride,” who discusses the wisdom of her people with her Greek lord (Greek Thinkers, vol. i. p. 95), does not convince me either. She would probably teach her maids the rites of strange goddesses; but she would not be likely to talk theology with her husband, and still less philosophy or science. The use of Babylonian as an international language will account for the fact that the Egyptians knew something of Babylonian astronomy; but it does not help us to explain how the Greeks could communicate with the Egyptians. It is plain that the Greeks did not even know of this international language; for it is just the sort of thing they would have recorded with interest if they had. In early days, they may have met with it in Cyprus, but that was apparently forgotten.
30. For the possibility that Indian philosophy came from Greece, see Weber,Die Griechen in Indien(Berl. Sitzb. 1890, pp. 901 sqq.), and Goblet d’Alviella,Ce que l’Inde doit à la Grèce(Paris, 1897).
30. For the possibility that Indian philosophy came from Greece, see Weber,Die Griechen in Indien(Berl. Sitzb. 1890, pp. 901 sqq.), and Goblet d’Alviella,Ce que l’Inde doit à la Grèce(Paris, 1897).
31. I am indebted for most of the information which follows to Cantor’sVorlesungen über Geschichte der Mathematik, vol. i. pp. 46-63. See also Gow’sShort History of Greek Mathematics, §§ 73-80; and Milhaud,La science grecque, pp. 91 sqq. The discussion in the last-named work is of special value because it is based on M. Rodet’s paper in theBulletin de la Société Mathématique, vol. vi., which in some important respects supplements the interpretation of Eisenlohr, on which the earlier accounts depend.
31. I am indebted for most of the information which follows to Cantor’sVorlesungen über Geschichte der Mathematik, vol. i. pp. 46-63. See also Gow’sShort History of Greek Mathematics, §§ 73-80; and Milhaud,La science grecque, pp. 91 sqq. The discussion in the last-named work is of special value because it is based on M. Rodet’s paper in theBulletin de la Société Mathématique, vol. vi., which in some important respects supplements the interpretation of Eisenlohr, on which the earlier accounts depend.
32. Plato,Laws, 819 b 4, μήλων τέ τινων διανομαὶ καὶ στεφάνων πλείοσιν ἄμα καὶ ἐλάττοσιν ἁρμοττόντων ἀριθμῶν τῶν αὐτῶν, καὶ πυκτῶν καὶ παλαιστῶν ἐφεδρείας τε καὶ συλλήξεως ἐν μέρει καὶ ἐφεξῆς καὶ ὡς πεφύκασι γίγνεσθαι. καὶ δὴ καὶ παίζοντες, φιάλας ἅμα χρυσοῦ καὶ χαλκοῦ καὶ ἀργύρου καὶ τοιούτων τινῶν ἄλλων κεραννύντες, οἱ δὲ καὶ ὅλας πως διαδιδόντες. In its context, the passage implies that no more than this could be learnt in Egypt.
32. Plato,Laws, 819 b 4, μήλων τέ τινων διανομαὶ καὶ στεφάνων πλείοσιν ἄμα καὶ ἐλάττοσιν ἁρμοττόντων ἀριθμῶν τῶν αὐτῶν, καὶ πυκτῶν καὶ παλαιστῶν ἐφεδρείας τε καὶ συλλήξεως ἐν μέρει καὶ ἐφεξῆς καὶ ὡς πεφύκασι γίγνεσθαι. καὶ δὴ καὶ παίζοντες, φιάλας ἅμα χρυσοῦ καὶ χαλκοῦ καὶ ἀργύρου καὶ τοιούτων τινῶν ἄλλων κεραννύντες, οἱ δὲ καὶ ὅλας πως διαδιδόντες. In its context, the passage implies that no more than this could be learnt in Egypt.
33. Herod. ii. 109; Arist.Met.Α, 1. 981 b 23.
33. Herod. ii. 109; Arist.Met.Α, 1. 981 b 23.
34. For a fuller account of this method, see Gow,Short History of Greek Mathematics, pp. 127 sqq.; and Milhaud,Science grecque, p. 99.
