James Adam, The Republic of Plato

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ἀντικαταστήσωμεν κτλ.: sc. as a counterpart or substitute for our own βέλτιστον (τῷ παρ᾽ ἡμῖν τοιούτῳ), by which he has hitherto been guided. Madvig's conjecture ὄντι καταστήσωμεν is both unnecessary and inelegant. On the singular αὐτῷ in spite of the plural παίδων see I 347 A note

591A - 592B It is also better for him who is guilty of Injustice to be detected and punished than to escape. The wise man will honour those studies which promote the welfare of his soul, and the same great object will be his guiding principle in all that appertains to the body and its state, as well as to the acquisition of riches and honours. Will he take part in political life? Perhaps not in the land of his birth, but in his own true city assuredly he will. It may be that the perfect city is an ensample laid up in Heaven for him who would plant a city in his soul.

ἀδικεῖν -- ποιεῖν. It is more natural and better in point of literary effect to make the infinitives coordinate (with the English translators) than to suppose (with Schneider) that ἢ—ἤ is ‘either—or’ and ἀκολασταίνειν and τι αἰσχρὸν ποιεῖν intended as different species of the genus ἀδικία.

πῇ δ᾽ ἀδικοῦντα κτλ. It was maintained in II 361 A ff., 365 C ff. that Injustice could evade detection and punishment. So much the worse, says Socrates, for the sinner, who thereby forfeits his only chance of reformation, since Punishment is the appointed cure for Vice. It may be doubted whether so humane a view altogether corresponded to the actual administration of the Athenian or any other State; but to an idealist like Plato ‘is’ means ‘should be,’ and in so far as human laws fulfil their true function by reflecting the divine ordinances, we may truly say that punishment is remedial. See on the whole subject II 380 B note