The Allegory of the Cave, or Plato's Cave, is an allegory presented by the Greek philosopher Plato in his work Republic (514a–520a) to compare "the effect of education (παιδεία) and the lack of it on our nature". It is written as a dialogue between Plato's brother Glaucon and his mentor Socrates, narrated by the latter. The allegory is presented after the analogy of the sun (508b–509c) and the analogy of the divided line (509d–511e).
In the allegory "The Cave", Plato describes a group of people who have lived chained to the wall of a cave all their lives, facing a blank wall. The people watch shadows projected on the wall from objects passing in front of a fire behind them and give names to these shadows. The shadows are the prisoners' reality, but are not accurate representations of the real world. The shadows represent the fragment of reality that we can normally perceive through our senses, while the objects under the sun represent the true forms of objects that we can only perceive through reason. Three higher levels exist: the natural sciences; mathematics, geometry, and deductive logic; and the theory of forms.
Socrates explains how the philosopher is like a prisoner who is freed from the cave and comes to understand that the shadows on the wall are actually not the direct source of the images seen. A philosopher aims to understand and perceive the higher levels of reality. However, the other inmates of the cave do not even desire to leave their prison, for they know no better life.
Socrates remarks that this allegory can be paired with previous writings, namely the analogy of the sun and the analogy of the divided line.
Plato begins by having Socrates ask Glaucon to imagine a cave where people have been imprisoned from childhood, but not from birth. These prisoners are chained so that their legs and necks are fixed, forcing them to gaze at the wall in front of them and not to look around at the cave, each other, or themselves (514a–b).
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The theory of Forms, theory of Ideas, Platonic idealism, or Platonic realism is a metaphysical theory, attributed to the Classical Greek philosopher Plato, suggesting that the physical world is not as real or true as timeless, absolute, unchangeable ideas. Ideas according to this theory, conventionally capitalized and translated as "Ideas" or "Forms", are the non-physical essences of all things, of which objects and matter in the physical world are merely imitations.
The analogy of the divided line (grammē dicha tetmēmenē) is presented by the Greek philosopher Plato in the Republic (509d–511e). It is written as a dialogue between Glaucon and Socrates, in which the latter further elaborates upon the immediately preceding analogy of the sun at the former's request. Socrates asks Glaucon to not only envision this unequally bisected line but to imagine further bisecting each of the two segments. Socrates explains that the four resulting segments represent four separate 'affections' (παθήματα) of the psyche.
The analogy of the sun (or simile of the sun or metaphor of the sun) is found in the sixth book of The Republic (507b–509c), written by the Greek philosopher Plato as a dialogue between his brother Glaucon and Socrates, and narrated by the latter. Upon being urged by Glaucon to define goodness, a cautious Socrates professes himself incapable of doing so. Instead he draws an analogy and offers to talk about "the child of goodness" ("ἔκγονός τε τοῦ ἀγαθοῦ").
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