But let us consider: Have we not admitted that the rulers may be mistaken about their own interest in what they command, and also that to obey them is justice?
Has not that been admitted?
Yes.
Then you must also have acknowledged justice not to be for the interest of the stronger, when the rulers unintentionally command things to be done which are to their own injury.

For if, as you say, justice is the obedience which the subject renders to their commands, in that case, O wisest of men, is there any escape from the conclusion that the weaker are commanded to do, not what is for the interest, but what is for the injury of the stronger?
Nothing can be clearer, Socrates, said Polemarchus.
SOCRATES - CLEITOPHON - POLEMARCHUS - THRASYMACHUS Yes, said Cleitophon, interposing, if you are allowed to be his witness.
But there is no need of any witness, said Polemarchus, for Thrasymachus himself acknowledges that rulers may sometimes command what is not for their own interest, and that for subjects to obey them is justice.
Yes, Polemarchus,--Thrasymachus said that for subjects to do what was commanded by their rulers is just.
Yes, Cleitophon, but he also said that justice is the interest of the stronger, and, while admitting both these propositions, he further acknowledged that the stronger may command the weaker who are his subjects to do what is not for his own interest; whence follows that justice is the injury quite as much as the interest of the stronger.
But, said Cleitophon, he meant by the interest of the stronger what the stronger thought to be his interest,--this was what the weaker had to do; and this was affirmed by him to be justice.
Those were not his words, rejoined Polemarchus.
SOCRATES - THRASYMACHUS Never mind, I replied, if he now says that they are, let us accept his statement.

Tell me, Thrasymachus, I said, did you mean by justice what the stronger thought to be his interest, whether really so or not?
Certainly not, he said.

Do you suppose that I call him who is mistaken the stronger at the time when he is mistaken?
Yes, I said, my impression was that you did so, when you admitted that the ruler was not infallible but might be sometimes mistaken.
You argue like an informer, Socrates.

Do you mean, for example, that he who is mistaken about the sick is a physician in that he is mistaken?
or that he who errs in arithmetic or grammar is an arithmetician or grammarian at the me when he is making the mistake, in respect of the mistake?
True, we say that the physician or arithmetician or grammarian has made a mistake, but this is only a way of speaking; for the fact is that neither the grammarian nor any other person of skill ever makes a mistake in so far as he is what his name implies; they none of them err unless their skill fails them, and then they cease to be skilled artists.