Plato's Republic is a dialogue in which Socrates investigates the nature of the city-state and what the ideal city-state should be. The philosophical inquiry in this dialogue can be seen as addressing two primary conceptions, conceptions which are linked under the heading of idealism, with one detailing Plato's epistemology and the other his political philosophy. The first is a more metaphysical consideration of the nature of life and the world and how we can know what we know, while the second is the practical application of various concepts to the state to demonstrate the relationship between the individual and his or her society in a utopian city-state such as Plato would create but which does not exist. To a degree, both Crito and Dionysius are correct--the Republic is a political work on its surface, but it has deeper intentions to bring together various philosophical conceptions around the definition of and application of the concept of justice, among others. Dionysius says Plato did not want the philosopher to become involved in politics, but explaining politics to others is different from becoming involved in it.
The primary subject of The Republic is justice, examined in broad terms:
The Republic is probably the most elaborate monograph on justice ever written. It examines a variety of views about justice, and it does this in a way which leads us to believe that Plato omitted none of the more important theories known to him. In fact, Plato clearly implies that because of his vain attempts to track it down among the current views, a new search for justice is necessary (Popper 49).
The entire discussion begins with a question about justice, which means not only what a state can impose but justice between and for individuals. The discussion indeed begins with the fact that there are inequities in society and in life, in society in terms of wealth, in life in terms of such things as age:
If it is true that a ...