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[987b] [1] And when Socrates, disregarding the physical universe and confining his study to moral questions, sought in this sphere for the universal and was the first to concentrate upon definition, Plato followed him and assumed that the problem of definition is concerned not with any sensible thing but with entities of another kind; for the reason that there can be no general definition of sensible things which are always changing.These entities he called "Ideas,"1 and held that all sensible things are named after2 them sensible and in virtue of their relation to them; for the plurality of things which bear the same name as the Forms exist by participation in them. (With regard to the "participation," it was only the term that he changed; for whereas the Pythagoreans say that things exist by imitation of numbers, Plato says that they exist by participation—merely a change of term.As to what this "participation" or "imitation" may be, they left this an open question.)

Further, he states that besides sensible things and the Forms there exists an intermediate class, the objects of mathematics,3 which differ from sensible things in being eternal and immutable, and from the Forms in that there are many similar objects of mathematics, whereas each Form is itself unique.

Now since the Forms are the causes of everything else, he supposed that their elements are the elements of all things. [20] Accordingly the material principle is the "Great and Small," and the essence <or formal principle> is the One, since the numbers are derived from the "Great and Small" by participation in the the One.In treating the One as a substance instead of a predicate of some other entity, his teaching resembles that of the Pythagoreans, and also agrees with it in stating that the numbers are the causes of Being in everything else; but it is peculiar to him to posit a duality instead of the single Unlimited, and to make the Unlimited consist of the "Great and Small." He is also peculiar in regarding the numbers as distinct from sensible things, whereas they hold that things themselves are numbers, nor do they posit an intermediate class of mathematical objects.His distinction of the One and the numbers from ordinary things (in which he differed from the Pythagoreans) and his introduction of the Forms were due to his investigation of logic (the earlier thinkers were strangers to Dialectic)4; his conception of the other principle as a duality to the belief that numbers other than primes5 can be readily generated from it, as from a matrix.6

1 I have translated ἰδέα by Idea and εἶδος by Form wherever Aristotle uses the words with reference to the Platonic theory. Plato apparently uses them indifferently, and so does Aristotle in this particular connection, but he also uses εἶδος in the sense of form in general. For a discussion of the two words see Taylor, Varia Socratica, 178-267, and Gillespie, Classical Quarterly, 6.179-203.

2 For this interpretation of παρὰ ταῦτα see Ross's note ad loc.

3 i.e. arithmetical numbers and geometrical figures.

4 See Aristot. Met. 4.2.19-20, and cf. Aristot. Met. 8.4.4.

5 ἔξω τῶν πρώτων is very difficult, but it can hardly be a gloss, and no convincing emendation has been suggested. Whatever the statement means, it is probably (as the criticism which follows is certainly) based upon a misunderstanding. From Plat. Parm. 143c, it might be inferred that the Great and Small (the Indeterminate Dyad) played no part in the generation of numbers; but there the numbers are not Ideal, as here they must be. In any case Aristotle is obsessed with the notion that the Dyad is a duplicative principle (Aristot. Met. 13.8.14), which if true would imply that it could generate no odd number. Hence Heinze proposed reading περιττῶν(odd) for πρώτων(which may be right, although the corruption is improbable) and Alexander tried to extract the meaning of "odd" from πρώτων by understanding it as "prime to 2." However, as Ross points out (note ad loc.), we may keep πρώτων in the sense of "prime" if we suppose Aristotle to be referring either (a) to the numbers within the decad (Aristot. Met. 13.8.17) and forgetting 9—the other odd numbers being primes; or (b) to numbers in general, and forgetting the entire class of compound odd numbers. Neither of these alternatives is very satisfactory, but it seems better to keep the traditional text.

6 For a similar use of the word ἐκμαγεῖον cf. Plat. Tim. 50c.

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