Book VI, 509–511

509a and truth, like light and sight in the other realm, are rightly thought sunlike, but not rightly thought to be the sun. So here too it is right to think both of them like the Good, but not right to think either of them is the Good itself. We must honor the condition of the Good even more highly.”

“What an extraordinary beauty you describe,” he said, “if it gives knowledge and truth, yet is itself above them in beauty. Surely you are not saying that it is pleasure.”

“Mind your words,” I said. “Look further instead at its image in this way.” 509b

“How?”

“You will say, I think, that the sun gives visible things not only the power to be seen, but also their coming into being, growth, and nourishment, though it is not itself coming into being.”

“Of course not.”

“Say likewise that the things we know receive from the Good not only their being known, but also their being and their essence; the Good is not essence, but is still beyond essence, surpassing it in dignity and power.” 509c

And Glaucon said, with a laugh, “Apollo! What a divine excess!”

“You are to blame,” I said, “for forcing me to say what I think about it.”

“Don't stop now,” he said. “At least continue through the comparison with the sun, if you have left anything out.”

“I have left a great deal out,” I said.

“Then don't leave out even a little of it,” he said.

“I suspect I will leave out much,” I said. “Still, insofar as I can speak now, I will not willingly omit anything.”

“Please don't,” he said.

509d “Then understand,” I said, “that, as we have said, there are these two, one ruling over the intelligible kind and realm, the other over the visible—I will not say ‘heaven,’ lest you think I am playing tricks with the word. Do you grasp these two kinds, the visible and the intelligible?”

“I do.”

“Imagine, then, a line divided into two unequal parts, and divide each part again in the same ratio, both the visible kind and the intelligible. According to their relative clarity and obscurity, one section in the visible part 509e will consist of images. By images I mean, first,

510a shadows, then reflections in water and in everything made of dense, smooth, shining matter, and everything else of this sort, if you follow me.”

“I do follow.”

“Take the other section to contain the things these images resemble: the living creatures around us, every sort of plant, and the entire class of manufactured things.”

“I take it so,” he said.

“Would you also be willing to say,” I asked, “that the division reflects a difference in truth and its absence: as what is believed stands to what is known, so a likeness stands to what it resembles?” 510b

“Certainly,” he said.

“Consider next how the intelligible part must be divided.”

“How?”

“In one section the soul is compelled to investigate by using the things imitated in the first section as images, proceeding from hypotheses not toward a first principle but toward a conclusion. In the other it proceeds from a hypothesis toward an unhypothetical first principle and makes its way without the images used in the former section, through the Forms themselves, with the Forms themselves as its means.”

“I haven't properly understood what you mean,” he said.

510c “Let me try again,” I said. “What I am about to say will be easier to understand after that introduction. I think you know that those who work in geometry, arithmetic, and similar disciplines assume the odd and the even, shapes, the three kinds of angles, and other things akin to these in each field of inquiry. They take these as hypotheses, as though they knew them, and think it unnecessary to give any account of them, either to themselves or to others, 510d since they are obvious to everyone. Starting from these, they proceed through the rest of the argument until, consistently, they arrive at the conclusion they set out to examine.”

“Yes,” he said, “that much I certainly know.”

“And you know that they also use visible figures and reason about them, though they are not thinking of these figures, but of the things they resemble. They reason for the sake of the square itself and the diagonal itself, not the diagonal 510e they draw, and similarly in other cases. The very things they mold and draw, which themselves cast shadows and have images in water, they use in turn as images, seeking

511a to see those things themselves that no one can see except by thought.”

“What you say is true,” he said.

“This, then, is the kind I called intelligible. Yet in the search for it the soul is compelled to use hypotheses and does not move toward a first principle, because it cannot rise above its hypotheses. It uses as images the very things that are imitated by the things in the lower section, and which, in comparison with those lower things, have been judged clear and honored as such.”

511b “I understand,” he said, “that you mean what falls under geometry and its kindred arts.”

“Now understand that by the other section of the intelligible I mean what reason itself grasps through the power of dialectic. It treats its hypotheses not as first principles but as hypotheses in the true sense, like stepping-stones and points of departure, so that it may ascend to the unhypothetical first principle of all things. Once it has grasped that, it follows what follows from that principle and descends in this way to a conclusion, 511c making no use whatever of anything perceptible, but proceeding through the Forms themselves, from Forms to Forms, and ending in Forms.”

“I understand,” he said, “though not fully, for you seem to be describing a considerable undertaking. But I do see that you want to distinguish what the science of dialectic contemplates in being and the intelligible as clearer than what the so-called arts contemplate. They treat hypotheses as first principles; those engaged in them must contemplate their subjects through thought and not the senses, but because they investigate from hypotheses rather than by ascending to a first principle, 511d you think they do not attain understanding of those subjects, though they are intelligible when apprehended with their first principle. And it seems to me that you call the condition of geometers and their like thought, not understanding, because thought is something between belief and understanding.”

“You have taken my meaning perfectly,” I said. “Now take these four conditions arising in the soul as corresponding to the four sections: understanding for the highest, thought 511e for the second, belief for the third, and conjecture for the last. Set them in proportion, judging that they share in clarity to the same extent that their objects share in truth.”

