semblance,
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 or which the soul uses
the figures given by the former division as images; the enquiry can
only be hypothetical, and instead of going upwards 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; these are their hypotheses, which they and
everybody are supposed to know, and therefore they do not deign to give
any account of them either to themselves or others; but they begin with
them, and go on until they arrive at last, and in a consistent manner,
at their conclusion?

Yes, he said, I know.

And do you not know also that although they make use of the visible
forms and reason about them, they are thinking not of these, but of the
ideals which they resemble; not of the figures which they draw, but of
the absolute square and the absolute diameter, and so on--the forms
which they draw or make, and which have shadows and reflections in
water of their own, are converted by them into images, but they are
really seeking to behold the things themselves, which can only be seen
with the eye of the mind?

That is true.

And of this kind I spoke as the intelligible, although in the search
after it the soul is compelled to use hypotheses; not ascending to a
first principle, because she is unable to rise above the region of
hypothesis, but employing the objects of which the shadows below are
resemblances in their turn as images, they having in relation to the
shadows and reflections of them a greater distinctness, a