In the Republic, we get two main questions: (i) What is justice?, (ii) Is it advantageous to be just?
The second question turns out to be very hard, since it looks like a lot of unjust people do quite well. Throughout the Republic there are a series of arguments that intend to show that one is better off if just, although it is flagged as very difficult to show.
For the first question, the interlocutors decide to “found a city in speech,” in particular, they are trying to describe the best city. First they try to find a satisfactory answer to “what is justice?” by looking at justice as a virtue of an individual person and are unable to find an answer. Socrates suggests that perhaps it is easier to see what justice is if it is studied in a political setting, as a feature of the best state/city. The idea is that one might more easily see the details if the object is larger. Once a blueprint of this best city is on the table, it should be easier to see what justice is. Discussion in the early books of the Republic explores what kind of education is needed in the best
city. Namely: children must come to love the good. The idea is that games, architecture, poetry, and everything that contributes to the designed environment and cultural environment in which children grow up makes a difference. Poetry should present you with heroes who really are good; the gods shouldn’t be portrayed as committing crimes, but instead as good; and so on. Note: it’s a remarkable fact about a political philosophy that it spends so much time on education. There is very little about laws, and a lot about the kinds of attitudes that people should have.
However, it is assumed that not everyone has the same talents. Plato proposes that people should engage in activities that they are good at. Everyone should do ‘their job’ (ergon), that which they are talented for, and they should do it well (and be trained for it, and to the extent relevant to their job in society).
This leads to a distinction between three classes: those who receive the most extensive education (including many years of mathematics) are the so-called guardians. They are the care-takers or rulers of the city. Second, the guardians need someone at their side to support them and to protect the city, and this is the ‘auxiliary’ class, the class of warriors. Third, there’s the class of those who have what today we might call ‘a regular job’: they have some skill and they make money by performing the relevant tasks, say, shipbuilding or shoemaking or farming.
Eventually, Plato will make explicit that the guardians are the philosophers. That is what is known as the claim that philosophers should rule (‘philosopher kings’). Plato is aware that no one trusts philosophers with this kind of job and that it is going to be perceived an outrageous idea. He calls it a “wave,” which means that it will create a stir – a wave of resistance is to be expected when one says this aloud. It is the third of three waves. The first wave is that there should be the same education for men and women. The second wave is the so-called community of women and children, which (roughly) means that life in the best city should not be arranged in such a way that the small-scale family we are used to is the most basic unit relevant to the social fabric. Instead, there are lots of communal arrangements, eating together, kids growing up with other kids (one should feel like a parent to every child of the next generation, not just to one’s own child), etc.