Analogy of the divided line

The Analogy of the Divided Line (Greek: γραμμὴ δίχα τετμημένη) 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 lower two sections are said to represent the visible while the higher two are said to represent the intelligible. These affections are described in succession as corresponding to increasing levels of reality and truth from conjecture (εἰκασία) to belief () to thought (διάνοια) and finally to understanding (). Furthermore this Analogy not only elaborates a theory of the psyche but also presents metaphysical and epistemological views.

This analogy is immediately followed by the Analogy of the Cave at 514a. Socrates returns once more to the elements of the divided line (533d-534a) as he summarizes his dialectic.

In The Republic (509d–510a), Plato describes the Divided Line this way:

Thus AB represents shadows and reflections of physical things, and BC the physical things themselves. These correspond to two kinds of knowledge, the illusion (εἰκασία eikasia) of our ordinary, everyday experience, and belief (πίστις pistis) about discrete physical objects which cast their shadows. In the Timaeus, the category of illusion includes all the "opinions of which the minds of ordinary people are full," while the natural sciences are included in the category of belief.

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