Definition of justice
In the first book, two definitions of justice are proposed but deemed inadequate. Returning debts owed, and helping friends while harming enemies, are common sense definitions of justice that, Socrates shows, are inadequate in exceptional situations, and thus lack the rigidity demanded of a definition. Yet he does not completely reject them, for each expresses a common sense notion of justice which Socrates will incorporate into his discussion of the just regime in books II through V.
At the end of Book I, Socrates agrees with Polemarchus that justice includes helping friends, but says the just man would never do harm to anybody. Thrasymachus believes that Socrates has done the men present an injustice by saying this and attacks his character and reputation in front of the group, partly because he suspects that Socrates himself does not even believe harming enemies is unjust. Thrasymachus gives his understanding of justice and injustice as "justice is what is advantageous to the stronger, while injustice is to one's own profit and advantage". Socrates finds this definition unclear and begins to question Thrasymachus. Socrates then asks whether the ruler who makes a mistake by making a law that lessens their well-being, is still a ruler according to that definition. Thrasymachus agrees that no true ruler would make such an error. This agreement allows Socrates to undermine Thrasymachus' strict definition of justice by comparing rulers to people of various professions. Thrasymachus consents to Socrates' assertion that an artist is someone who does his job well, and is a knower of some art, which allows him to complete the job well. In so doing Socrates gets Thrasymachus to admit that rulers who enact a law that does not benefit them firstly, are in the precise sense not rulers. Thrasymachus gives up, and is silent from then on. Socrates has trapped Thrasymachus into admitting the strong man who makes a mistake is not the strong man in the precise sense, and that some type of knowledge is required to rule perfectly. However, it is far from a satisfactory definition of justice.
At the beginning of Book II, Plato's two brothers challenge Socrates to define justice in the man, and unlike the rather short and simple definitions offered in Book I, their views of justice are presented in two independent speeches. Glaucon's speech reprises Thrasymachus' idea of justice; it starts with the legend of Gyges who discovered a ring that gave him the power to become invisible. Glaucon uses this story to argue that no man would be just if he had the opportunity of doing injustice with impunity. With the power to become invisible, Gyges is able to seduce the queen, murder the king, and take over the kingdom. Glaucon argues that the just as well as the unjust man would do the same if they had the power to get away with injustice exempt from punishment. The only reason that men are just and praise justice is out of fear of being punished for injustice. The law is a product of compromise between individuals who agree not to do injustice to others if others will not do injustice to them. Glaucon says that if people had the power to do injustice without fear of punishment, they would not enter into such an agreement. Glaucon uses this argument to challenge Socrates to defend the position that the unjust life is better than the just life. Adeimantus adds to Glaucon's speech the charge that men are only just for the results that justice brings one fortune, honor, reputation. Adeimantus challenges Socrates to prove that being just is worth something in and of itself, not only as a means to an end.
Socrates says that there is no better topic to debate. In response to the two views of injustice and justice presented by Glaucon and Adeimantus, he claims incompetence, but feels it would be impious to leave justice in such doubt. Thus the Republic sets out to define justice. Given the difficulty of this task as proven in Book I, Socrates in Book II leads his interlocutors into a discussion of justice in the city, which Socrates suggests may help them see justice not only in the person, but on a larger scale, "first in cities searching for what it is; then thusly we could examine also in some individual, examining the likeness of the bigger in the idea of the littler" (368e–369a).
For over two and a half millennia, scholars have differed on the aptness of the city-soul analogy Socrates uses to find justice in Books II through V. The Republic is a dramatic dialogue, not a treatise. Socrates' definition of justice is never unconditionally stated, only versions of justice within each city are "found" and evaluated in Books II through Book V. Socrates constantly refers the definition of justice back to the conditions of the city for which it is created. He builds a series of myths, or noble lies, to make the cities appear just, and these conditions moderate life within the communities. The "earth born" myth makes all men believe that they are born from the earth and have predestined natures within their veins. Accordingly, Socrates defines justice as "working at that which he is naturally best suited," and "to do one's own business and not to be a busybody" (433a–433b) and goes on to say that justice sustains and perfects the other three cardinal virtues: Temperance, Wisdom, and Courage, and that justice is the cause and condition of their existence. Socrates does not include justice as a virtue within the city, suggesting that justice does not exist within the human soul either, rather it is the result of a "well ordered" soul. A result of this conception of justice separates people into three types; that of the soldier, that of the producer, and that of a ruler. If a ruler can create just laws, and if the warriors can carry out the orders of the rulers, and if the producers can obey this authority, then a society will be just.
