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Returning to the philosophy of Pythagoras, in its relation to the general development of Greek theory, we may note, to begin with, that it is not necessary, or perhaps possible, to disentangle the theory of Pythagoras himself from that of his followers, Philolaus and others. The teaching was largely oral, and was developed by successive leaders of the school. The doctrine, therefore, is generally spoken of as that, not of Pythagoras, but of the Pythagoreans. Nor can we fix for certain on one fundamental conception, upon which the whole structure of their doctrine was built.

 

One dictum we may start with because of its analogies with what has been said of the earlier philosophies. The universe, said the Pythagoreans, was constituted of indefinites and definers, i.e. of that which has no character, but has infinite capacities of taking a character; and secondly, of things or forces which impose a character upon this. Out of the combination of these two elements or principles all knowable existences come into being. “All things,” they said, “as known have Number; and this number has two natures, the Odd and the Even; the known thing is the Odd-Even or union of the two.”

 

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Cf. Guthrie, The Early Presocratics and the Pythagoreans - A Synopsis of Greek Philosophy

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