While visiting Athens's port, Piraeus, with Glaucon, Socrates is invited to join Polemarchus for a dinner and festival. They eventually end up at Polemarchus' house where Socrates encounters Polemarchus' father Cephalus.

In his first philosophical conversation with the group members, Socrates gets into a conversation with Cephalus. The first real philosophical question posed by Plato in the book is when Socrates asks "is life painful at that age, or what report do you make of it?" when speaking to the aged Cephalus.

Cephalus answers by saying that many are unhappy about old age because they miss their youth, but he finds that "old age brings us profound repose and freedom from this and other passions. When the appetites have abated, and their force is diminished, the description of Sophocles is perfectly realized. It is like being delivered from a multitude of furious masters." The repose gives him time to dedicate himself to sacrifices and justice so that he is prepared for the afterlife.

Socrates then asks his interlocutors for a definition of justice. Three are suggested:
• Cephalus: To give each what is owed to them (331c)
• Polemarchus: To give to each what is appropriate to him (332c)
• Thrasymachus: What is advantageous for the stronger (338c)
Socrates refutes each definition in turn:
• One may owe it to someone to return them a knife one has borrowed, but if he has since gone mad and would only harm himself with it, returning the knife would not be just.
• Polemarchus suggests that what is appropriate is to do good to friends and bad to enemies, but harming someone tends to make them unjust, and so on his definition, justice would tend to create injustice.
• If it is just to do what rulers (the stronger) say and rulers make mistakes about their advantage, then it is just to do what is disadvantageous for the stronger.
Thrasymachus then responds to this refutation by claiming that insofar as the stronger make mistakes, they are not in that regard the stronger. Socrates refutes Thrasymachus with a further argument: Crafts aim at the good of their object, and therefore to rule is for the benefit of the ruled and not the ruler.

At this point, Thrasymachus claims that the unjust person is wiser than the just person, and Socrates gives three arguments refuting Thrasymachus. However, Thrasymachus ceases to engage actively with Socrates's arguments, and Socrates himself seems to think that his arguments are inadequate, since he has not offered any definition of justice. The first book ends in aporia concerning the essence of justice.
Glaucon and Adeimantus are unsatisfied with Socrates's defense of justice. They ask Socrates to defend justice against an alternative view that they attribute to many. According to this view, the origin of justice is in social contracts. Everyone would prefer to get away with harm to others without suffering it themselves, but since they cannot, they agree not to do harm to others so as …

Read more on Wikipedia

Aristotle systematises many of Plato's analyses in his Politics, and criticizes the propositions of several political philosophers for the ideal city-state.

Zeno of Citium, the founder of Stoicism, wrote his version of an ideal society, Zeno's Republic, in opposition to Plato's Republic. Zeno's Republic was controversial and was viewed with some embarrassment by some of the later Stoics due to its defenses of free love, incest, and cannibalism and due to its opposition to ordinary education and the building of temples, law-courts, and gymnasia.

The English title of Plato's dialogue is derived from Cicero's De re publica, written some three centuries later. Cicero's dialogue imitates Plato's style and treats many of the same topics, and Cicero's main character Scipio Aemilianus expresses his esteem for Plato and Socrates.

Augustine of Hippo wrote his The City of God; Augustine equally described a model of the "ideal city", in his case the eternal Jerusalem, using a visionary language not unlike that of the preceding philosophers.
Islamic philosophers were much more interested in Aristotle than Plato, but not having access to Aristotle's Politics, Ibn Rushd (Averroes) produced instead a commentary on Plato's Republic. He advances an authoritarian ideal, following Plato's paternalistic model. Absolute monarchy, led by a philosopher-king, creates a justly ordered society. This requires extensive use of coercion, although persuasion is preferred and is possible if the young are properly raised. Rhetoric, not logic, is the appropriate road to truth for the common man. Demonstrative knowledge via philosophy and logic requires special study. Rhetoric aids religion in reaching the masses.

Following Plato, Ibn Rushd accepts the principle of women's equality. They should be educated and allowed to serve in the military; the best among them might be tomorrow's philosophers or rulers. He also accepts Plato's illiberal measures such as the censorship of literature. He uses examples from Arab history to illustrate just and degenerate political orders.
The medieval jurist Gratian in his Decretum (ca 1140) quotes Plato as agreeing with him that "by natural law all things are common to all people." He identifies Plato's ideal society with the early Church as described in the Acts of the Apostles. "Plato lays out the order", Gratian comments, "for a very just republic in which no one considers anything his own."
Thomas More, when writing his Utopia, invented the technique of using the portrayal of a "utopia" as the carrier of his thoughts about the ideal society. More's island Utopia is also similar to …

Read more on Wikipedia

In his 1934 Plato und die Dichter (Plato and the Poets), as well as several other works, Hans-Georg Gadamer describes the utopic city of the Republic as a heuristic utopia that should not be pursued or even be used as an orientation-point for political development. Rather, its purpose is said to be to show how things would have to be connected, and how one thing would lead to another—often with highly problematic results—if one would opt for certain principles and carry them through rigorously. This interpretation argues that large passages in Plato's writing are ironic, a line of thought initially pursued by Kierkegaard.
The city portrayed in the Republic struck some critics as harsh, rigid, and unfree; indeed, as totalitarian. Karl Popper gave a voice to that view in his 1945 book The Open Society and Its Enemies, where he singled out Plato's state as a dystopia. Popper distinguished Plato's ideas from those of Socrates, claiming that the former in his later years expressed none of the humanitarian and democratic tendencies of his teacher. Popper thought Plato's envisioned state totalitarian as it advocated a government composed only of a distinct hereditary ruling class, with the working class—who Popper argues Plato regards as "human cattle"—given no role in decision making. He argues that Plato has no interest in what are commonly regarded as the problems of justice—the resolution of disputes between individuals—because Plato has redefined justice as "keeping one's place".

Popper insists that the Republic "was meant by its author not so much as a theoretical treatise, but as a topical political manifesto", and Bertrand Russell argues that at least in intent, and all in all not so far from what was possible in ancient Greek city-states, the form of government portrayed in the Republic was meant as a practical one by Plato.
Many critics have suggested that the dialogue's political discussion actually serves as an analogy for the individual soul, in which there are also many different "members" that can either conflict or else be integrated and orchestrated under a just and productive "government." Among other things, this analogical reading would solve the problem of certain implausible statements Plato makes concerning an ideal political republic. Norbert Blössner (2007) argues that the Republic is best understood as an analysis of the workings and moral improvement of the individual soul with remarkable thoroughness and clarity. This view, of course, does not preclude a legitimate reading of the Republic as a political treatise (the work could operate at both levels). It merely implies that it deserves more attention as a work on psychology and moral philosophy than it has sometimes received.

Eric Voegelin in Plato and Aristotle (Baton Rouge, 1957), gave meaning to the concept of 'Just City in Speech' (Books II–V). For instance, there is evidence in the dialogue that Socrates himself would not be a member of his 'ideal' state. His life was almost solely dedicated to the private pursuit of knowledge. More practically, Socrates suggests that members of the lower classes could rise to the higher ruling class, and vice versa, if they had 'gold' in their veins—a version of the concept of social mobility. The exercise of power is built on the 'noble lie' that all men are brothers, born of the earth, yet there is a clear hierarchy and class divisions. There is a tripartite explanation of human psychology that is extrapolated to the city, the relation among peoples. There is no family among …

Read more on Wikipedia