The challenge Thrasymachus presents to Socrates in Book 1 of the Republic is that might makes right in any state at all. Nobody can figure out right and wrong, for the government of a state is alone powerful enough to decide what is right and just (237). Thus the interest of the stronger is to be identified with justice. It is for the people only to obey.
Socrates' questions force Thrasymachus to admit that from time to time, those who rule in a state make mistaken judgments and mistaken laws, even against their own best interests. Thus Thrasymachus falls into a contradiction. For if the government is mistaken even though strong, it is logically impossible for it to be right, however strong. Furthermore, if it is still just for the ruled to obey their rulers' laws, then justice is a sham, for obeying a mistaken judgment or law cannot be just for either subjects or state.
Thrasymachus answers this by saying that it is only under conditions of serious rule that a ruler cannot be mistaken. That is because he is ruling in his own best interest, always in the interest of strength. Socrates' answer to that the ruler is not right just because he is strong and further that rulers may make laws that are not merely in their own interests but in the interests of their weaker subjects. In this, rulers resemble other professionals, such as physicians, who do not make medical judgments for their own interest but in the interests of either the medical art or patients under their care.
According to Thrasymachus, the comparison does not apply, since whether a ruler is just or unjust he makes laws that will benefit him. Moreover, the larger the scale of control the unjust ruler has, the more likely it is that he will rule in ways to benefit him and not his people. Thus does injustice triumph, says Thrasymachus: "Injustice, when on a sufficient scale, has more strength and freedom and mastery than justice; and, as I said at first, justice is in ...