A different party in this same school say that the first principles are ten, named according to the following table:—finite and infinite, even and odd, one and many, right and left, male and female, rest and motion, straight and crooked, light and darkness, good and bad, square and oblong. After this manner Alkmaeon of Kroton seems to have conceived them, and either he received this doctrine from them or they from him; for Alkmaeon arrived at maturity when Pythagoras was an old man, and his teachings resembled theirs. For he says that most human affairs are twofold, not meaning opposites reached by definition, as did the former party, but opposites by chance—as, for example, white-black, sweet-bitter, good-bad, small-great. This philosopher let fall his opinions indefinitely about the rest, but the Pythagoreans declared the number of the opposites and what they were. From both one may learn this much, that opposites are the first principles of things; but from the latter he may learn the number of these, and what they are. But how it is possible to bring them into relation with the causes of which we have spoken if they have not clearly worked out; but they seem to range their elements under the category of matter, for they say that being is compounded and formed from them, and that they inhere in it. 987 a 9-27. Down to the Italian philosophers and with the exception of them the rest have spoken more reasonably about these principles, except that, as we said, they do indeed use two principles, and the one of these, whence is motion, some regard as one and others as twofold. The Pythagoreans, however, while they in similar manner assume two first principles, add this which is peculiar to themselves: that they do not think that the finite and the infinite and the one are certain other things by nature, such as fire or earth or any other such thing, but the infinite itself and unity itself are the essence of the things of which they are predicated, and so they make number the essence of all things. So they taught after this manner about them, and began to discourse and to define what being is, but they made it altogether too simple a matter. For they made their definitions superficially, and to whatever first the definition might apply, this they thought to be the essence of the matter; as if one should say that twofold and two were the same, because the twofold subsists in the two. But undoubtedly the two and the twofold are not the same; otherwise the one will be many—a consequence which even they would not draw. So much then may be learned from the earlier philosophers and from their successors. i. 6; 987 b 10. And Plato only changed the name, for the Pythagoreans say that things exist by imitation of numbers, but Plato, by sharing the nature of numbers.