The philosophies described above were succeeded by the system of Plato, Footnote 1Compare Aristot. Met. 12.4.2-5. which in most respects accorded with them, but contained also certain peculiar features distinct from the philosophy of the Italians.
In his youth Plato first became acquainted with Cratylus Footnote 2Cf. Aristot. Met. 4.5.18. and the Heraclitean doctrines—that the whole sensible world is always in a state of flux, Footnote 3Plat. Crat. 402a (fr. 41 Bywater). and that there is no scientific knowledge of it—and in after years he still held these opinions. 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,
Footnote 4I 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. and held that all sensible things are named after Footnote 5For this interpretation of παρὰ ταῦτα see Ross’s note ad loc. 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, Footnote 6i.e. arithmetical numbers and geometrical figures. 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. 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) Footnote 7See Aristot. Met. 4.2.19-20, and cf. Aristot. Met. 8.4.4. ; his conception of the other principle as a duality to the belief that numbers other than primes Footnote 8ἔξω 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. can be readily generated from it, as from a matrix. Footnote 9For a similar use of the word ἐκμαγεῖον cf. Plat. Tim. 50c.
The fact, however, is just the reverse, and the theory is illogical; for whereas the Platonists derive multiplicity from matter although their Form generates only once, Footnote 10Aristotle’s objection is that it is unreasonable that a single operation of the formal upon the material principle should result in more than one product; i.e. that the material principle should be in itself duplicative. it is obvious that only one table can be made from one piece of timber, and yet he who imposes the form upon it, although he is but one, can make many tables. Such too is the relation of male to female: the female is impregnated in one coition, but one male can impregnate many females. And these relations are analogues of the principles referred to.
This, then, is Plato’s verdict upon the question which we are investigating. From this account it is clear that he only employed two causes Footnote 11Plato refers several times in the dialogues to an efficient cause (e.g. the Demiurgus,Plat. Soph. 265b-d, Plat. Tim. 28c ff.) and a final cause (e.g. Plat. Phil. 20d, 53e, Plat. Tim. 29d ff.); but Aristotle does not seem to take these allusions seriously. : that of the essence, and the material cause; for the Forms are the cause of the essence in everything else, and the One is the cause of it in the Forms.
He also tells us what the material substrate is of which the Forms are predicated in the case of sensible things, and the One in that of the Forms—that it is this the duality, the Great and Small.
Further, he assigned to these two elements respectively the causation of good Footnote 12Cf. Plat. Phil. 25e-26b. and of evil; a problem which, as we have said, Footnote 13Aristot. Met. 3.17; 4.3. had also been considered by some of the earlier philosophers, e.g. Empedocles and Anaxagoras.