The city is challenged by Adeimantus and Glaucon throughout its development: Adeimantus cannot find happiness in the city, and Glaucon cannot find honor and glory. This hypothetical city contains no private property, no marriage, or nuclear families. These are sacrificed for the common good and doing what is best fitting to one's nature. In Book V Socrates addresses the question of "natural-ness" of and possibility for this city, concluding in Book VI, that the city's ontological status regards a construction of the soul, not of an actual metropolis.
The rule of philosopher-kings appear as the issue of possibility is raised. Socrates never positively states what justice is in the human soul/city; it appears he has created a city where justice is not found, but can be lost. It is as though in a well-ordered state, justice is not even needed, since the community satisfies the needs of humans.
In terms of why it is best to be just rather than unjust for the individual, Plato prepares an answer in Book IX consisting of three main arguments. Plato says that a tyrant's nature will leave him with "horrid pains and pangs" and that the typical tyrant engages in a lifestyle that will be physically and mentally exacting on such a ruler. Such a disposition is in contrast to the truth-loving philosopher king, and a tyrant "never tastes of true freedom or friendship." The second argument proposes that of all the different types of people, only the Philosopher is able to judge which type of ruler is best since only he can see the Form of the Good. Thirdly, Plato argues, "Pleasures which are approved of by the lover of wisdom and reason are the truest." In sum, Plato argues that philosophical pleasure is the only true pleasure since other pleasures experienced by others are simply a neutral state free of pain.
Socrates points out the human tendency to be corrupted by power leads down the road to timocracy, oligarchy, democracy and tyranny. From this, he concludes that ruling should be left to philosophers, who are the most just and therefore least susceptible to corruption. This "good city" is depicted as being governed by philosopher-kings; disinterested persons who rule not for their personal enjoyment but for the good of the city-state (polis). The paradigmatic society which stands behind every historical society is hierarchical, but social classes have a marginal permeability; there are no slaves, no discrimination between men and women. The men and women are both to be taught the same things, so they are both able to be used for the same things (451e). In addition to the ruling class of guardians (φύλακες), which abolished riches, there is a class of private producers (demiourgoi), who may be rich or poor. A number of provisions aim to avoid making the people weak: the substitution of a universal educational system for men and women instead of debilitating music, poetry and theatre—a startling departure from Greek society. These provisions apply to all classes, and the restrictions placed on the philosopher-kings chosen from the warrior class and the warriors are much more severe than those placed on the producers, because the rulers must be kept away from any source of corruption.
In Books V-VI the abolition of riches among the guardian class (not unlike Max Weber's bureaucracy) leads controversially to the abandonment of the typical family, and as such no child may know his or her parents and the parents may not know their own children. Socrates tells a tale which is the "allegory of the good government". No nepotism, no private goods. The rulers assemble couples for reproduction, based on breeding criteria. Thus, stable population is achieved through eugenics and social cohesion is projected to be high because familial links are extended towards everyone in the City. Also the education of the youth is such that they are taught of only works of writing that encourage them to improve themselves for the state's good, and envision (the) god(s) as entirely good, just, and the author(s) of only that which is good.
In Books VII-X stand Plato's criticism of the forms of government. It begins with the dismissal of timocracy, a sort of authoritarian regime, not unlike a military dictatorship. Plato offers an almost psychoanalytical explanation of the "timocrat" as one who saw his father humiliated by his mother and wants to vindicate "manliness". The third worst regime is oligarchy, the rule of a small band of rich people, millionaires that only respect money. Then comes the democratic form of government, and its susceptibility to being ruled by unfit "sectarian" demagogues. Finally the worst regime is tyranny, where the whimsical desires of the ruler became law and there is no check upon arbitrariness.
Theory of universals
The Republic contains Plato's Allegory of the cave with which he explains his concept of The Forms as an answer to the problem of universals.
The allegory of the cave primarily depicts Plato's distinction between the world of appearances and the 'real' world of the Forms, as well as helping to justify the philosopher's place in society as king. Plato imagines a group of people who have lived their entire lives as prisoners, chained to the wall of a cave in the subterranean so they are unable to see the outside world behind them. However a constant flame illuminates various moving objects outside, which are silhouetted on the wall of the cave visible to the prisoners. These prisoners, through having no other experience of reality, ascribe forms to these shadows such as either "dog" or "cat".