“I understand,” he said, “and agree, and arrange them as you say.”

509a and truth are like the sun in this respect: it is right to call light and sight sunlike, but wrong to call either one the sun. Likewise, it is right to call knowledge and truth like the Good, but wrong to call either one the Good. The Good must be valued even more highly.”

“That is an extraordinary beauty you are describing,” he said. “It gives us knowledge and truth, yet is itself more beautiful than either. Surely you don’t mean that it is pleasure.”

“Don’t say that,” I replied. “But look at its image in this further way.” 509b

“How?”

“You would say, I think, that the sun gives visible things not only the power to be seen, but also their birth, growth, and nourishment, though the sun itself is not birth.”

“Of course.”

“Then say that the Good gives things we can know not only their being known, but also their being and reality. Yet the Good is not itself being. It is beyond being, surpassing it in dignity and power.” 509c

Glaucon laughed and said, “Apollo! What an astonishing claim!”

“You are to blame,” I said, “for forcing me to say what I think about it.”

“And don’t stop,” he said. “At least continue the comparison with the sun, if you have left anything out.”

“I have left out a great deal,” I said.

“Then don’t leave out even a little,” he said.

“I expect I will leave out a lot,” I said. “Still, I will not deliberately omit anything I can tell you now.”

“Please don’t,” he said. 509d

“Now consider this,” I said. “As we have been saying, there are two things, one ruling the kind and realm that can be understood by thought, the other ruling the visible kind and realm. I say ‘visible’ rather than ‘heavenly’ so you won’t think I am playing tricks with the words. Do you see these two kinds, the visible and the intelligible?”

“Yes.”

“Take a line divided into two unequal parts. Divide each part again in the same proportion, both the visible part and the intelligible part. The resulting parts differ in clarity and lack of clarity. In the visible part, 509e one section consists of images. By images I mean first shadows, then reflections in water and in things with dense, smooth, shiny surfaces, and everything of that sort. Do you follow?”

510a “I do.”

“Now put in the other section the things those images resemble: the living creatures around us, all plants, and every kind of manufactured object.”

“I will,” he said.

“And would you agree,” I asked, “that this division also separates what has more truth from what has less? As the objects of opinion stand in relation to the objects of knowledge, so an image stands in relation to what it resembles.” 510b

“I certainly agree,” he said.

“Now consider how to divide the intelligible part.”

“How?”

“In one section, the soul must investigate by starting from assumptions and using as images the things represented in the visible section. It moves not toward a first principle but toward a conclusion. In the other section, it starts from assumptions and moves toward a first principle that needs no assumption. It makes its way by the Forms themselves, not by using the images from the other section.”

“I haven’t quite understood what you mean,” he said. 510c

“Let me try again,” I said. “What I have said first will make this easier to grasp. You know that people who study geometry, arithmetic, and similar subjects assume the odd and the even, the various shapes, the three kinds of angles, and other things of that sort relevant to each inquiry. They treat these as things they know and make them their starting assumptions. They think it unnecessary to give any account of them, either to themselves or to anyone else, 510d as though they were obvious to everyone. Starting there, they go through the remaining steps and reach a conclusion that agrees with the aim of their investigation.”

“Yes, I know that,” he said.

“And you know that they also use visible shapes and discuss them, but they are not thinking about those particular shapes. They are thinking about the things these shapes resemble. They reason about the square itself and its diagonal, not the particular one they draw. The same goes for everything else. The shapes they mold or draw themselves have shadows and reflections in water, 510e but they use those shapes in turn as images. They seek to see the things themselves, which no one can see except with thought.”

511a “That is true,” he said.

“This is what I meant by the intelligible kind. When the soul investigates it, it must use assumptions. It cannot move up to a first principle, because it cannot get beyond those assumptions. It uses as images things that are themselves represented by things in the section below. Those things, compared with their own images, were thought clearer and given greater value.” 511b

“I understand,” he said. “You mean what is studied by geometry and related subjects.”

“Now understand what I mean by the other section of the intelligible. Reason itself grasps it through the power of discussion. It treats assumptions not as first principles, but as genuine assumptions, like steps and starting points. It uses them to reach the principle of everything, which rests on no assumption. When it has grasped that principle, it follows what comes from it back down to a conclusion. 511c It makes no use at all of anything that can be sensed. It moves from Forms through Forms to Forms, and ends with Forms.”

“I understand,” he said, “though not completely, since you seem to be describing a great undertaking. But you want to distinguish what the practice of discussion studies, reality and the intelligible, as clearer than what the so-called sciences study. In those sciences, assumptions serve as first principles. The people studying their objects have to use thought rather than their senses. But because they start from assumptions instead of going up to a first principle, you think they do not have full understanding of those objects, 511d even though those objects can be understood when seen in light of the first principle. You seem to call the state of mind of geometers and others like them ‘thought,’ not ‘understanding,’ because thought falls between opinion and understanding.”

“You have grasped it very well,” I said. “Now match these four sections with four states of mind. Give understanding to the highest section, thought to 511e the second, belief to the third, and imagining to the last. Arrange them in proportion: the more truth their objects have, the clearer these states of mind are.”

“I understand,” he said, “and agree to arrange them as you say.”