29 The Analysis of the Divided Line
The Analysis of the Divided Line
[509d] he said. “Conceive then,” said I, “as we were saying, that there are these two entities, and that one of them is sovereign over the intelligible order and region and the other over the world of the eye-ball, not to say the sky-ball, but let that pass. 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 (63) [509e] of the visible world, images. By images I mean (64) [510a] 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 (65) [510b] 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.” “I don’t fully understand what you mean by this,” he said. “Well, I will try again,” (66) [510c] said I,” for you will better understand after this preamble. For I think you are aware that students of geometry and reckoning and such subjects first postulate the odd and the even and the various figures and three kinds of angles and other things akin to these in each branch of science, regard them as known, and, treating them as absolute assumptions, do not deign to render any further account of them to themselves or others, taking it for granted that they are obvious to everybody. (67)
They take their start (67) [510d] from these, and pursuing the inquiry from this point on consistently, conclude with that for the investigation of which they set out.” “Certainly,” he said, “I know that.” “And do you not also know that they further make use of the visible forms and talk about them, though they are not thinking of them but of those th