Plato then goes on to explain how the philosopher is akin to a prisoner who is freed from the cave. The prisoner is initially blinded by the light, but when he adjusts to the brightness he sees the fire and the statues and how they caused the images witnessed inside the cave. He would see that the fire and statues in the cave were just copies of the real objects; merely imitations. This is analogous to the Forms. What we see from day to day are merely appearances, reflections of the Forms. The philosopher, however, will not be deceived by the shadows and will hence be able to see the 'real' world, the world above that of appearances; the philosopher will gain knowledge of things in themselves. In this analogy the sun is representative of the Good. This is the main object of the philosopher's knowledge. The Good can be thought of as the form of Forms, or the structuring of the world as a whole.
The prisoner's stages of understanding correlate with the levels on the divided line which he imagines. The line is divided into what the visible world is and what the intelligible world is, with the divider being the Sun. When the prisoner is in the cave, he is obviously in the visible realm that receives no sunlight, and outside he comes to be in the intelligible realm.
The shadows witnessed in the cave correspond to the lowest level on Plato's line, that of imagination and conjecture. Once the prisoner is freed and sees the shadows for what they are he reaches the second stage on the divided line, the stage of belief, for he comes to believe that the statues in the cave are real. On leaving the cave, however, the prisoner comes to see objects more real than the statues inside of the cave, and this correlates with the third stage on Plato's line, understanding. Lastly, the prisoner turns to the sun which he grasps as the source of truth, or the Form of the Good, and this last stage, named as dialectic, is the highest possible stage on the line. The prisoner, as a result of the Form of the Good, can begin to understand all other forms in reality.
At the end of this allegory, Plato asserts that it is the philosopher's burden to reenter the cave. Those who have seen the ideal world, he says, have the duty to educate those in the material world. Since the philosopher recognizes what is truly good only he is fit to rule society according to Plato.
The dialectical forms of government
While Plato spends much of the Republic having Socrates narrate a conversation about the city he founds with Glaucon and Adeimantus "in speech", the discussion eventually turns to considering four regimes that exist in reality and tend to degrade successively into each other: timocracy, oligarchy (also called plutocracy), democracy and tyranny (also called despotism).
Socrates defines a timocracy as a government of people who love rule and honor. Socrates argues that the timocracy emerges from aristocracy due to a civil war breaking out among the ruling class and the majority. Over time, many more births will occur to people who lack aristocratic, guardian qualities, slowly drawing the populace away from knowledge, music, poetry and "guardian education", toward money-making and the acquisition of possessions. This civil war between those who value wisdom and those who value material acquisition will be in struggle until a just medium is compromised. The timocracy values war insofar as it satisfies a love of victory and honor. The timocratic man loves physical training, and hunting, and values his abilities in warfare.
Temptations create a confusion between economic status and honor which is responsible for the emergence of oligarchy. In Book VIII, Socrates suggests that wealth will not help a pilot to navigate his ship, as his concerns will be directed centrally toward increasing his wealth by whatever means, rather than seeking out wisdom or honor. The injustice of economic disparity divides the rich and the poor, thus creating an environment for criminals and beggars to emerge. The rich are constantly plotting against the poor and vice versa. The oligarchic constitution is based on property assessment and wealth qualification. Unlike the timocracy, oligarchs are also unable to fight war, since they do not wish to arm the majority for fear of their rising up against them (even more so fearing the majority than their enemies), nor do they seem to pay mercenaries, since they are reluctant to spend money.
As this socioeconomic divide grows, so do tensions between social classes. From the conflicts arising out of such tensions, the poor majority overthrow the wealthy minority, and democracy replaces the oligarchy preceding it. The poor overthrow the oligarchs and grant liberties and freedoms to citizens, creating a most variegated collection of peoples under a "supermarket" of constitutions. A visually appealing demagogue is soon lifted up to protect the interests of the lower class. However, with too much freedom, no requirements for anyone to rule, and having no interest in assessing the background of their rulers (other than honoring such people because they wish the majority well) the people become easily persuaded by such a demagogue's appeal to try and satisfy people's common, base, and unnecessary pleasures.
The excessive freedoms granted to the citizens of a democracy ultimately leads to a tyranny, the furthest regressed type of government. These freedoms divide the people into three socioeconomic classes: the dominating class, the elites and the commoners. Tensions between the dominating class and the elites cause the commoners to seek out protection of their democratic liberties. They invest all their power in their democratic demagogue, who, in turn, becomes corrupted by the power and becomes a tyrant with a small entourage of his supporters for protection and absolute control of his people.