Book 1
4
We have treated this subject in greater detail elsewhereIn the lost work On the Pythagoreans; but cf. Aristot. De Caelo 2.13.; but the object of our present review is to discover from these thinkers too what causes they assume and how these coincide with our list of causes.
5
Well, it is obvious that these thinkers too consider number to be a first principle, both as the materialSee Burnet, E.G.P 143-146. of things and as constituting their properties and states.i.e., as a formal principle. Cf. Ross ad loc. The elements of number, according to them, are the Even and the Odd. Of these the former is limited and the latter unlimited; Unity consists of both (since it is both odd and even)Either because by addition it makes odd numbers even and even odd (Alexander, Theo Smyrnaeus) or because it was regarded as the principle of both odd and even numbers (Heath).; number is derived from Unity; and numbers, as we have said, compose the whole sensible universe.
6
OthersZeller attributes the authorship of this theory to Philolaus. of this same school hold that there are ten principles, which they enunciate in a series of corresponding pairs: (1.) Limit and the Unlimited; (2.) Odd and Even; (3.) Unity and Plurality; (4.) Right and Left; (5.) Male and Female; (6.) Rest and Motion; (7.) Straight and Crooked; (8.) Light and Darkness; (9.) Good and Evil; (10.) Square and Oblong.
7
Apparently Alcmaeon of Croton speculated along the same lines, and either he derived the theory from them or they from him; for [Alcmaeon was contemporary with the old age of Pythagoras, and]This statement is probably true, but a later addition. his doctrines were very similar to theirs.He was generally regarded as a Pythagorean. He says that the majority of things in the world of men are in pairs; but the contraries which he mentions are not, as in the case of the Pythagoreans, carefully defined, but are taken at random, e.g. white and black, sweet and bitter, good and bad, great and small.
