Now, as you and I, Glaucon, are not convinced by him, we must reply to him; but if we try to compare their respective gains we shall want a judge to decide for us; we had better therefore proceed by making mutual admissions of the truth to one another.
Thrasymachus had asserted that perfect injustice was more gainful than perfect justice, and after a little hesitation he is induced by Socrates to admit the still greater paradox that injustice is virtue and justice vice.

Socrates praises his frankness, and assumes the attitude of one whose only wish is to understand the meaning of his opponents.

At the same time he is weaving a net in which Thrasymachus is finally enclosed.
The admission is elicited from him that the just man seeks to gain an advantage over the unjust only, but not over the just, while the unjust would gain an advantage over either.

Socrates, in order to test this statement, employs once more the favourite analogy of the arts.

The musician, doctor, skilled artist of any sort, does not seek to gain more than the skilled, but only more than the unskilled (that is to say, he works up to a rule, standard, law, and does not exceed it), whereas the unskilled makes random efforts at excess.