Plato The Republic: Is Justice of Wisdom?

In The Republic, Plato addresses the virtues of justice in general and the meaning of justice.  Through Socratic dialogue, Plato slowly breaks down conventional definitions of justice.   It is not returning all debts, or paying a man what he deserves.  It is not obeying your leader or benefiting the stronger.  What then, is it?  And is it a virtue at all?  The discussion reaches a point in which someone challenges whether or not justice is worthwhile.  Thrasymachus, the caustic debater who seems to play devil's advocate whenever opportunity arises takes the stance of supporting injustice.  But, Socrates counters, injustice cannot be virtuous since it opposes wisdom.  A wise man is just because he does not seek to be better than those around him but rather to be the best for himself.  He who has mastered a trade has no need to compete with others in the same field. 
So brings us to the question: is this kind of wisdom truly justice? 
The kind of justice that Socrates is pursuing is one in which all men are treated fairly.  But, if the world were full of wise men as Socrates described, how would it be just?  True, people would pursue their work for the benefit of themselves and the people they serve (a justness described in earlier arguments), but they would pursue these fields in isolation.  How can one know what is unfair or fair if they only know what is theirs?