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Plato's Divided Line and Dialectic

Published online by Cambridge University Press:  11 February 2009

R. Hackforth
R. Hackforth
Affiliation:
Sidney Sussex CollegeCambridge
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Extract

The old question whether or no the doctrine of ‘intermediate mathematical objects’ ascribed to Plato by Aristotle (Met. 987b14, 1059b6) is to be found in the Divided Line of Republic vi, has been recently raised again in a careful and lucid discussion by Mr. W. F. R. Hardie. I may clear the ground by saying at once that I agree with that part of Mr. Hardie's chapter which deals with those criticisms of the traditional view that have been put forward by Prof. Ferguson and the late Prof. Stocks; nevertheless I do not believe that the objects of the third segment are intermediate between Forms and Sensibles: I propose to argue that they, like the objects of the highest segment, are Forms.

Type
Research Article
Information
The Classical Quarterly , Volume 36 , Issue 1-2 , January 1942 , pp. 1 - 9
Copyright
Copyright © The Classical Association 1942

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References

page 1 note 1 A Study in Plato, chapter vi.

page 2 note 1 Not the whole purpose: for the Cave is already in Plato's mind, and with the Cave the dominating idea has become the soul's gradual ascent to the νοητς ππος (517 B). Therewith a new significance has been given to the lower half of the Line: it is no longer merely illustrative of the upper half, and its objects are no longer merely τ ρατ but all δοξαοτο. The occurrence of τ δοξαοτο at 510 A—unexpected and perplexing—is a hint that a second purpose is later to be served by the quadripartition.

page 3 note 1 Ar. Met. vol. i, p. 168 (commenting on 987b 14). I may say that my main object in the first part of this paper is to reinforce Ross's sentence ‘It seems then that Plato does not state, as he had undertaken (509 D) to do, a difference between the objects of δινοια and of νησις; his whole stress is on the difference between their methods.’ My only point of disagreement is that I do not think he does undertake to do so at 509 D.

page 3 note 2 τ ὐπ ταῖς γεωμετραις is a vague expression which, so far as I can judge, may quite as likely mean ‘the procedure in geometrical reasonings’ as ‘the objects of geometry’.

page 4 note 1 Op. cit., p. 167.

page 4 note 2 Op. cit., p. 53.

page 4 note 3 Mind, xli, pp. 37 ff.

page 4 note 4 In Eud. I, 211, 18 ff.

page 4 note 5 vii, Introd. I owe the reference to Prof. Cornford's paper, from which I borrow the translation.

page 5 note 1 Loc. cit., p. 181.

page 5 note 2 It is true that at 454 A SOC. speaks of many people falling into τν ντιλογικν τχνην because they are unable κατ' εἴδη διαιρομενοι τ λεγμενον πισκοπεῖν but this is merely a warning against using wide concepts like ‘Same’ and ‘Different’ without specifying the points of sameness and difference between the things in question. There is no implication of a method of denning species by διαρεσις κατ' εἴδη.

page 5 note 3 I do not discuss the distinction which Prof. Cornford draws between programmes of Education and Research, for this does not affect my argument.

page 6 note 1 Was Aristotle perhaps thinking of this in his well-known plea for the study of the ‘ignobler’ animals at de part. anim. i. 5?

page 6 note 2 Whether or no the τι ἱκανν of 101 E is the αὐτ γαθν, the ȏετερος πλος could not be completed short of reaching that.

page 6 te 3 The insistence on a ‘synoptic’ study of the various branches of Mathematics (537 c) is not a demand for their reform by Dialectic, but aims at preparing the mind for that higher study.

page 7 note 1 Hence I take τ λγῳ to ‘in a abandoned them, formula’ but ‘by his reasoning’.

page 7 note 2 This curious word προσχρηομενα seems to imply that particular acts which are just, etc., participate directly in the Idea of Just, etc., and indirectly, through that, also (πρς) in the Idea of Good.

page 7 note 3 I suggest that, just as it has been wrongly argued from the absence of mention of moral Ideas in the Timaeus that Plato had by then abandoned them, so we should not conclude from the absence of mention of Ideas of natural species in Republic vi–vii that he did not then postulate them.

page 7 note 4 The magnificent faith of the idealist of the Republic declares that he can. Probably in a less exalted mood Plato would admit that he can only indefinitely approximate to it. Man is never σοφς, but only φιλσοφος (Symp. 204 A).

page 7 note 5 The expression is retained when Division has become the method par excellence of diallectic. Pol. 258 C. δεῖ γρ αὐτν (sc. τν πολιτικν) νευρεῖν, κα χωρς φελντας π τ ἂλλων ἰδαν αὐτῇ μαν πισφραγσασθαι. 291 C τν πντων τν σοφιστν μγιστον γητα … ν π τν ντως ντων πολιτικν … φαιρετον.

page 8 note 1 Prof. Cornford (loc. cit., p. 182) implies the same interpretation: ‘when he’ (sc. the mathematician) ‘“abolishes” demonstrable hypotheses, he does so by going behind them and showing how they can be obtained by deduction and finally confirmed (βɛβαιοὐν)’.

page 8 note 2 A Study in Plato, p. 69.

page 8 note 3 On this topic there is a valuable article by ProfField, G. C. in Philosophy, viii (1933), pp. 131–41CrossRefGoogle Scholar.

page 9 note 1 Tim. 68 E χρ δὕ αἰτας εἴδη διορζεσθαι, τ μν ναγκαῖον τ δ θεῖον, κα τ μν θεῖον ν ἃπασιν ζητεῖν κτσεως ἓνεκα ɛὐδαμονος βογ … τ δ ναγκαῖον κενων χριν, λογιζμενον ὡς ἅνɛυ τοὐτων οὐ δυνατ αὐτ φ' οἶς σπουδζομɛν μνα κατανοɛῖν οὐδ' αὖ λαβɛῖν οὐδ' ἄλλως πως μɛτασχɛῖν. Cf. 46 E.

page 9 no 2 Plato's Method of Dialectic (trans. Allan, D. J.), especially pp. 54 ffGoogle Scholar.

page 9 note 3 I have to thank Mr. F. H. Sandbach and Mr. W. K. C. Guthrie for valuable criticisms.