James Adam, The Republic of Plato

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τὰ τῶν πολλῶν κτλ.: “the multitude's multitudinous formulae” Bosanquet. The words refer to general rules, standards, canons, believed in by the multitude (cf. τὰ τῶν πολλῶν δόγματα VI 493 A), who have on every single subject many such standards (πολλὰ νόμιμα), mutually inconsistent and uncoordinated, because they do not know that τὸ καλόν, τὸ ἀγαθόν etc. are each of them ἕν. They say, for example, ‘τὸ ἡδύ is καλόν,’ ‘τὸ συμφέρον is καλόν,’ ‘τὸ ἀγαθόν is καλόν,’ and so on. Such assertions give the appearance of plurality to τὸ καλόν, by connecting it, not indeed with the objects of sense, but with other εἴδη (cf. 476 A, 476 C notes). The form in which Plato expresses his conclusion (τὰ τῶν πολλῶν πολλὰ νόμιμα καλοῦ πέρι and not simply τὰ πολλὰ καλά) prepares us for VI 484 C, where the whole purpose of this enquiry is disclosed. It is the business of the philosopher-king to bring order out of chaos by remodelling the νόμιμα of the many in conformity with the Idea. He must not allow them to predicate κοινωνία of εἴδη unless the εἴδη really intercommunicate.

πολλὰ καλά. Is καλά the plural of ‘the beautiful,’ or of ‘a beautiful’? This question is raised by Bosanquet, who answers it thus: “the sentence about formulae leads me to interpret it in the former sense=‘many standards,’ or cases accepted as standards, ‘of beauty.’” Cf. 479 A, where however we have πολλὰ τὰ καλά, and its antithesis ἓν τὸ καλόν. The expression πολλὰ καλά must, I think, be taken in its usual sense, as the plural of καλόν τι; but it includes not only the objects of sense, but also νόμιμα περὶ καλοῦ, which are themselves πολλὰ καλά, because they connect αὐτὸ τὸ καλόν with another εἶδος. See last note.