Early Greek Philosophy by John Burnet, with Burnet's notes
152. The Harmony of the Spheres 154. Relation to Predecessors

From Chapter VII., The Pythagoreans

153. The Likenesses of Numbers
We have still to consider a view, which Aristotle sometimes attributes to the Pythagoreans, that things were "like numbers." He does not appear to regard this as inconsistent with the doctrine that things are numbers, though it is hard to see how he could reconcile the two.116 There is no doubt, however, that Aristoxenos represented the Pythagoreans as teaching that things were like numbers,117 and there are other traces of an attempt to make out that this was the original doctrine. A letter was produced, purporting to be by Theano, the wife of Pythagoras, in which she says that she hears many of the Hellenes think Pythagoras said things were made of number, whereas he really said they were made according to number.118

When this view is uppermost in his mind, Aristotle seems to find only a verbal difference between Plato and the Pythagoreans. The metaphor of "participation" was merely substituted for that of "imitation." This is not the place to discuss the meaning of the so-called "theory of ideas"; but it must be pointed out that Aristotle's ascription of the doctrine of "imitation" to the Pythagoreans is abundantly justified by the Phaedo. When Simmias is asked whether he accepts the doctrine, he asks for no explanation of it, but replies at once and emphatically that he does. The view that the equal itself is alone real, and that what we call equal things are imperfect imitations of it, is quite familiar to him,119 and he is finally convinced of the immortality of the soul just because Sokrates makes him see that the theory of forms implies it.

It is also to be observed that Sokrates does not introduce the theory as a novelty. The reality of the "ideas" is the sort of reality "we are always talking about," and they are explained in a peculiar vocabulary which is represented as that of a school. The technical terms are introduced by such formulas as "we say."120 Whose theory is it? It is usually supposed to be Plato's own, though some call it his "early theory of ideas," and say that he modified it profoundly in later life. But there are serious difficulties in this view. Plato is very careful to tell us that he was not present at the conversation recorded in the Phaedo. Did any philosopher ever propound a new theory of his own by representing it as already familiar to a number of distinguished living contemporaries?121 It is not easy to believe that. It would be rash, on the other hand, to ascribe the origin of the theory to Sokrates, and there seems nothing for it but to suppose that the doctrine of "forms" (εἴδη, ἰδέαι) originally took shape in Pythagorean circles, though it was further developed by Sokrates. There is nothing startling in this. It is a historical fact that Simmias and Kebes were not only Pythagoreans but disciples of Sokrates, and there were, no doubt, more "friends of the ideas"122 than we generally recognise. It is certain, in any case, that the use of the words εἴδη and ἰδέαι to express ultimate realities is pre-Platonic, and it seems most natural to regard it as of Pythagorean origin.

We have really exceeded the limits of this work by tracing the history of Pythagoreanism down to a point where it becomes practically indistinguishable from the theories which Plato puts into the mouth of Sokrates; but it was necessary to do so in order to put the statements of our authorities in their true light. Aristoxenos is not likely to have been mistaken with regard to the opinions of the men he had known personally, and Aristotle's statements must have had some foundation.

Burnet's Notes


116. Cf. especially Met. A, 6. 787, b 10 (R. P. 65 d). It is not quite the same thing when he says, as in A, 5. 985 b 23 sqq. (R. P. ib.), that they perceived many likenesses in things to numbers. That refers to the numerical analogies of justice, Opportunity, etc.

117. Aristoxenos ap. Stob. i. pr. 6 (p. 20), Πυθαγόρας . . . πάντα τὰ πράγματα ἀπεικάζων τοῖς ἀριθμοῖς.

118. Stob. Ecl. i. p. 125, 19 (R. P. 65 d).

119. Plato, Phaed. 74 a sqq.

120. Cf. especially the words ὃ θρυλοῦμεν ἀεί (76 d 8). The phrases αὐτὸ ὃ ἔστιν, αὐτὸ καθ' αὑτό, and the like are assumed to be familiar. "We" define reality by means of question and answer, in the course of which "we" give an account of its being (ἧς λόγον δίδομεν τοῦ εἶναι , 78 d 1, where λόγον . . . τοῦ εἶναι is equivalent to λόγον τῆς οὐσίας). When we have done this, "we" set the seal or stamp of αὐτὸ ὃ ἔστιν upon it (75 d 2). Technical terminology implies a school. As Diels puts it (Elementum, p. 20), it is in a school that "the simile concentrates into a metaphor, and the metaphor condenses into a term."

121. In the Parmenides Plato makes Sokrates expound the theory at a date which is carefully marked as at least twenty years before his own birth.

122. Plato, Soph. 248 a 4. Proclus says (in Parm. iv. p. 149, Cousin) ἦν μὲν γὰρ καὶ παρὰ τοῖς Πυθαγορείοις ἡ περὶ τῶν εἰδων θεωρία, καὶ δηλοῖ καὶ αὐτὸς ἐν Σοφιστῇ τῶν εἰδων φίλους προσαγορεύων τοὺς ἐν Ἰταλίᾳ σοφούς, ἀλλ' ὅ γε μάλιστα πρεσβεύσας καὶ διαρρήδην ὑποθέμενος τὰ εἴδη Σωκράτης ἐστίν. This is not in itself authoritative; but it is the only statement on the subject that has come down to us, and Proclus (who had the tradition of the Academy at his command) does not appear to have heard of any other interpretation of the phrase. In a later passage (v. p. 4, Cousin) he says it was natural for Parmenides to ask Sokrates whether he had thought of the theory for himself, since he might have heard a report of it.

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