1. Plato's Republic is essentially a conflict between two radically different views of how to live and of the meaning of happiness, that of many Athenians, expressed by Thrasymachus and Plato's brothers, and that of Plato and Socrates. What, exactly, is the conflict and how does Socrates answer the challenge laid down by Thrasymachus and also by Plato's brothers Glaucon and Adeimantus, who ask him to explain what justice and injustice do to the soul? What argument does Thrasymachus make about justice and how does Socrates respond to Thrasymachus' claim that the happy life is the life of injustice, that is, how does he argue that the truth is the opposite? [Do not rely on the preliminary arguments against Thrasymachus at the end of Book I. This question is asking you to explain how and why justice makes a soul truly happy.]
2. What role does the Allegory of the Cave play in The Republic? Explain in some detail. How is it related to Socrates' speech in The Symposium and to the discussion of the life of philosophy in The Phaedo? What does The Good mean to Plato? Why does he begin The Republic with the Greek verb that means "I went down"?