The Allegory of the Cave is arguably the most famous part of the Republic. Although it is clearly related to the Sun and Divided Line analogies (indeed, Socrates explicitly connects the Cave and the Sun at 7.517bc), Plato marks its special status by opening Book VII with it, emphasizing its importance typographically, so to speak (he will do much the same thing in Book IX with the discussion of the tyrannical soul). Although an allegory is sometimes defined as a symbolic narrative that can be interpreted as having a hidden meaning, Plato is not cagey about the Cave Allegory’s meaning: it is about ‘the effect of education (παιδεία [paideia]) and the lack of it on our nature’ (7.514a). Education, the Allegory’s topic, is not what most people think it is, says Plato: it is not ‘putting knowledge into souls that lack it’ (7.518b). Though education sometimes requires that kind of transmission of knowledge from teacher to student, this is not its essence, which instead is ‘turning the whole soul’ (7.518d)—turning it around, ultimately toward the Form of the good. Education as turning around is a powerful metaphor, capturing the way in which learning involves gaining new perspectives, seeing everyday things and events from new points of view. Everyone, Plato insists, is capable of education in this sense (7.518c).

Stages in the Cave Allegory
First Stage
In the first stage, the cave’s residents are prisoners, chained to their seats and unable to move not only their bodies but—crucially—their heads. They can only look straight ahead, and thus have only one perspective on what they see on the cave’s wall. What they see are the shadows of a sort of puppet show taking place behind them, with shadows cast by the light of a fire. The puppets are various artifacts: ‘statues of people and other animals, made out of stone, wood, and every material’ (7.514b). The prisoners watch the shadow-play, ignorant of the true nature of what they see: they ‘believe that the truth is nothing other than the shadows of those artifacts’ (7.515c). They take for reality what is a mere image of it. Some readers will have already noticed that Stage One is parallel to the lowest section of the Divided Line (segment a), the objects of which are images and shadows.
Image
Second Stage
In the second stage, one of the prisoners is freed from their bonds. Plato does not tell us by whom or how; we are left to wonder whether the prisoner was saved by human agency or by the natural decay of their fetters. There is reason to think it is the former, since the freed prisoner is ‘suddenly compelled to stand up, turn his head, walk, and look up toward the light’ (7.515c), and somebody else seems to be doing the compelling. This is not the only time Plato connects education with compulsion, with being forced to turn one’s head and gain a new perspective. Nor is it the only time when the head-turning that constitutes education will be painful. When the freed prisoner is forced to look at the shadow-casting fire that until this moment they were unaware of, they will be ‘pained and dazzled and unable to see the things whose shadows they had seen before’ (7.515c). They will probably not like the experience at all, even though in being freed from their fetters they are thereby ‘cured of [their] ignorance’ (7.515c)—not merely freed but cured, as if ignorance is a disease. It is a comfortable disease, to borrow a phrase from e. e. cummings, for it is a world the cave-dweller is familiar with and comfortable in. Turned around and out of their comfort zone, they are unable to recognize the shadow-casting puppets, despite their skill at recognizing the shadows the puppets cast on the wall. Although the artifacts are, like any sensible particulars, not fully real, they are more real than the shadows they cast.
Thus in looking at the shadow-casting artifacts the freed prisoner is ‘a bit closer to the things that are and is turned towards things that are more’ (7.515d); this is the existential sense of the verb ‘to be’ that we distinguished earlier: the prisoner is closer to the things that are real—that exist—and indeed is coming closer to the things that are fully real: the Forms. While not everyone is capable of making it out of the Cave, Plato thinks that everyone is capable of being turned from the shadows to the shadow-casting artifacts—of moving from the lowest segment (segment a) of the Divided Line to the next highest (segment b), the realm of belief proper.
