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.”
A History of Greek Philosophy /
PYTHAGORAS AND THE PYTHAGOREANS
