Analogy of the divided line
Plato, in The Republic Book IV (509d-513e), uses the literary device of a "divided line" to teach his basic views about four levels of existence (especially "the intelligible" world of the forms and "the visible" world we see around us) and the corresponding ways we come to know what exists.
The Divided Line
Plato asks us to imagine a line divided into two parts. The first part (segment AC) represents the intelligible world and the second (segment CE), the visible world. Then, he says, imagine each part of the line further divided. As it turns out, the divisions in the segment for the intelligible world represent higher (DE) and lower (CD) forms, respectively. Moreover, the divisions in the segment for the visible world represent ordinary visible objects (BC), on the one hand, and their shadows, reflections, and other representations (AB), on the other.
To clarify the basic metaphor, the reader could do far worse than to turn to the text itself. In the following passage, Socrates, who is made to be the narrator, is the first speaker, and he speaks for Plato; Glaucon, Plato's older brother, is represented as Socrates' pupil:
- You surely apprehend the two types, the visible and the intelligible.
- I do.
- Represent them then, as it were, by a line divided into two unequal sections and cut each section again in the same ratio--the section, that is, of the visible and that of the intelligible order--and then as an expression of the ratio of their comparative clearness and obscurity you will have, as one of the sections of the visible world, images. By images I mean, first, shadows, and then reflections in water and on surfaces of dense, smooth, and bright texture, and everything of that kind, if you apprehend.
- I do.
- As the second section assume that of which this is a likeness or an image, that is, the animals about us and all plants and the whole class of objects made by man.
- I so assume it, he said.
- Would you be willing to say, said I, that the division in respect of reality and truth or the opposite is expressed by the proportion--as is the opinable to the knowable so is the likeness to that of which it is a likeness?
- I certainly would.
- Consider then again the way in which we are to make the division of the intelligible section.
- In what way?
- By the distinction that there is one section of it which the soul is compelled to investigate by treating as images the things imitated in the former division, and by means of assumptions from which it proceeds not up to a first principle but down to a conclusion, while there is another section in which it advances from its assumption to a beginning or principle that transcends assumption, and in which it makes no use of the images employed by the other section, relying on ideas only and progressing systematically through ideas. (The Republic bk. VI, 509d-510b; trans. Paul Shorey)
| Thought | Objects | ||
| Knowledge | Reason (Dialectic) |
Higher Forms | Intelligible World |
| Understanding (Science, Mathematics) |
Forms of Science and Mathematics | ||
| Opinion | Belief (Perception) |
Things, Objects | Visible World |
| Conjecture (Imagining) |
Shadows, Images, Reflections |
This knowledge is the lowest degree of truth; it is all mere reflections or dreams, and only shadows of the real object itself. Plato is thus saying that a still-life painting of an apple points less to the truth of the apple than the apple itself.
This knowledge is higher and helps explain (or make more intelligible) the Conjecture level; this level is the physical apple itself. However, this level is still very limited in that its knowledge of the physical apple cannot grasp the botanist's knowledge of an apple. The botanist's knowledge, what defines an apple, is in the above levels, past the "divided line" between knowledge and opinion.
This level puts us into knowledge instead of belief or opinion; at this level the apple is understood by the botanist's definition of it. Here, all is abstract and universal and unchanging; below, all is concrete and in flux. The limitation, however, is that science and mathematics depend on particulars and physical (the level below, Belief) representations.
Finally, we reach pure reason itself. At this level all of the Forms developed in the Understanding level are brought together into unity and into a single Form, the Idea of the Good. Through dialectic reasoning, one can analyze all forms and see their relation to one another.
To complete the example of the apple:
- Conjecture: a mirror image, a painting, or a reflection off the water
- Belief: seeing and feeling
- Understanding: the definition or concept
- Reason: the form of the apple is brought together with all other forms and melded into the supreme and complete Idea of the Good
(Source: From Socrates to Sartre: the Philosophic Quest, by T.Z. Lavine)