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Socrates believes he has adequately responded to Thrasymachus and is through with the discussion of justice, but the others are not satisfied with the conclusion they have reached. Glaucon, one of Socrates’s young companions, explains what they would like him to do. Glaucon states that all goods can be divided into three classes: things that we desire only for their consequences, such as physical training and medical treatment; things that we desire only for their own sake, such as joy; and, the highest class, things we desire both for their own sake and for what we get from them, such as knowledge, sight, and health. What Glaucon and the rest would like Socrates to prove is that justice is not only desirable, but that it belongs to the highest class of desirable things: those desired both for their own sake and their consequences.
Glaucon points out that most people class justice among the first group. They view justice as a necessary evil, which we allow ourselves to suffer in order to avoid the greater evil that would befall us if we did away with it. Justice stems from human weakness and vulnerability. Since we can all suffer from each other’s injustices, we make a social contract agreeing to be just to one another. We only suffer under the burden of justice because we know we would suffer worse without it. Justice is not something practiced for its own sake but something one engages in out of fear and weakness.
To emphasize his point, Glaucon appeals to a thought experiment. Invoking the legend of the ring of Gyges, he asks us to imagine that a just man is given a ring which makes him invisible. Once in possession of this ring, the man can act unjustly with no fear of reprisal. No one can deny, Glaucon claims, that even the most just man would behave unjustly if he had this ring. He would indulge all of his materialistic, power-hungry, and erotically lustful urges. This tale proves that people are only just because they are afraid of punishment for injustice. No one is just because justice is desirable in itself.
Glaucon ends his speech with an attempt to demonstrate that not only do people prefer to be unjust rather than just, but that it is rational for them to do so. The perfectly unjust life, he argues, is more pleasant than the perfectly just life. In making this claim, he draws two detailed portraits of the just and unjust man. The completely unjust man, who indulges all his urges, is honored and rewarded with wealth. The completely just man, on the other hand, is scorned and wretched.
His brother, Adeimantus, breaks in and bolsters Glaucon’s arguments by claiming that no one praises justice for its own sake, but only for the rewards it allows you to reap in both this life and the afterlife. He reiterates Glaucon’s request that Socrates show justice to be desirable in the absence of any external rewards: that justice is desirable for its own sake, like joy, health, and knowledge.
Coming on the heels of Thrasymachus’ attack on justice in Book I, the points that Glaucon and Adeimantus raise—the social contract theory of justice and the idea of justice as a currency that buys rewards in the afterlife—bolster the challenge faced by Socrates to prove justice’s worth. With several ideas of justice already discredited, why does Plato further complicate the problem before Socrates has the chance to outline his own ideas about justice?
The definitions on this list are mostly helpful, but the term "Understanding" is incorrect and misleading. The highest grade of cognitive activity in Plato's fourfold epistemological scheme is, in Greek, "noesis." In English this should be called Intellection, Higher Reason, or simply Noesis. To call it Understanding badly confuses things because of the myriad unrelated meanings and senses of "understanding" in English.
Similarly, what the list above calls "Reason" would be better termed ratiocination, calculation, reasoning, or lower reason. To simply call this faculty Reason confounds two distinct faculties: ratiocination (dianoia) and Higher Reason (nous or Nous). Ratiocination is somewhat like the ability that animals have to think and plan. It is the Higher Reason that is associated with mans immortal soul, and on which basis, according to Plato, man may attain "likeness to God insofar as possible."
Spouses in the republic are not drawn by lot, as is asserted in the summary for Book V. Rather, they are chosen so that 'bronze-souled' individuals will be paired off with other bronze-souled individuals, and gold-souled with other gold-souled. The idea of the lottery is a lie fabricated by the framers of the city to placate citizens.