34. For a fuller account of this method, see Gow,Short History of Greek Mathematics, pp. 127 sqq.; and Milhaud,Science grecque, p. 99.
35. R. P. 188.
35. R. P. 188.
36. The real meaning of ἁρπεδονάπτης was first pointed out by Cantor. The gardener laying out a flower-bed is the true modern representative of the “harpedonapts.”
36. The real meaning of ἁρπεδονάπτης was first pointed out by Cantor. The gardener laying out a flower-bed is the true modern representative of the “harpedonapts.”
37. See Milhaud,Science grecque, p. 103.
37. See Milhaud,Science grecque, p. 103.
38. The word πυραμίς is often supposed to be derived from the termpiremusused in the Rhind papyrus, which does not mean pyramid, but “ridge.” It is really, however, a Greek word too, and is the name of a kind of cake. The Greeks called crocodiles lizards, ostriches sparrows, and obelisks meat-skewers, so they may very well have called the pyramids cakes. We seem to hear an echo of the slang of the mercenaries that carved their names on the colossus at Abu-Simbel.
38. The word πυραμίς is often supposed to be derived from the termpiremusused in the Rhind papyrus, which does not mean pyramid, but “ridge.” It is really, however, a Greek word too, and is the name of a kind of cake. The Greeks called crocodiles lizards, ostriches sparrows, and obelisks meat-skewers, so they may very well have called the pyramids cakes. We seem to hear an echo of the slang of the mercenaries that carved their names on the colossus at Abu-Simbel.
39. Three different positions of the equinox are given in three different Babylonian tablets, namely, 10°, 8° 15′, and 8° 0′ 30″ of Aries. (Kugler,Mondrechnung, p. 103; Ginzel,Klio, i. p. 205.) Given knowledge of this kind, and the practice of formulating recurrences in cycles, it is scarcely conceivable that the Babylonians should not have invented a cycle for precession. It is equally intelligible that they should only have reached a rough approximation; for the precessional period is really about 27,600 years and not 36,000. It is to be observed that Plato’s “perfect year” is also 36,000 solar years (Adam’sRepublic, vol. ii. p. 302), and that it is probably connected with the precession of the equinoxes. (Cf.Tim.39 d, a passage which is most easily interpreted if referred to precession.) This suggestion as to the origin of the “Great Year” was thrown out by Mr. Adam (op. cit.p. 305), and is now confirmed by Hilprecht,The Babylonian Expedition of the University of Pennsylvania(Philadelphia, 1906).
39. Three different positions of the equinox are given in three different Babylonian tablets, namely, 10°, 8° 15′, and 8° 0′ 30″ of Aries. (Kugler,Mondrechnung, p. 103; Ginzel,Klio, i. p. 205.) Given knowledge of this kind, and the practice of formulating recurrences in cycles, it is scarcely conceivable that the Babylonians should not have invented a cycle for precession. It is equally intelligible that they should only have reached a rough approximation; for the precessional period is really about 27,600 years and not 36,000. It is to be observed that Plato’s “perfect year” is also 36,000 solar years (Adam’sRepublic, vol. ii. p. 302), and that it is probably connected with the precession of the equinoxes. (Cf.Tim.39 d, a passage which is most easily interpreted if referred to precession.) This suggestion as to the origin of the “Great Year” was thrown out by Mr. Adam (op. cit.p. 305), and is now confirmed by Hilprecht,The Babylonian Expedition of the University of Pennsylvania(Philadelphia, 1906).
40. In classical Greek literature, no planets but Ἕσπερος and Ἑωσφόρος are mentioned by name at all. Parmenides (or Pythagoras) first identified these as a single planet (§ 93). Mercury appears for the first time by name inTim.38 e, and the other divine names are given inEpin.987 b sq., where they are said to be “Syrian.” The Greek names Φαίνων, Φαέθων, Πυρόεις, Φωσφόρος, Στίλβων, may be older, but this cannot be proved.
