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[986a] [1] they assumed the elements of numbers to be the elements of everything, and the whole universe to be a proportion1 or number. Whatever analogues to the processes and parts of the heavens and to the whole order of the universe they could exhibit in numbers and proportions, these they collected and correlated;and if there was any deficiency anywhere, they made haste to supply it, in order to make their system a connected whole. For example, since the decad is considered to be a complete thing and to comprise the whole essential nature of the numerical system, they assert that the bodies which revolve in the heavens are ten; and there being only nine2 that are visible, they make the "antichthon"3 the tenth.We have treated this subject in greater detail elsewhere4; 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.Well, it is obvious that these thinkers too consider number to be a first principle, both as the material5 of things and as constituting their properties and states.6 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 [20] (since it is both odd and even)7; number is derived from Unity; and numbers, as we have said, compose the whole sensible universe.Others8 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.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]9 his doctrines were very similar to theirs.10 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.Thus Alcmaeon only threw out vague hints with regard to the other instances of contrariety,

1 Or "harmony." Cf. Aristot. De Caelo 2.9, and E.G.P. 152.

2 Earth, sun, moon, five planets, and the sphere of the fixed stars.

3 i.e. "counter-earth"; a planet revolving round the "central fire" in such a way as to be always in opposition to the earth.

4 In the lost work On the Pythagoreans; but cf. Aristot. De Caelo 2.13.

5 See Burnet, E.G.P 143-146.

6 i.e., as a formal principle. Cf. Ross ad loc.

7 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).

8 Zeller attributes the authorship of this theory to Philolaus.

9 This statement is probably true, but a later addition.

10 He was generally regarded as a Pythagorean.

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