James Adam, The Republic of Plato

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ὀνειρώττουσι κτλ. Krohn (Pl. St. pp. 179—181) accuses Plato of a sudden volte face in regard to mathematical studies. It is true that the same language is used of δόξα in V 476 C (cf. VII 520 C), but there are dreams and dreams, and we may fairly say that if the προπαιδεία is only a dream in comparison with Dialectic, at least it is one of those dreams which come through the gates of horn.

ᾧ γὰρ ἀρχὴ κτλ. See VI 510 C, D notes ὁμολογίαν means ‘agreement’ ‘harmony’ (“Übereinstimmung” Schneider), viz. of ἀρχή, τελευτή and τὰ μεταξύ, not ‘admissions’ (as D. and V. translate): cf. ὁμολογουμένως l.c.

οὐκοῦν κτλ. ‘Well then,’ said I, ‘the method of dialectic alone proceeds by the destruction of hypotheses to the actual first principle, in order to make its results secure.’ Dialectic examines and cancels (ἀναιρεῖ) one ὑπόθεσις after another, till in the end it reaches the Idea of Good. Suppose for example that ὁσιότης is the subject of discussion. Various ὑποθέσεις are proposed, tested, and overthrown. Out of the ruins of the former ὑποθέσεις we built a new and better one, which must in its turn be thoroughly tested, tried, and perhaps overthrown, before it can serve as a stepping-stone to one which is higher, truer and better: cf. 534 B, C. Now this process of testing, revising, discarding, is not, ideally speaking, complete until we examine the relations of our ὑπόθεσις of ὁσιότης with all νοητά, and in such an examination we apply the same ‘hypothetical method’ throughout the whole noetic sphere, testing and correcting all our ὑποθέσεις by one another. In the final stage, which is of course only an ideal, all our ὑποθέσεις become exact counterparts of the Ideas, and we have reached the ἀρχή or Good. Thereafter the results of Dialectic are βέβαια: see VI 511 B. The earlier steps in this dialectical ascent may be illustrated from many, if not most, of the Platonic dialogues. For ἀναιροῦσα cf. Arist. Topic. Γ 6. 120^{a} 6—31, and especially Eth. Eud. II 6. 1222^{b} 27 f. κινουμένης τῆς ἀρχῆς πάντα μάλιστ᾽ ἂν τὰ δεικνύμενα μεταβάλλοι, αὐτὰ δ᾽ αὑτὰ οὐ μεταβάλλει ἀναιρουμένου θατέρου ὑπὸ θατέρου, ἂν μὴ τῷ τὴν ὑπόθεσιν ἀνελεῖν καὶ δἰ ἐκείνης δεῖξαι. The word is often used in connexion with the Eleatic dialectic, of which Plato's ἡ ἐξ ὑποθέσεως ἀνάλυσις (Alcin. Isag. 7), here described, is a development: see RP^{7}. §§ 95 note a, 105 A—106, 110—115. For other views on this passage see App. XV: and for a farther discussion of the method itself and its permanent value in the history of investigation consult App. III.