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:

Now take a line which has been cut into two unequal parts, and divide each of them again in the same proportion, and suppose the two main divisions to answer, one to the visible and the other to the intelligible, and then compare the subdivisions in respect of their clearness and want of clearness, and you will find that the first section in the sphere of the visible consists of images. And by images I mean, in the first place, shadows, and in the second place, reflections in water and in solid, smooth and polished bodies and the like: Do you understand?

Yes, I understand.

Imagine, now, the other section, of which this is only the resemblance, to include the animals which we see, and everything that grows or is made.

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