An argument for the definition of justice in Plato's Republic (433E6–434A1)
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My interpretation of the argument, then, fully generalized, is this:
To do one's own is to act in such a way as to aim for each having his own.
For each to have his own is justice(h) and to act in such a way as to aim for justice(h) is justice(d).
Therefore, the having of one's own is justice(h) and the doing of one's own is justice(d).
The advantage of this view is that it, unlike that of Vlastos, does not need to supply problematic premisses, such as (S2), in order to render Plato's argument valid. Moreover, I have argued that there is good reason to suppose that a proper reading of Plato's first premiss contains a notion that Vlastos' interpretation had to supply in an additional premiss (S1). One aspect of what I have argued is the correct understanding of Plato's argument does need to be supplied, however, namely, that for one to do one's own one must accomplish one's beneficent aims. Although it is true that Plato only talks of the rulers' aims in the law courts, I think there is good reason to supply the accomplishment condition, for without it, Plato leaves open two possibilities that would embarass his view. First, without this added condition, we could have a case where A did his own with reference to B and C, yet B and C did not have their own as a result of A 's action. Secondly, there could be a case where A did his own, and B and C had their own as a result of A's doing something, yet B and C would not have their own as a result of A's doing his own with reference to B and C.The reason Plato does not consider these problems, I think, is because he would not have considered cases in which his rulers had beneficent aims, but were ineffective in achieving them purposefully. The guarantee of justice in Plato's just state is that it would be administrated by rulers who are both utterly beneficent and utterly efficient. Under these conditions, all will have their own, for all will do their own. This implication, I have argued, is all we need to protect Plato's utopian state from the potential for πλεoνεξία, and it is all we need to provide a valid reading of the argument from 433E6–434A1.
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