Episode 05: The Divided Line idealinthewest.com /episode-5-the-divided-line
Socrates, from "The School of Athens" by Raphael
Now Plato goes for a more “left-brain” approach. Some may find it helpful to have a graphic representation of the divided line, and examples abound. But it can also be instructive not to look at a drawing, but to treat the description as an exercise of the “intelligible” rather than the “sensible.” For one, it avoids pointless questions like whether the line is vertical or horizontal, or left or right. Also, to do so is an example of using what Plato describes as “that other sort of knowledge which reason herself attains by the power of dialectic, using the hypotheses not as first principles, but only as hypotheses….” If you need to “see” in order to “believe,” you are stuck in the sensible end of the line, and will never be able to see light as opposed to things in the light. (That said, this is arguably the most difficult of the three descriptions, and a diagram can be helpful.)
Socrates: You have to imagine, then, that there are two ruling powers, and that one of them is set over the intellectual world, the other over the visible. I do not say heaven, lest you should fancy that I am playing upon the name (ovpavos, opatos)¹. May I suppose that you have this distinction of the visible and intelligible fixed in your mind? I have. 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. Very good. Would you not admit that both the sections of this division have different degrees of truth, and that the copy is to the original as the sphere of opinion is to the sphere of knowledge? Most undoubtedly. Next proceed to consider the manner in which the sphere of the intellectual is to be divided. In what manner? Thus: There are two subdivisions, in the lower of which the soul uses the figures given by the former division as images; the inquiry can only be hypothetical, and instead of going upward to a principle descends to the other end; in the higher of the two, the soul passes out of hypotheses, and goes up to a principle which is above hypotheses, making no use of images as in the former case, but proceeding only in and through the ideas themselves. I do not quite understand your meaning, he said. Then I will try again; you will understand me better when I have made some preliminary remarks. You are aware that students of geometry, arithmetic, and the kindred sciences assume the odd, and the even, and the figures, and three kinds of angles, and the like, in their several branches of science; 1/3