James Adam, The Republic of Plato

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εἶναι is not of course used in its technical sense, otherwise it would be inconsistent with the end of Book V. Socrates means only that the Platonist distinguishes between two categories—τὰ πολλά, and the Ideas.

καὶ αὐτὸ δὴ κτλ. The literal meaning of the text above printed is as follows: ‘So likewise a Beautiful itself, and a Good itself and similarly about all which we formerly took’ (or ‘postulated’) ‘as many: reversing our procedure (πάλιν αὖ), we postulate also one Idea of each, believing that there is but one, and call it the essential so-and-so.’ καὶ—ἐτίθεμεν is best explained as still under the influence of φαμέν—λόγῳ. τότε (as Schneider observes) refers ‘ad eam, quae modo facta est, multorum commemorationem’: cf. 510 B. Stallbaum is mistaken in supposing that the allusion is to V 475 E ff. Plato's meaning will appear from a single example. We postulate both πολλὰ δίκαια and also ἓν δίκαιον, viz. the ἰδέα μία δικαίου, and we call the latter ὃ ἔστιν δίκαιον: cf. Phaed. 75 B τοῦ ὃ ἔστιν ἴσον, Symp. 211 C and elsewhere. We postulate only one ἰδέα δικαίου, because we believe that there is but one: see X 597 C, D, where Plato shews why there cannot be more. For αὐτό used of the Ideas, see on IV 438 B, 438 C and V 476 A note Instead of καὶ ἰδέαν, the MSS— see cr. n.—read κατ᾽ ἰδέαν (κατιδέαν Vind. F.). For the interchange of καί and κατά see Schaefer's Greg. Cor. p. 234 note 26. An unduly sloping accent is enough to account for the corruption of ΚΑΙ`ΙΔΕΑΝ into ΚΑΤΙΔΕΑΝ (as in uncial MSS it would be written: see Thompson Gk. Palaeogr. p. 127). See also my article in Cl. Rev. XIII p. 100. Other views on the text and interpretation of this difficult passage are discussed in App. VII.