absolute truth.

Thus, to explain a problem in geometry, the geometers make certain
hypotheses (namely, definitions and postulates) about numbers and
angles, and the like, and reason from them--giving no reason for their
assumptions, but taking them as evident to all; and, reasoning from
them, they prove the propositions which they have in view. And in such
reasonings, they use visible figures or diagrams--to reason about a
square, for instance, with its diagonals; but these reasonings are not
really about these visible figures, but about the mental figures, and
which they conceive in thought.

The diagrams which they draw, being visible, are the images of thoughts
which the geometer has in his mind, and these images he uses in his
reasoning. There may be images of these images--shadows and reflections
in water, as of other visible things; but still these diagrams are only
images of conceptions.

This, then, is _one_ kind of intelligible things: _conceptions_--for
instance, geometrical conceptions of figures. But in dealing with these
the mind depends upon assumptions, and does not ascend to first
principles. It does not ascend above these assumptions, but uses images
borrowed from a lower region (the visible world), these images being
chosen so as to be as distinct as may be.

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_, which does not depend upon assumption, 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
contemplates the _idea alone_; and with these ideas the process begins,
goes on, and terminates.

"I apprehend," said Glaucon, "but not very clearly, for the matter is
somewhat abstruse. _You wish to prove that the knowledge which by the
reason, in an intuitive manner, we may acquire of real existence and
intelligible things is of a higher degree of certainty than the
knowledge which belongs to what are commonly called the Sciences_. Such
sciences, you say, have certain assumptions for their basis; and these
assumptions are by the student of such sciences apprehen