James Adam, The Republic of Plato

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ff. The arguments by means of which Plato establishes his conclusion may be briefly described as the political argument, the psychological argument, and the metaphysical argument. The first (577 B—580 C) depends on the resemblance between the soul and the State, the second (580 C—583 A) on the threefold division of the soul into λογιστικόν, θυμοειδές, and ἐπιθυμητικόν, the third (583 B—587 B) on Plato's theory of Reality or Being. Now it is just these three methods of investigation, and these alone, which have been employed in the different parts of the dialogue, the political and psychological in II—IV and VIII—IX, the metaphysical in V—VII; and it is therefore altogether appropriate and right that Plato should bring them together now, and use their united forces ‘in making up the last account.’ The sequence of the three arguments follows the usual Platonic way of progression from the exoteric to the esoteric, and as the ideal city culminated in metaphysical idealism, so it is a metaphysical argument that crowns our citadel of proof.

καθ̓ ἕκαστον κτλ. καθ̓ ἕκαστον=‘point by point,’ ‘in detail,’ not ‘singly’ (D. and V.), which would be καθ᾽ ἑκάτερον here, since only two objects of comparison are involved. ἀθρῶν: sc. ἑκάτερον, viz. the city and the man (J. and C.). On ὡς πόλιν εἰπεῖν and ὡς ἔπος εἰπεῖν (‘I might almost say’) see I 341 B note