What is the divided line Plato?

Plato, answered from the texts and cited to the page.

Plato answers

The line is a figure for the whole of what can be known and how it can be known — drawn once, but cutting through everything. Imagine a line divided into two unequal sections: the visible and the intelligible.1 Each section is then divided again in the same ratio. In the lower subsection of the visible you find images — shadows, reflections in water, everything of that shiny, close-packed sort.2

In the upper subsection of the visible sit the originals of those images: the animals around us, the plants, the manufactured things.2 The relation between image and original within the visible realm is the same proportion that holds between the opinable and the knowable taken as wholes — as the likeness is to the thing it is like, so opinion is to knowledge.2

Cross into the intelligible and the structure repeats, but now the soul itself does the traveling. In the lower intelligible subsection, it uses the visible originals as images and reasons from hypotheses toward conclusions — this is what the geometers do: they posit the odd and the even, the kinds of angles, the figures, and proceed from these without giving any account of them, as if they were clear to everyone.3

Their thought is not really directed at the diagrams they draw but at the square itself, the diagonal itself — things one cannot see except by means of thought.3 This is dianoia, discursive mathematical reasoning: powerful, but still resting on unexamined hypotheses. The upper intelligible subsection is the domain of noēsis, understanding proper.

Here the soul moves from a hypothesis not toward a conclusion but toward a first principle that is itself no hypothesis — proceeding without images, using the forms themselves.3 This is dialektikē, the capacity to give and receive an account of the being of each thing; and whoever cannot do this, either to himself or to another, lacks understanding of it, whatever else he may possess.4

What illuminates the whole ascent — what gives truth to the things known and the power to know to the knower — is the form of the good.1 As the sun provides visible things not only with the power to be seen but with coming-to-be and nourishment, so the good provides intelligible things with being and truth, while itself surpassing them in beauty and power.1

Knowledge and truth are beautiful things; the good is other and more beautiful than they.1 The soul that focuses on what is illuminated by truth and being understands and knows; the soul that focuses on what is mixed with obscurity, on what comes to be and passes away, opines and is dimmed, shifting its opinions this way and that.1 Opinion is concerned with becoming, intellect with being — and as being is to becoming, so intellect is to opinion, and as intellect is to opinion, so knowledge is to belief and thought to imaging.4 The line, then, is not merely a diagram. It is an account of where you are standing when you think you know something.

Sources

  1. there are these two things, one sovereign of the intelligible kind and place, the other of the visible... you have two kinds of thing, visible and intelligible... It is like a line divided into two unequal sections.
    Complete Works, pp. 1158–1160
  2. one subsection of the visible consists of images... shadows, then reflections in water and in all close-packed, smooth, and shiny materials... In the other subsection of the visible, put the originals of these images, namely, the animals around us, all the plants, and the whole class of manufactured things... As the opinable is to the knowable, so the likeness is to the thing that it is like.
    Complete Works, p. 1160
  3. students of geometry, calculation, and the like hypothesize the odd and the even, the various figures, the three kinds of angles... They make their claims for the sake of the square itself and the diagonal itself, not the diagonal they draw... in seeking to see those others themselves that one cannot see except by means of thought.
    Complete Works, p. 1160
  4. do you call someone who is able to give an account of the being of each thing dialectical? But insofar as he's unable to give an account of something, either to himself or to another, do you deny that he has any understanding of it?... Opinion is concerned with becoming, intellect with being. And as being is to becoming, so intellect is to opinion, and as intellect is to opinion, so knowledge is to belief and thought to imaging.
    Complete Works, pp. 1178–1179