In reading the Republic, there is no reason to search for arguments which show that Platonic justice ('inner justice' or 'psychic harmony') entails ordinary justice. The relationship between inner justice and ordinary justice is of no importance in Plato's Republic. We note that Plato tries to argue from the very first book that the true source of normativity lies in knowledge attained by philosophical reason. What is crucial, then, is the relationship between inner justice and acts which brings about a just polis.
I. The Unimportance of Ordinary Justice
The issue of the relationship between inner justice and ordinary justice has been the subject of critical discussion since it was famously raised by David Sachs. (1) In this essay, I shall argue that the relationship between inner (or 'Platonic') justice and ordinary justice (conceived as doing acts which Glaucon, Adeimantus and the rest of the gathering consider to be just) was of no importance in Plato's Republic. (2) What was important, rather, was the relationship between inner justice and acts which bring about a just polis.
My claim about the unimportance of ordinary justice in relation to inner justice is pre-empted to some degree by Gregory Vlastos and Julia Annas. Vlastos distinguished two senses of ordinary justice:(3) (a) the degenerate morality of those who see it as a path to gratification, and (b) the common morality of those who respect virtue and have a firm disposition to act justly ('justice' as Cephalus possessed, for example).
Vlastos rejected any connection between inner justice and ordinary justice in the sense of (a), but assumed that inner justice entailed ordinary justice in the sense of (b) and argued for the connection. However, at least the following difficulty stands in the way of any argument for the entailment, namely, Plato sometimes drew a distinction between the vices of discord and ignorance, and held that it was possible to overcome discord in the soul and yet act ignorantly. This is the condition characterizing Cephalus. But the point made is that it is impossible to be in Cephalus' condition if one has not overcome discord in one's soul, and nowhere is it suggested that psychic harmony necessarily entails the form of morality practiced by Cephalus. It would seem too quick to assume an entailment relationship as Vlastos does.
A Fallacy of Equivocation?
The reason that Vlastos and others have tried to argue that inner justice entails ordinary justice might be that it is often assumed that Plato was committed to answering the challenge of Glaucon and Adeimantus to show that justice as they knew it to be was beneficial to the agent apart from its consequences. If the results of inner justice fail to match their ordinary knowledge of justice, Plato would be guilty of committing a fallacy of equivocation. But it is not often noticed that Glaucon and Adeimantus have no definition of justice. They have instead the haphazard intuitions of the rest,...