republic (books 6 - 10)
ple which is above hypotheses, making no use of images as
in the former case, but proceeding only in and through the ideas
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 as-
sume 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 as-
cending 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, and therefore a higher value.
I understand, he said, that you are speaking of the province
of geometry and the sister arts.
And when I speak of the other division of the intelligible,
you will understand me to speak of that other sort of knowledge
which reason herself attains by the power of dialectic, using
the hypotheses not as first principles, but only as hypotheses--
that is to say, as steps and points of departure into a world
which is above hypotheses, in order that she may soar beyond
them to the first principle of the whole; and clinging to this
and then to that which depends on this, by successive steps she
descends again without the aid of any sensible object, from
ideas, through ideas, and in ideas she ends.
I understand you, he replied; not perfectly, for you seem to
me to be describing a task which is really tremendous; but,
at any rate, I understand you to say that knowledge and being,
which the science of dialectic contemplates, are clearer than the
notions of the arts, as they are termed, which proceed from hy-
potheses only: these are also contemplated by the understand-
ing, and not by the senses: yet, because they start from hypoth-
eses and do not ascend to a principle, those who contemplate
them appear to you not to exercise the higher reason upon them,
although when a first principle is added to them they are cogniz-
able by the higher reason. And the habit which is concerned