What is Plato’s problem with democracy? Are his objections to democracy valid? Are they sound? Justify your answer.
Has any society ever been run by philosophers? If so, which? If not, why does Plato think that it is possible?
Present the strongest argument in support of Thrasymachus’ definition of justice in Book I of the Republic.
What does it mean to prove something through reason? What is an example of such proof? How does this form of reasoning relate to the mode of reasoning Plato employs in the Republic? In your opinion, can philosophical questions ever be answered mathematically? Why or why not? Fully explore your answer, with at least some reference to the arguments presented in the Republic.