In Book 1 of The Republic, Thrasymachus sets up a challenge to justice. Thrasymachus is a Sophist, one of the teachers-for-hire who preached a creed of subjective morality to the wealthy sons of Athens. The Sophists did not believe in objective truth, including objective moral truth. They did not think, in other words, that anything was absolutely “right” or “wrong.” Instead they viewed all actions as either advantageous or disadvantageous to the person performing them. If an action was advantageous then they thought you should engage in it, and if it was disadvantageous then they thought that you should refrain. Taking this belief to its logical conclusion, some of them went so far as to claim that law and morality are nothing but mere convention, and that one ought to try to get away with injustice and illegality whenever such action would be to one’s advantage. Plato meant to combat this attitude in The Republic.

Thrasymachus introduces the Sophist challenge by remarking that justice is nothing but the advantage of the stronger. He does not mean to define justice with this statement, but to debunk it. His claim proceeds from the basic Sophistic moral notion: that the norms considered just are nothing more than conventions which hamper those who adhere to them, and benefit those who flout them. Those who behave unjustly naturally gain power and become the rulers, the strong people in society. Justice is the advantage of the stronger because when stupid, weak people behave in accordance with justice, they are disadvantaged, and the strong (those who behave unjustly) are advantaged.

An alternate reading of Thrasymachus’s bold statement makes his claim seem slightly more subtle. According to this reading (put forward by C.D.C. Reeve), Thrasymachus is not merely making the usual assertion that the norms of justice are conventions; he claims further that these mores and norms are conventions that were put in place by the rulers (the “stronger”) for the purpose of promoting their own interests. Conceptions of justice, in this reading, are the products of propaganda and tools of oppressors.

Regardless of the interpretation we give to Thrasymachus’ statement, the challenge to Socrates is the same: he must prove that justice is something good and desirable, that it is more than convention, that it is connected to objective standards of morality, and that it is in our interest to adhere to it. His attempt to meet this challenge occupies the rest of The Republic.