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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.
3 i.e. arithmetical numbers and geometrical figures.
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.
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