Plato s Analogy of the Divided Line From the Republic Book 6
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Socrates: And we say that the many beautiful things in nature and all the rest are visible but not intelligible, while the forms are intelligible but not visible. Glaucon: That s completely true. Socrates: Now, with what part of ourselves do we see visible things? Glaucon: We see visible things with our sight. Socrates: And audible things are heard by hearing. And with our other senses, we perceive all the other perceptible things. Glaucon: That s right. Socrates: Have you considered how lavish the maker of our senses was in making the power to see and be seen? Glaucon: I can t say I have. Socrates: Well, consider it this way. Do hearing and sound need another kind of thing in order for the former to hear and the latter to be heard, a third thing in whose absence the one won t hear or the other be heard? Glaucon: No, they need nothing else. Socrates: And if there are any other senses that need such a thing, there can t be many of them. Or can you think of one? Glaucon: I can t. Socrates: But you don t realize then that sight and the visible have such a need of a third thing? Glaucon: How so? 2
Socrates: Sight may be present in the eyes, and the person who has it may try to use it, and colors may be present in things, but unless a third kind of thing is present, which is naturally adapted for this very purpose, then that sight will see nothing, and the colors will remain unseen. Glaucon: What kind of thing do you mean? Socrates: I mean what you call light. Glaucon: You re right. Socrates: Then it isn t an insignificant kind of link that connects the sense of sight and the power of a thing to be seen by sight. In fact, it is a more valuable link than any other linked things have got, if indeed light is something valuable. Glaucon: Of course, it s very valuable, Socrates. Socrates: Which of the gods in heaven would you name as the cause and controller of this, the one whose light causes our sight to see in the best way and causes the visible things to be seen? Glaucon: The same one you and others would name. Obviously, the answer to your question is the sun. The sun is that god. Socrates: And isn t sight by nature related to the sun in this way? Glaucon: Which way? Socrates: Neither sight itself nor that in which it comes to be (what we call the eye) is the sun. Glaucon: Surely not. Socrates: But I suppose the eye is the most sun-like of all the different sense organs. 3
Glaucon: Yes, by far. Socrates: Doesn't it get the power it has as a sort of overflow from the sun's treasury? Glaucon: Most certainly. Socrates: And the sun isn't sight either, is it? But as its cause, the sun is seen by sight itself? Glaucon: That's so. Socrates: Well, then, say that the sun is the offspring of The Good 1. I mean, an offspring that The Good generated in a proportion with itself: so, just as the good is in the intelligible 2 region with respect to intelligence and what is intellected, so the sun is in the visible region with respect to sight and what is seen by sight. Glaucon: How? Explain it to me still further. Socrates: You know that when eyes no longer gaze upon things over whose colors daylight extends but rather when eyes gaze upon those over which the gleams of night extend, then the eyes are dimmed; appear nearly blind as though pure sight were not in them. Glaucon: Quite so. Socrates: But, I suppose, when one gazes with the eyes upon those things illuminated by the sun, then they see clearly and sight shows itself to be in these same eyes that seemed blind before. 1 The Good, is not an easy concept to understand. When Socrates refers to The Good, think of it as the source of truth and knowledge. 2 The intelligible refers to objects that are know through the intellect, while the visible refers to objects that are known through the senses. 4
Glaucon: Surely. Socrates: Well, we must understand the soul [mind, intellect, reason] in the same away, Glaucon. When the soul focuses on something illuminated by the truth and what is, the soul understands; the soul knows, and apparently possesses understanding. But when the soul focuses on what is mixed with obscurity, on what comes to be and passes away, on what is the object of opinion, the soul is dimmed; it changes its opinions this way and that way, and seems incapable of understanding. Glaucon: It does seem that way. Socrates: So that which gives truth to the things known and gives to the knower the power to know is the Form of The Good. And though The Good is the cause of knowledge and truth, it is also an object of knowledge. Both knowledge and truth are beautiful things, but The Good is altogether different and more beautiful than they are. In the visible realm, light and sight are rightly considered to be sun-like, but it is wrong to think that they are the sun, so here it is right to think of knowledge and truth as Good-like, but it is wrong to think that either of them is The Good for The Good is yet more prized. Glaucon: The Good is an inconceivably beautiful thing that you re referring to, Socrates, if it provides both knowledge and truth and is superior to them in beauty. You surely don t think a thing like that might be pleasure? Socrates: Hush! Let s examine its image in more detail as follows. Glaucon: How? Socrates: You ll be willing to say, I think, that the sun not only provides visible things with the power to be seen, but also allows 5
them to come to be providing them with the power of generation, growth and nourishment although it itself is not coming to be. Glaucon: How could it be? Socrates: Therefore, you should draw this conclusion also. It is not only that the attribute of being known is present in the objects known as a consequence of The Good, but also the very existence and being of those objects themselves is the result of The Good although the good isn't a being but is still beyond all being, exceeding it in dignity and power. 3 Glaucon [comically]: By Apollo, what a daemonic excesses! Socrates: It s your own fault; you forced me to tell you my opinion about it. Glaucon: And don t under any conditions stop here, Socrates. Please, continue to explain The Good s similarity to the sun, if you ve omitted anything. Socrates: Oh, I m certainly omitting a lot. Glaucon: Well, don t. Not even the smallest thing. Socrates: I think I ll have to omit a fair bit, but, as far as is possible at the moment, I won t omit anything voluntarily. Glaucon: Don t. 3 This is a crucial, but difficult, line in the analogy. Here is slightly different wording of the passage: Therefore, you should also say that not only do the objects of knowledge owe their being-known to The Good, but they owe their very being to it, although the good is not being, but superior to it in rank and power. 6