40. In classical Greek literature, no planets but Ἕσπερος and Ἑωσφόρος are mentioned by name at all. Parmenides (or Pythagoras) first identified these as a single planet (§ 93). Mercury appears for the first time by name inTim.38 e, and the other divine names are given inEpin.987 b sq., where they are said to be “Syrian.” The Greek names Φαίνων, Φαέθων, Πυρόεις, Φωσφόρος, Στίλβων, may be older, but this cannot be proved.
41. The Platonic account of this matter is to be found in theEpinomis, 986 e 9 sqq., and is summed up by the words λάβωμεν δὲ ὡς ὅτιπερ ἂν Ἕλληνες βαρβάρων παραλάβωσι, κάλλιον τοῦτο εἰς τέλος ἀπεργάζονται (987 d 9). The point is well put by Theon (Adrastos),Exp.p. 177, 20 Hiller, who speaks of the Chaldaeans and Egyptians as ἄνευ φυσιολογίας ἀτελεῖς ποιούμενοι τὰς μεθόδους, δέον ἅμα καὶ φυσικῶς περὶ τούτων ἐπισκοπεῖν· ὅπερ οἱ παρὰ τοῖς Ἕλλησιν ἀστρολογήσαντες ἐπειρῶντο ποιεῖν, τὰς παρὰ τούτων λαβόντες ἀρχὰς καὶ τῶν φαινομένων τηρήσεις. The importance of this last passage is that it represents the view taken at Alexandria, where the facts were accurately known.
41. The Platonic account of this matter is to be found in theEpinomis, 986 e 9 sqq., and is summed up by the words λάβωμεν δὲ ὡς ὅτιπερ ἂν Ἕλληνες βαρβάρων παραλάβωσι, κάλλιον τοῦτο εἰς τέλος ἀπεργάζονται (987 d 9). The point is well put by Theon (Adrastos),Exp.p. 177, 20 Hiller, who speaks of the Chaldaeans and Egyptians as ἄνευ φυσιολογίας ἀτελεῖς ποιούμενοι τὰς μεθόδους, δέον ἅμα καὶ φυσικῶς περὶ τούτων ἐπισκοπεῖν· ὅπερ οἱ παρὰ τοῖς Ἕλλησιν ἀστρολογήσαντες ἐπειρῶντο ποιεῖν, τὰς παρὰ τούτων λαβόντες ἀρχὰς καὶ τῶν φαινομένων τηρήσεις. The importance of this last passage is that it represents the view taken at Alexandria, where the facts were accurately known.
42. Still, the word θεωρία never wholly lost its early associations, and the Greeks always felt that the θεωρητικὸς βίος meant literally “the life of the spectator.” Its special use, and the whole theory of the “three lives,” seem to be of Pythagorean origin. See my edition of Aristotle’sEthics, p. 19 n.
42. Still, the word θεωρία never wholly lost its early associations, and the Greeks always felt that the θεωρητικὸς βίος meant literally “the life of the spectator.” Its special use, and the whole theory of the “three lives,” seem to be of Pythagorean origin. See my edition of Aristotle’sEthics, p. 19 n.
43. These two points are rightly emphasised by Staigmüller,Beiträge zur Gesch. der Naturwissenschaften im klassischen Altertume(Progr. Stuttgart, 1899, p. 8).
43. These two points are rightly emphasised by Staigmüller,Beiträge zur Gesch. der Naturwissenschaften im klassischen Altertume(Progr. Stuttgart, 1899, p. 8).
44. The gnomon was not a sundial, but an upright erected on a flat surface, in the centre of three concentric circles. These were drawn so that the end of the gnomon’s shadow touched the innermost circle at midday on the summer solstice, the intermediate circle at the equinoxes, and the outermost circle at the winter solstice. See Bretschneider,Die Geometrie vor Euklid, p. 60.