Third Stage
In the third stage we again see the role that compulsion plays in the Cave Allegory, for an unnamed, unidentified someone will ‘drag [the freed prisoner] away from there by force, up the rough, steep path’ (7.515e). Although Socrates devotes just one sentence to the third stage, what he says later in Book VII indicates that this rough, steep path symbolizes the formal education that potential philosopherrulers receive. This four-subject education is the basis of the quadrivium of classical liberal education, the sort of education suitable to a free person. It is education centered on number: arithmetic (number itself), geometry (number in space), harmonics or music theory (number in time), and physics or astronomy (number in space and time). All these number-based subjects ‘lead the soul and turn it around towards the study of that which is’ (7.524e), which ultimately is the Form of the good. While there are certainly practical applications of these subjects, the would-be philosopher-queens and -kings study them ‘not like tradesmen and retailers [… but] for ease in turning the soul around, away from becoming and towards truth and being’ (7.525c). These disciplines prepare would-be philosophers not for craft-based careers in the sensible world, where they might be bakers or cobblers or doctors (although it will prepare them to be generals, as they are the city’s guardians), but rather for citizenship in the intelligible world. They will learn to think abstractly, grasping essences and integrating Forms, which is presumably why studying geometry ‘tends to make it easier to see the Form of the good’ (7.526d). As the way out of the Cave, these subjects are ‘merely preludes to […] the song that dialectic sings’ (7.531d–32a), and that is a tune that is sung only in the intellectual sunlight of the intelligible world outside of the Cave.
Fourth Stage
In stage four, the prisoner is not just freed from their fetters but has made it out of the Cave into the intelligible world above, which corresponds to the top half of the Divided Line (segments c and d). Looking at the fire in the cave hurt their eyes, and they find emerging into the sunlight painful, just as a mid-afternoon moviegoer who leaves a dark theater is pained by the bright parking lot outside. At first, they will only be able to look at shadows of the objects in the world above, here cast by the light of the sun rather than the fire, or their reflections in water, or look at the objects at night. Just as the shadows on the cave wall were mere copies of the artifacts held before the fire, those artifacts are mere copies of the Forms, which are ‘the things themselves’ (7.516a). Although Socrates does not say, we can assume that there is one Form for each of the many particular objects in the cave. Whether there is one tree—the Form of treeness itself—or one oak tree, one maple tree, one white pine, one yellow pine, etc. is an interesting question to ponder, but it is not one we need to answer to understand the Cave Allegory or the Republic as a whole.
Fifth Stage
At stage five, the former cave dweller is able to look directly at the sun, ‘not images of it in water or some alien place, but the sun itself, in its own place, and be able to study it’ (7.516b). Presumably not everyone who makes it out of the Cave is able to do this. Mathematicians and scientists study the Forms relevant to their disciplines, but they do not see other Forms or how the Forms they contemplate are related to these other Forms, and they certainly do not see the Form of the good—that vision is reserved for genuine philosophers, and there are very few of them. So presumably the fourth stage in the Cave Allegory corresponds to Thought on the Divided Line, while the fifth stage is where Understanding operates.
Sixth Stage
In stage six, the sun-contemplating philosopher first thinks back on his life in the cave, and reflecting on ‘what passed for wisdom there’ (7.516c), smiles ruefully and feels pity for the others still trapped in their ignorance, who ‘know’ only the shadows on the wall or the artifacts casting them. What would happen if the enlightened philosopher descended into the cave? They will not be greeted as a returning, liberating hero, Socrates thinks. The denizens of the dark world below will first think the returning philosopher a fool: until their eyes, used to the bright light of the intelligible world, have adjusted to the darkness of the cave, they will be unable to recognize the shadows or the puppets. Like the ship owner who thinks the true captain is a useless stargazer (6.489c), the cave dwellers will think the enlightened philosopher a fool who has ruined their eyesight (not to mention his economic prospects) by looking too long at the sun. But if they persist and try to free the prisoners and turn them toward the firelight or drag those who are able out of the cave, they will think their ‘liberator’ is worse than useless: they will think them dangerous, and ‘if they could somehow get their hands on him […] they [would] kill him’ (7.517a).
Going Back Down into the Cave (7.519b–520b)