Socrates: Understand then, Glaucon, that just as we said there are these two things one is the king of the intelligible region, while the other is the king of the visible region so you have two kinds of things, visible things and intelligible things, and two regions: a visible region and an intelligible region. Glaucon: Right. [Socrates depicts a divided line, for both to look at] Socrates: See, these regions are like a line that is divided into two unequal segments. Now, divide each of the two segments namely, that of the visible region and that of the intelligible region in the same ratio as the line. 7
Now, in terms of relative clarity and obscurity, one subsection of the visible region consists of images. And by images I mean, first, shadows, then reflections in water, and all lose-grained, smooth, and shiny materials, and everything of that sort, if you understand. Glaucon: I do understand. Socrates: In the other subsection of the visible region, put the originals of these images, namely, the animals around us, all the plants, and the whole class of manufactured things that cast the shadows and reflections. Glaucon: Consider them put. Socrates: Would you be willing to say that, as regards truth and untruth, the division is in this proportion: As the opinionable is to the knowable, so also the likeness is to the thing that it is like? Glaucon: Certainly. [from instructor: the diagram on the next page represent the division of how we know, as opposed to the above line which represent what we know. Two full diagrams of what is known, and how it is known are on pg. 14] 8
Socrates: OK, now let s consider now how the section of the intelligible region is to be divided. Glaucon: How? Socrates: Like this: In one subsection, the soul, using as images the things that were imitated before, is forced to investigate from hypotheses, proceeding not to a first principle but to a conclusion. In the other subsection, however, it does make its way to a first principle that is not a hypothesis, proceeding from a hypothesis 9
but without the images used in the previous subsection, using forms themselves and making its investigation through them. Glaucon: I don t yet fully understand what you mean. Socrates: Let s try again. You ll understand it more easily after the following introduction. I think you know that students of geometry, calculation, and the like hypothesize the odd and the even, the various shapes and figures, the three kinds of angles, and other things akin to these in each of their investigations, as if they knew them. They make these their hypotheses and don t think it necessary to give any account of them, either to themselves or to others, as if they were clear to everyone. And going from these first principles through the remaining steps, they arrive in full agreement. Glaucon: I certainly know that much. 10
Socrates: Then you should also know this. Although they make use of and even draw themselves various visible shapes and diagrams, and make claims about them although they do this, their thought isn t directed to those images and diagrams, but rather, their thought is directed to those other things that the mathematical diagrams represent. They draw their mathematical images for the sake of the square itself and the diagonal itself, not the square they draw, not the diagonal they draw, and similarly with the other geometrical figures. These figures that they make and draw of which there are shadows and images in water they now in turn use as stepping stones in order to see those things themselves things that one cannot see except by means of thought. Glaucon: What you say is true, Socrates. Socrates: This, then, is the kind of thing that, on the one hand, I said is intelligible, and, on the other, is such that the soul is forced to use hypotheses in the investigation of it, not travelling up to a first principle, since it cannot reach beyond its hypotheses, but using as images those very things of which images were made in the section below, and which, by comparison to their images, were thought to be clear and to be valued as such. Glaucon: I understand. You are describing the methods used in geometry and the related sciences. 11
Socrates: Then understand this in turn. By the other subsection of the intelligible, I mean that which reason itself grasps by the power of dialectic. It does not consider these hypotheses as beginning principles but true hypotheses that is, as steppingstones and springs boards to take off from, enabling reason to reach the unhypothetical first principle of everything. Having grasped this principle, reason reverses its direction and, keeping hold of what follows from it, comes down to a conclusion without making use of anything visible at all, but only of forms themselves, moving on from forms to forms, and ending in forms. Glaucon: I understand, if not yet adequately for in my opinion, you re speaking of an enormous task. You want to distinguish the intelligible part of that which is, the part studied by the science of dialectic, as clearer than the part studied by the so-called sciences (geometry, mathematic), for which their hypotheses function as axioms or beginning principles. And although those who study the objects of these sciences are forced to do so by means of thought rather than sense perception, still, because they do not go back to a genuine first principle, but proceed from hypotheses, you don t think that they understand them, even though, given such a principle, they are intelligible. And it seems to me that you are referring to the state of the geometers as thought but not understanding, thought being intermediate between opinion and understanding. 12
Socrates: Your exposition is most adequate. Thus there are four such conditions in the soul, corresponding to the four subsections of our line: Understanding for the highest, thought for the second, belief for the third, and imagining for the last. Arrange them in a ratio, and consider that each shares in clarity to the degree that the subsection it is set over shares in truth. Glaucon: I understand, agree, and will arrange them as you say. BOOK 7 Socrates: Next then, let me offer an image of human nature in its being educated or enlightened and its being uneducated or unenlightened. I shall liken it to a condition of the following kind: Behold! Human beings living in an underground cave, which has a long entrance open to the daylight 13
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