44. The gnomon was not a sundial, but an upright erected on a flat surface, in the centre of three concentric circles. These were drawn so that the end of the gnomon’s shadow touched the innermost circle at midday on the summer solstice, the intermediate circle at the equinoxes, and the outermost circle at the winter solstice. See Bretschneider,Die Geometrie vor Euklid, p. 60.
45. The term κόσμος seems to be Pythagorean in this sense. It was not familiar even at the beginning of the fourth century. Xenophon speaks of “what the sophists call the κόσμος” (Mem. i. 11). For δίκη, see below, §§ 14, 72.
45. The term κόσμος seems to be Pythagorean in this sense. It was not familiar even at the beginning of the fourth century. Xenophon speaks of “what the sophists call the κόσμος” (Mem. i. 11). For δίκη, see below, §§ 14, 72.
46. This phrase originated in the school of Plato. The method of research in use there was for the leader to “propound” (προτείνειν, προβάλλεσθαι) it as a “problem” (πρόβλημα) to find the simplest “hypothesis” (τίνων ὑποτεθέντων) on which it is possible to account for and do justice to all the observed facts (σῴζειν τὰ φαινόμενα). It was in its French form,sauver les apparences, that the phrase acquired the meaning it usually has now.
46. This phrase originated in the school of Plato. The method of research in use there was for the leader to “propound” (προτείνειν, προβάλλεσθαι) it as a “problem” (πρόβλημα) to find the simplest “hypothesis” (τίνων ὑποτεθέντων) on which it is possible to account for and do justice to all the observed facts (σῴζειν τὰ φαινόμενα). It was in its French form,sauver les apparences, that the phrase acquired the meaning it usually has now.
47. See Appendix,§ 7.
47. See Appendix,§ 7.
48.Tht.179 e 4, αὐτοῖς ... τοῖς περὶ τὴν Ἔφεσον. The humorous denial that the Herakleiteans had any disciples (180 b 8, Ποίοις μαθηταῖς, ὦ δαιμόνιε;) implies that this was the normal and recognised relation.
48.Tht.179 e 4, αὐτοῖς ... τοῖς περὶ τὴν Ἔφεσον. The humorous denial that the Herakleiteans had any disciples (180 b 8, Ποίοις μαθηταῖς, ὦ δαιμόνιε;) implies that this was the normal and recognised relation.
49.Soph.242 d 4, τὸ ... παρ’ ἡμῖν Ἐλεατικὸν ἔθνος. Cf. ib. 216 a 3, ἑταῖρον δὲ τῶν ἀμφὶ Παρμενίδην καὶ Ζήνωνα [ἑταίρων] (where ἑταίρων is probably interpolated, but gives the right sense); 217 a, 1, οἱ περὶ τὸν ἐκεῖ τόπον.
49.Soph.242 d 4, τὸ ... παρ’ ἡμῖν Ἐλεατικὸν ἔθνος. Cf. ib. 216 a 3, ἑταῖρον δὲ τῶν ἀμφὶ Παρμενίδην καὶ Ζήνωνα [ἑταίρων] (where ἑταίρων is probably interpolated, but gives the right sense); 217 a, 1, οἱ περὶ τὸν ἐκεῖ τόπον.
50.Crat.409 b 6, εἴπερ ἀληθῆ οἱ Ἀναξαγόρειοι λέγουσιν.
50.Crat.409 b 6, εἴπερ ἀληθῆ οἱ Ἀναξαγόρειοι λέγουσιν.
51. Cf. Chap. VI.§ 122; and, on the whole subject, see Diels,“Über die ältesten Philosophenschulen der Griechen”inPhilosophische Aufsätze Eduard Zeller gewidmet(Leipzig, 1887).
51. Cf. Chap. VI.§ 122; and, on the whole subject, see Diels,“Über die ältesten Philosophenschulen der Griechen”inPhilosophische Aufsätze Eduard Zeller gewidmet(Leipzig, 1887).