In Book VII, Socrates presents the most beautiful and famous metaphor in Western philosophy: the allegory of the cave. This metaphor is meant to illustrate the effects of education on the human soul. Education moves the philosopher through the stages on the divided line, and ultimately brings him to the Form of the Good.
Socrates describes a dark scene. A group of people have lived in a deep cave since birth, never seeing the light of day. These people are bound so that they cannot look to either side or behind them, but only straight ahead. Behind them is a fire, and behind the fire is a partial wall. On top of the wall are various statues, which are manipulated by another group of people, lying out of sight behind the partial wall. Because of the fire, the statues cast shadows across the wall that the prisoners are facing. The prisoners watch the stories that these shadows play out, and because these shadows are all they ever get to see, they believe them to be the most real things in the world. When they talk to one another about “men,” “women,” “trees,” or “horses,” they are referring to these shadows. These prisoners represent the lowest stage on the line—imagination.
A prisoner is freed from his bonds, and is forced to look at the fire and at the statues themselves. After an initial period of pain and confusion because of direct exposure of his eyes to the light of the fire, the prisoner realizes that what he sees now are things more real than the shadows he has always taken to be reality. He grasps how the fire and the statues together cause the shadows, which are copies of these more real things. He accepts the statues and fire as the most real things in the world. This stage in the cave represents belief. He has made contact with real things—the statues—but he is not aware that there are things of greater reality—a world beyond his cave.
Next, this prisoner is dragged out of the cave into the world above. At first, he is so dazzled by the light up there that he can only look at shadows, then at reflections, then finally at the real objects—real trees, flowers, houses and so on. He sees that these are even more real than the statues were, and that those were only copies of these. He has now reached the cognitive stage of thought. He has caught his first glimpse of the most real things, the Forms.
When the prisoner’s eyes have fully adjusted to the brightness, he lifts his sight toward the heavens and looks at the sun. He understands that the sun is the cause of everything he sees around him—the light, his capacity for sight, the existence of flowers, trees, and other objects. The sun represents the Form of the Good, and the former prisoner has reached the stage of understanding.
The goal of education is to drag every man as far out of the cave as possible. Education should not aim at putting knowledge into the soul, but at turning the soul toward right desires. Continuing the analogy between mind and sight, Socrates explains that the vision of a clever, wicked man might be just as sharp as that of a philosopher. The problem lies in what he turns his sharp vision toward.
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."
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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.