In The Republic, Plato hypothesizes the formation of the ideal city, the kallipolis, as a way to embody the philosophical definition of perfect justice. In the just city, one is most likely to see the execution of perfect justice, and so the composition of this city will be the best indicator of justice as an idea. For Plato, justice had a simple definition (with a much more complicated rationalization): justice is each person in the city doing only the work to which they are best suited:

“Then, it turns out that this doing one’s own work – provided that it comes to be in a certain way – is justice.” (433b)

The argument that justice is each doing one’s own work transitions naturally into Plato’s (speaking through Socrates) next one, that the kallipolis should be ruled by philosopher-kings. If each person in the city-state is only best suited to one kind of work, if they want to carry out that work perfectly, then only a very select few people will actually possess the aptitude and skills necessary for leading the city as its kings. Plato argues that these people are the philosophers.

The ideal society of course contains many other kinds of people. The guardians of the city must possess a perfect balance of temperance and courage, and they must be loyal only to their own city-state. In fact, they should behave as dogs do—for Plato argues that dogs love their owners unconditionally, even if they have only ever received abuse from them. This is because dogs know their owners, and do not know strangers, of whom they are always suspicious. Dogs, therefore, only form loyalties based on things that they know—on their knowledge—and are thus good models for the guardians of the city. The ideal city should also contain carpenters, poets, farmers, tradesmen, musicians, and every other kind of person who holds an occupation that gives the city its material and cultural life. However, these people must only engage in the craft to which they have the highest affinity.

But philosophers, above all other people, are fit to rule the kallipolis. The reason for this is because, according to Plato, the philosophers are the only people wise enough to act in accordance with the idea of justice. In Plato’s philosophy, the idea of a metaphysical concept, such as justice, love, beauty, etc., was that concept abstracted from any of its physical manifestations in the sensible world. One does not speak of the true, unchangeable concept of beauty, for example, if they are talking about the individual beauty of a person or of nature. This is because, over time, the things in the physical world that represent beauty (or any other concept) change, as do individuals’ perceptions of them, and are therefore impermanent.

Plato argued that true beauty, or justice, are never-changing, eternal, and allow things in the physical world to have such attributes. This inveterate form of the metaphysical concept of Justice is what Plato referred to as the “Idea” of it, and he further argued that only the philosophers were capable of understanding the Ideas. Because of this unique ability of theirs, the philosophers were the only individuals capable of making decisions and acting on a form of Justice that was eternal and pure, and they would therefore not be capricious, arbitrary, or cruel in their administration of the city.

This social composition, and the philosophic rationalization that lie behind it, were the most important features of Plato’s ideal city.

Plato's ideal society consisted of a strict division of labor between the three classes:

The Guardians or Philosopher-Kings/Queens ruled the city.

The Auxiliaries were the warriors who protected the city.

The Producers were the artisans and merchants.

According to Book IV of the Republic, justice required each of the three parts to perform the task that was proper to it. His ideal city was an aristocracy of sorts.

In addition to this, Plato introduces the "three waves of paradox" in Book V of the Republic. First, he suggests men and women receive the same musical and gymnastic education; this was remarkable for his time. Second, he suggests that women and children are all in common. The third wave has to do with philosopher-kings; these are men who are true philosophers but who are also rulers in the city. 

A very strict educational program lies at the foundation of Plato's ideal state. This is laid out in Book II of the Republic. Plato advocates a censorship of the arts in his ideal city and emphasizes the importance of athletics as well. The guardians have to undergo an additional ten years of mathematical education (as described in Book VII of the Republic).

Plato's ideal society, as outlined in his Republic, is primarily composed of two classes. The guardians are responsible for protecting the state, and are divided into two sub-classes: the rulers and auxiliaries. Rulers are the wisest of the guardians, and establish laws for the rest of society to follow. The auxiliaries are soldiers who defend the state, but also preserve order inside the state and serve as an example for the rest of the citizenry to follow. The second class is the citizenry, or those who perform basic societal roles.

For Plato, the education of the guardians is central in his discussion of the ideal state. His theory of education rests on the notion of "mimesis," or imitation. In order to characterize the four classical virtues of courage, wisdom, justice, and temperance, the guardians are to imitate heroes found in poetry and those of a superior rank. However, the guardians may only read poetry that depicts heroes acting virtuously; otherwise, the guardians may learn that sometimes heroes act unvirtuously and thereby act unvirtuously themselves.

The guardians are also instructed to simultaneously study music and gymnastics. Music, according to Plato, awakens the individual's passion, thereby motivating them to serve the state. Music also soothes the individual, which balances out what Plato claims are the negative consequences of gymnastics, or exercise. Exercise, for Plato, makes one hostile and aggressive. The proper balancing of music and exercise then allows the guardian to be courageous and capable in war, but also calm, collected, and willing to serve the polity.

Through this education, Plato concluded that the guardians, and by extension the citizenry since the guardians serve as role models for the citizenry, could best rule themselves and thereby establish a strong, stable society.

Plato's ideal society is built on the ideal of justice. Just as he believed the soul was composed of three hierarchical parts—appetitive, rational, and spiritual—he believed a just society should be composed of three corresponding classes: the guardians (philosophers charged with governing the republic), the auxiliaries (soldiers who defend the republic), and the producers (farmers/craftsmen, etc.). This class structure should be kept in harmony through strict, totalitarian laws and robust censorship (poets, for instance, were banished from the republic).

Moreover, Plato eliminated virtually every distinction between public and private life, as this distinction could serve to corrupt the harmony of the republic. Consequently, Plato's society abolished the traditional family; both wives and children would be communal. Further, private property was abolished insofar as was possible. This emphasis on public rather than private life was meant to cause the citizens to put the republic before their own selfish interests.