James Adam, The Republic of Plato

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ὑπερβαίνοντες καὶ ἁμαρτάνοντες are subordinate to λισσόμενοι: “by praying when we transgress and sin, we shall persuade them,” etc. There is again a reference to λισσόμενοι ὅτε κέν τις ὑπερβήῃ καὶ ἁμάρτῃ quoted in 364 E. The position of the participles is justified by the allusion to this line.

ἢ -- ἤ. It was a common Greek belief that the sins of the fathers are visited upon the children: see the passages cited by Nägelsbach Nachhom. Theol. pp. 34 ff. If we take Plato at his word, Adimantus represents this vicarious punishment as extending even to the other world.

ἢ παῖδες παίδων. Baiter conjectures <ἢ παῖδες> ἢ παῖδες παίδων, and so I formerly printed. But παῖδες παίδων means little more than ‘descendants’ (cf. Laws 927 B), and the text may stand. Similarly in Ruskin Modern Painters Ch. 1 “all those labours which men have given their lives and their sons' sons' lives to complete.”

ὦ φίλε -- λογιζόμενος . ὦ φίλε is the objector who urges ἀλλὰ γὰρ—παίδων. In φήσει Plato recurs to the singular of 365 B λέγοι γὰρ ἂν κτλ. λογιζόμενος is not ‘reasoning,’ but ‘making his calculation,’ ‘calculos subducens’: such a man's morality is nothing but a balancing of profit and loss. Hermann's devotion to Paris A led him to conjecture ἀλλ᾽ ὠφελήσουσιν ἁγνιζομένους αἰ τελεταί rather than admit a simple case of omission arising from homoioteleuton: see cr. n. Vermehren proposes ἀλλ᾽ ὠφελήσουσιν αἱ νομιζόμεναι τελεταί (Plat. Stud. p. 90), but we should certainly follow Π here. See also Introd. § 5.

λύσιοι: ‘givers of absolution’: cf. 364 E. Certain Chthonian deities of the Orphic theology are meant, such as Hecate, Demeter, Dionysus λύσιος or λυσεύς, and above all Ζεὺς μειλίχιος. See Lobeck Aglaoph. p. 303.