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[985b] [1] treating fire on the one hand by itself, and the elements opposed to it—earth, air and water—on the other, as a single nature.1 This can be seen from a study of his writings.2Such, then, as I say, is his account of the nature and number of the first principles.

Leucippus,3 however, and his disciple Democritus4 hold that the elements are the Full and the Void—calling the one "what is" and the other "what is not." Of these they identify the full or solid with "what is," and the void or rare with "what is not" (hence they hold that what is not is no less real than what is,5 because Void is as real as Body); and they say that these are the material causes of things.And just as those who make the underlying substance a unity generate all other things by means of its modifications, assuming rarity and density as first principles of these modifications, so these thinkers hold that the "differences"6 are the causes of everything else.These differences, they say, are three: shape, arrangement, and position; because they hold that what is differs only in contour, inter-contact, and inclination .7(Of these contour means shape, inter-contact arrangement, and inclination position.) Thus, e.g., A differs from N in shape, AN from NA in arrangement, and Z from N8 in position.As for motion, whence and how it arises in things, [20] they casually ignored this point, very much as the other thinkers did. Such, then, as I say, seems to be the extent of the inquiries which the earlier thinkers made into these two kinds of cause.

At the same time, however, and even earlier the so-called9 Pythagoreans applied themselves to mathematics, and were the first to develop this science10; and through studying it they came to believe that its principles are the principles of everything.And since numbers are by nature first among these principles, and they fancied that they could detect in numbers, to a greater extent than in fire and earth and water, many analogues11 of what is and comes into being—such and such a property of number being justice ,12 and such and such soul or mind , another opportunity , and similarly, more or less, with all the rest—and since they saw further that the properties and ratios of the musical scales are based on numbers,13 and since it seemed clear that all other things have their whole nature modelled upon numbers, and that numbers are the ultimate things in the whole physical universe,

1 Cf. 3.14.

2 e.g. Empedocles, Fr. 62 (Diels).

3 Of Miletus; fl. circa 440 (?) B.C. See Burnet, E.G.P. 171 ff.

4 Of Abdera; fl. circa 420 B.C. E.G.P loc. cit.

5 For the probable connection between the Atomists and the Eleatics see E.G.P. 173, 175, and cf. De Gen. et Corr. 324b 35-325a 32.

6 i.e., of the atoms.

7 Cf. R.P. 194.

8 These letters will convey Aristotle's point better to the English reader, but see critical note.

9 Aristotle seems to have regarded Pythagoras as a legendary person.

10 Pythagoras himself (fl. 532 B.C.) is said by Aristoxenus (ap. Stobaeus 1.20.1) to have been the first to make a theoretical study of arithmetic.

11 Cf. Aristot. Met. 14.6ff..

12 Apparently (cf. infra, Aristot. Met. 1.17) they identified these not only with properties of number but with numbers themselves. Thus justice (properly=squareness)=4, the first square number; soul or mind=1, opportunity=7 (Alexander).

13 Pythagoras himself is credited with having discovered the ratios of the octave (2 : 1), the fifth (3 : 2) and the fourth (4 : 3). Burnet, E.G.P. 51.

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