Before continuing on to discover the four other virtues of the just city (and soul), Glaucon and Adeimantus demand Socrates explain his idea of the guardians sharing their wives and children. Socrates begins to discuss the guardian lifestyle at length.
The first is that women will be trained and raised in the same way as the men, thus taking on the same political roles. Socrates acknowledges the differences that men and women have in their nature, but posits that both have a demand in their souls. Some will be appetitive, some spirited, and some will be rational. Society will make use them accordingly.
Socrates then discusses the requirement that women and children be shared among the guardians. The guardians are only permitted to have sex during annual mating festivals. Some guardians will only be permitted to have one couple, while the more admirable ones can have multiple couplings. The children that are born from this festival will be taken and raised together. If there are any children born outside of this yearly festival, they will be killed.
The idea that Socrates has for this is a more unified city. In most cities, an individual's care is divided between care for their city and their family. In the kallipolis, everyone is considered family. Thus, there are no divided loyalties. Everyone says "mine" about the same things and carries forward with the same goals and concerns.
The next question Socrates must answer is if this lifestyle and city is possible outside of theory. Before answering this question, Socrates explores the guardians lifestyle relating to war. Children training to become guardians should be taken to the frontlines to see firsthand how war is conducted. They are to be put on the backs of the fastest horses to escape any harm. Any child that is considered cowardly in the face of war will lose their status as a guardian.
Socrates finally arrives at discussion of this city and lifestyle being possible. The only way it can become a reality, in Socrates' eyes, is if philosophers rule the city. This idea has come to be known as the "philosopher-king". Naturally, Socrates first has to define what he envisions for the philosopher-kings. He takes care to distinguish them from the "lovers of sights and sounds" that pervade Athenian society, ushering in the first discussion of the Theory of Forms.
The Forms are eternal, unchanging, universal absolute ideas. Some examples are the Good, the Beautiful, and the Equal. The Forms cannot be seen, but only understood with the mind. They are responsible for making the things we see around us into the things they are. Anything we see that is red participates in the Form of Red, anything beautiful participates in the Form of Beauty, and so on. The true philosophers have knowledge of these Forms. The "lovers of sights and sounds" claim to know beautiful things but have no knowledge of the Form of Beauty. Thus, they can only have opinions of Beauty but no knowledge of it.
To demonstrate philosophers only have knowledge, Socrates divides all of existence into three classes: what is, what is not, and what both is and is not. What is, is knowable; what is not is the object of ignorance; and what both is and is not is the object of opinion or belief. The only things completely are the Forms. Only the Form of the Beautiful is completely beautiful, and so on. Beautiful things witnessed in the world both are and are not. A beautiful person can also be not beautiful, depending on the standards applied. Therefore, we can only know the Forms, not their representations in the real world.