In the first book of Plato's The Republic the topic being discussed is "what is justice for the individual?- From this common foundation, the conversation is expanded to a broader level with the explanation and definition of morality and traditional society. Plato's aim throughout this discussion is to understand social and political solidity on a basis of moral resolutions that every man should live by. The protagonist uses various methods in pursuit of this absolute definition, and that is how Thrasymachus' entry into the conversation is a fundamental break from what has previously occurred in the story.
Socrates begins questioning Cephalus out of natural curiosity. Socrates' philosophy is about asking questions and finding the answers through rational inquiry, discovering inevitable missteps along the way. He admires Cephalus' positive opinions on aging and death, but then inquires about Cephalus' happiness, wondering if he owes it all to the comforts of wealth. From this subject matter the conversation is steered towards the topic of justice. Cephalus says that justice is telling the truth and paying one's debts, and that this is how his wealth has been beneficial. When Socrates proves Cephalus' theory wrong, the conversation is then "bequeathed- from Cephalus to Polemarchus.
The main problem with Polemarchus' definition of justice, "doing good to your friends and harm to your enemies," is the weakness of its specific terms. Predictably, Socrates explores each one, revealing every little imperfection in his search for the truth. It is this diligence that leads Thrasymachus to accuse Socrates of only asking questions and never answering them. Until the entry of Thrasymachus, Socrates' associates have accepted his philosophical suppositions as a process rather than a viewpoint, as Socrates has been offering positive solutions and ideas.
Thrasymachus' definition of justice is that the stronger uses his advantage over the weaker in order to act in his own self-interest.
