This analogy is assented to by Glaucon; and thus there is assumed a ground for a further construction of the diagram.
"Now," he says, "we have to divide the segment which represents Intelligible Things in the same way in which we have divided that which represents Visible Things. The one part must represent the knowledge which the mind gets by dealing as it were with images, and by reasoning downwards from Principles; the other that which it has by dealing with the Ideas themselves, and going to First Principles.
"The one part depends upon assumptions or hypotheses[343], the other is unhypothetical or absolute truth.
"One kind of Intelligible Things, then, is Conceptions; for instance, geometrical conceptions of figures, by means of which we reason downwards, assuming certain First Principles.
"Now the other kind of Intelligible Things is this:—that which the Reason includes in virtue of its power of reasoning, when it regards the assumptions of the Sciences as, what they are, assumptions only; and uses them as occasions and starting points, that from these it may ascend to the absolute, (ἀνυπόθετον, unhypothetical,) which does not depend upon assumption, but is the origin of scientific truth. The Reason takes hold of this first principle of truth; and availing itself of all the connections and relations of this principle, it proceeds to the conclusion; using no sensible image in doing this, but contemplating the Ideas alone; and with these Ideas the process begins, goes on, and terminates."
This account of the matter will probably seem to require at least further explanation; and that accordingly is acknowledged in the Dialogue itself. Glaucon says:
"I apprehend your meaning in a certain degree, but not very clearly, for the matter is somewhat abstruse. You wish to prove that the knowledge which, by the Reason, we acquire, of Real Existence and Intelligible Things, is of a higher degree of certainty than the knowledge which belongs to what are commonly called Sciences. Such sciences, you say, have certain assumptions for their bases; and these assumptions are, by the students of such sciences, apprehended, not by Sense (that is, the Bodily Senses), but by a Mental Operation,—by Conception. But inasmuch as such students ascend no higher than the assumptions, and do not go to the First Principles of Truth, they do not seem to you to have true knowledge—intuitive insight—Nous—on the subject of their reasonings, though the subjects are intelligible, along with their principle. And you call this habit and practice of the Geometers and others by the name Conception, not Intuition[344]; taking Conception to be something between Opinion on the one side, and Intuitive Insight on the other."
"You have explained it well, said I. And now consider the four sections (of the line) of which we have spoken, as corresponding to four affections in the mind. Intuition, the highest; Conception, the next; the third, Belief; and the fourth, Conjecture (from likenesses); and arrange them in order, so that they may have more or less of certainty, as their objects have more or less of truth[345].
"I understand, said he. I agree to what you say, and I arrange them as you direct."
And so the Sixth Book ends: and the Seventh Book opens with the celebrated image of the Cave, in which men are confined, and see all external objects only by the shadows which they cast on the walls of their prison. And this imperfect knowledge of things is to the true vision of them, which is attained by those who ascend to the light of day, as the ordinary knowledge of men is to the knowledge attainable by those whose minds are purged and illuminated by a true philosophy.