The Nature of Justice. The question which opens this immense dialogue is: what is justice? Several inadequate definitions are put forward, but the most emphatically presented definition is given by a young Sophist, Thrasymachus. He defines justice as whatever the strongest decide it is, and that the strong decide that whatever is in their best interest is just (review again the Athenian position in Melian Debate). Socrates dismisses this argument by proving that the strong rarely figure out what is in their best interest, and this can't be just since justice is a good thing.
The Analogy of the Ideal Republic. After Thrasymachus leaves in a royal huff, Socrates starts the question all over again. If one could decide what a just state is like, one could use that as an analogy for a just person. Plato then embarks on a long exposition about how a state might embody the four great virtues: courage, wisdom, temperance, and justice. The remainder of the dialogue is a long exposition of what justice in a state is; this section is considered one of the first major, systematic expositions of abstract political theory . This type of thinking, that is, speculating about an ideal state or republic, is called "utopian" thinking (utopia is a Greek word which means "no-place").
Plato (speaking through Socrates) divides human beings up based on their innate intelligence, strength, and courage. Those who are not overly bright, or strong, or brave, are suited to various productive professions: farming, smithing, building, etc. Those who are somewhat bright, strong, and especially courageous are suited to defensive and policing professions. Those who are extraordinarily intelligent, virtuous, and brave, are suited to run the state itself; that is, Plato's ideal state is an aristocracy, a Greek word which means "rule by the best." The lower end of human society, which, as far as Plato is concerned, consists of an overwhelming majority of people in a state, he calls the "producers," since they are most suited for productive work. The middle section of society, a smaller but still large number of people, make up the army and the police and are called "Auxiliaries." The best and the brightest, a very small and rarefied group, are those who are in complete control of the state permanently; Plato calls these people "Guardians." In the ideal state, "courage" characterizes the Auxiliaries; "wisdom" displays itself in the lives and government of the Guardians. A state may be said to have "temperance" if the Auxiliaries obey the Guardians in all things and the Producers obey the Auxiliaries and Guardians in all things. A state may be said to be intemperate if any of the lower groups do not obey one of the higher groups. A state may be said to be just if the Auxiliaries do not simply obey the Guardians, but enjoy doing so, that is, they don't grumble about the authority being exercised over them; a just state would require that the Producers not only obey the Auxiliaries and Guardians, but that they do so willingly.
When the analogy is extended to the individual human being, Plato identifies the intellect with the Guardians, the spirit or emotions with the Auxiliaries, and the bodily appetites with the Producers. Therefore, an individual is courageous if his or her spirit is courageous and an individual is wise if his or her intellect is wise. Temperance occurs when the emotions are ruled over by the intellect, and the bodily appetites are ruled over by the emotions and especially the intellect. An individual may be said to be just when the bodily appetites and emotions are not only ruled over by the intellect, but do so willingly and without coercion.
The Allegory of the Cave and the Divided Line: Far and away the most influential passage in Western philosophy ever written is Plato's discussion of the prisoners of the cave and his abstract presentation of the divided line. For Plato, human beings live in a world of visible and intelligible things. The visible world is what surrounds us: what we see, what we hear, what we experience; this visible world is a world of change and uncertainty. The intelligible world is made up of the unchanging products of human reason: anything arising from reason alone, such as abstract definitions or mathematics, makes up this intelligible world, which is the world of reality. The intelligible world contains the eternal "Forms" (in Greek, idea ) of things; the visible world is the imperfect and changing manifestation in this world of these unchanging forms. For example, the "Form" or "Idea" of a horse is intelligible, abstract, and applies to all horses; this Form never changes, even though horses vary wildly among themselvesthe Form of a horse would never change even if every horse in the world were to vanish. An individual horse is a physical, changing object that can easily cease to be a horse (if, for instance, it's dropped out of a fifty story building); the Form of a horse, or "horseness," never changes. As a physical object, a horse only makes sense in that it can be referred to the "Form" or "Idea" of horseness.
Plato imagines these two worlds, the sensible world and the intelligible world, as existing on a line that can be divided in the middle: the lower part of the line consists of the visible world and the upper part of the line makes up the intelligible world. Each half of the line relates to a certain type of knowledge: of the visible world, we can only have opinion (in Greek: doxa); of the intelligible world we achieve "knowledge" (in Greek, epistemŽ). Each of these divisions can also be divided in two. The visible or changing world can be divided into a lower region, "illusion," which is made up of shadows, reflections, paintings, poetry, etc., and an upper region, "belief," which refers to any kind of knowledge of things that change, such as individual horses. "Belief" may be true some or most of the time but occasionally is wrong (since things in the visible world change); belief is practical and may serve as a relatively reliable guide to life but doesn't really involve thinking things out to the point of certainty. The upper region can be divided into, on the lower end, "reason," which is knowledge of things like mathematics but which require that some postulates be accepted without question, and "intelligence," which is the knowledge of the highest and most abstract categories of things, an understanding of the ultimate good.