[44] Theophrast. Metaphys. 9. Probably the recognition of one dominant antithesis — Τὸ Ἕν — ἡ ἀόριστος Δυὰς — is the form given by Plato to the Pythagorean doctrine. Eudorus (in Simplikius ad Aristot. Physic. fol. 39) seems to blend the two together.
The arithmetical and geometrical view of nature, to which such exclusive supremacy is here given by the Pythagoreans, is one of the most interesting features of Grecian philosophy. They were the earliest cultivators of mathematical science,[45] and are to be recognised as having paved the way for Euclid and Archimedes, notwithstanding the symbolical and mystical fancies with which they so largely perverted what are now regarded as the clearest and most rigorous processes of the human intellect. The important theorem which forms the forty-seventh Proposition of Euclid’s first book, is affirmed to have been discovered by Pythagoras himself: but how much progress was made by him and his followers in the legitimate province of arithmetic and geometry, as well as in the applications of these sciences to harmonics,[46] which they seem to have diligently cultivated, we have not sufficient information to determine with certainty.
[45] Aristot. Metaph. A. 5, p. 985, b. 23. οἱ Πυθαγορεῖοι τῶν μαθημάτων ἀψάμενοι πρῶτοι ταῦτα προήγαγον, καὶ ἐντραφέντες ἐν αὐτοῖς τὰς τούτων ἀρχὰς τῶν ὄντων ἀρχὰς ᾠήθησαν εἶναι πάντων.
[46] Concerning the Pythagorean doctrines on Harmonics, see Boeckh’s Philolaus, p. 60-84, with his copious and learned comments.
Eleatic philosophy — Xenophanes.
Contemporary with Pythagoras, and like him an emigrant from Ionia to Italy, was Xenophanes of Kolophon. He settled at the Phokæan colony of Elea, on the Gulf of Poseidonia; his life was very long, but his period of eminence appears to belong (as far as we can make out amidst conflicting testimony) to the last thirty years of the sixth century B.C. (530-500 B.C.). He was thus contemporary with Anaximander and Anaximenes, as well as with Pythagoras, the last of whom he may have personally known.[47] He composed, and recited in person, poems — epic, elegiac, and iambic — of which a very few fragments remain.
[47] Karsten. Xenophanis Fragm., s. 4, p. 9, 10.
His censures upon the received Theogony and religious rites.
Xenophanes takes his point of departure, not from Thales or Anaximander, but from the same ancient theogonies which they had forsaken. But he follows a very different road. The most prominent feature in his poems (so far as they remain), is the directness and asperity with which he attacks the received opinions respecting the Gods — and the poets Hesiod and Homer, the popular exponents of those opinions. Xenophanes not only condemns these poets for having ascribed to the Gods discreditable exploits, but even calls in question the existence of the Gods, and ridicules the anthropomorphic conception which pervaded the Hellenic faith. “If horses or lions could paint, they would delineate their Gods in form like themselves. The Ethiopians conceive their Gods as black, the Thracians conceive theirs as fair and with reddish hair.”[48] Dissatisfied with much of the customary worship and festivals, Xenophanes repudiated divination altogether, and condemned the extravagant respect shown to victors in Olympic contests,[49] not less than the lugubrious ceremonies in honour of Leukothea. He discountenanced all Theogony, or assertion of the birth of Gods, as impious, and as inconsistent with the prominent attribute of immortality ascribed to them.[50] He maintained that there was but one God, identical with, or a personification of, the whole Uranus. “The whole Kosmos, or the whole God, sees, hears, and thinks.” The divine nature (he said) did not admit of the conception of separate persons one governing the other, or of want and imperfection in any way.[51]
[48] Xenophanis Fragm. 5-6-7, p. 39 seq. ed. Karsten; Clemens Alexandr. Strom. v. p. 601; vii. p. 711.