Nettleship on Limit and Pleonexia

Here is Nettleship's explanation of the point of the argument:

In all other arts the man who is without the idea of right or wrong (in the wider sense of the words), or the idea of a limit at which he must stop, is not the man who understands his art; he is the man who knows nothing about it. For suppose two musicians meet over the tuning of an instrument; if they are really musicians, they at once recognize a principle of right and wrong, which sets a limit beyond which it would never occur to them to go; in plain English, if the instrument is rightly tuned, the musician, the man who knows, would never think of tuning it further.

He then points out that principles of maximization (to achieve or get as much as possible) are opposed to this conception of correct action:

The word[s] 'limit' [and 'measure'] certainly suggest[] to us something that stops progress, and prevents us reaching perfection in anything. The Greek associations of the words, at least in Plato and Aristotle, are quite different. The idea of limit is that of something on the attainment of which perfection is attained; it is not that which puts a stop to progress, but that without which progress would be a meaningless process ad infinitum.

This correct (I believe) construction of Plato's argument cannot be arrived at if we take pleonektein competitively, as 'winning out over someone'. The way Plato understands it, to say that an unjust person pleonektei as regards an unjust person is to say that he is unsatisfied even with what he has, as an unjust person: if he could, he would take even more than he has. In contrast, a just person is satisfied--he does not want more than a just person should get in a just action--but he would not be satisfied if he received what an unjust person should receive, because, he thinks, less is due to an unjust in comparison with a just person. (Note that a just person wishes for no more than he thinks it right that he gets--this is the reason, I think, why Plato uses both ethelein and axioun.)

And now we can see, too, why David Reeve's criticisms are off the mark. Reeve says:

Now it is true that the Craftsman does not try to "outdo" his fellow Craftsmen in that he does not try to go beyond the principles of his (and their) Craft. But the Unjust man does not try to "outdo" his fellows in that way either. Instead, he tries to get the better of them by practicing the Craft of Injustice as well as possible.

Not so. A just person aims to practice the craft of justice by seeing that his actions conform to a 'limit' (as Nettleship says); but an unjust person does not aim to practice injustice in this way. To suggest that he does is to suggest, wrongly, that he takes something about his unjust action as inherently desirable. On the contrary, he always wants more: that is, if he could do something that would result in his getting more, whatever this was, he would prefer that.

Reeve then says:

Moreover, the fact that the Unjust man tries to "outdo" everyone in the sense of trying to get the better of them does not in the least show that Injustice is not a Craft--practitioners of competitive Crafts, such as Generalship or Boxing, do it all the time.

But we've seen that this competitive sense of pleonektein is not what Plato has in mind.

(I'm not sure yet what to think of Rachel Barney's gloss, in her article at SEP: "The use of pleonektein in this argument is confusing, and perhaps confused, but the important point seems to be that the goods realized by genuine crafts are not zero-sum. The doctor's restoration of the patient's health does not make anyone else less healthy; if one musician plays in tune, so may another." )