The analogy of the divided line () 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 not only to 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 (πίστις) to thought (διάνοια) and finally to understanding (νόησις). Furthermore, this analogy not only elaborates a theory of the psyche but also presents metaphysical and epistemological views.
Description
In The Republic (509d–510a), Plato describes the divided line to Glaucon this way:
thumb|left|upright=1.3|The Divided Line – (AC) is generally taken as representing the visible world and (CE) as representing the intelligible world.
The visible world
Thus AB represents shadows and reflections of physical things, and BC the physical things themselves. These correspond to two kinds of knowledge, the illusion (eikasía) 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. Particularly, it is identified as the lower subsection of the visible segment and represents images, which Plato described as "first shadows, then reflections in water and in all compacted, smooth, and shiny materials". According to the philosopher, eikasia and pistis add up to doxa, which is concerned with genesis (becoming).
Eikasia has several interpretations. For instance, it is the inability to perceive whether a perception is an image of something else. It therefore prevents us from perceiving that a dream or memory or a reflection in a mirror is not reality as such. Another variation posited by scholars such Yancey Dominick, explains that it is a way of understanding the originals that generate the objects that are considered as eikasia. This allows one to distinguish the image from reality such as the way one can avoid mistaking a reflection of a tree in a puddle for a tree.