We grant (do we not?) that, as Sachs emphasizes, the argument of the Republic requires:
(A) If a person has internal justice, then he has ordinary justice (i-just --> o-just).
(B) If a person has ordinary justice, then he has internal justice (o-just --> i-just).
Yet we may wonder:
1. Does Plato (in the Republic) believe them?
2. If so, does he assert them?
3. If he believes or asserts them, does he indicate that they need to be justified in some way, or does he simply take them for granted (perhaps with good reason)?
4. If he indicates that they need to be justified in some way, does he attempt to justify them?
5. If he attempts to justify them, are his attempts plausible?
Sachs takes different positions as regards (A) and (B). As regards (A), he says that, clearly, Plato believes it, and he asserts it; however, Plato seems to take it for granted, not offering any argument or indicating even that an argument is required.
As regards (B), Sachs says there is no evidence in the text that Plato even believes it.
Is Sachs right about this? Does he set up the problem correctly? Is he correct that Plato asserts (A) but offers no support for it, and that Plato does not assert (B) and may not believe it?
Here are the relevant passages from Sachs (by the way, 'internal justice' = 'Platonic justice' and 'ordinary justice' = 'vulgar justice'). As regards (A):
Both explicitly and by implication, Plato distinguished his special conception of justice from the ordinary understanding of morality. Moreover, he repeatedly alleged connections between the two. In Book IV, after Socrates defines the virtues (441c-442d), he and Glaucon agree that the Platonically just man is least likely of all men to commit what would ordinarily be thought immoral acts; and in Book VI, Socrates attributes the vulgar moral virtues to men of a philosophical nature-to men, that is, whose souls are pre-eminently ordered by Platonic justice (484a-487a). Doubtless, then, Plato thought that men who were just according to his conception of justice would pass the tests of ordinary morality. But although Plato more than once has Socrates say things to this effect, he nowhere tries to prove it. Attempts to show that Platonic justice entails ordinary morality are strikingly missing from the Republic; Plato merely assumes that having the one involves having the other. The assumption, moreover, is implausible. On Plato's view, the fulfillment of the functions of the soul's parts constitutes wisdom or intelligence, courage, and self-control; and if these obtain, justice, according to Plato, also obtains. Intelligence, courage, and self-control are, however, prima facie compatible with a variety of vulgar injustices and evil doing. Neither as usually understood nor as Plato characterizes them are those virtues inconsistent with performing any of the acts Thrasymachus and Glaucon mention as examples of injustice. In this regard it is tempting to assert that the most that can be said on behalf of Plato's argument is that crimes and evils could not be done by a Platonically just man in a foolish, unintelligent, cowardly, or uncontrolled way.
As regards (B):
[Plato] nowhere so much as assumes that men who are just according to the ordinary conception are also Platonically just. Indeed, there is no reason to suppose that this was his belief; but the omission of a claim to that effect within the framework of his argument cannot but seem surprising. Plato abundantly represents Thrasymachus, Glaucon, and Adeimantus as questioning the happiness of ordinarily just, moral men. It seems incontrovertible that when they ask to be shown how justice, because of its power, constitutes the greatest good of the soul, Glaucon and Adeimantus are taking for granted that the souls of vulgarly just men will enjoy the efects of justice. Nonetheless, an examination of Socrates' reply to Glaucon and Adeimantus (an examination, that is, of Book II, 367e to Book X, 612b) fails to uncover any claim whose import is that vulgar justice entails Platonic justice.