PLATO’S BOOK OF IMAGESepistemic approval of the mathematicians—must be understood in the
light of his conception of the cognitive powers. Notice how the dreamer
is distinguished from the non-dreamer in book 5:
One who recognizes beautiful things, but does not recognize The
Beautiful Itself and cannot be led to the knowledge of it—do you
believe he is living in a dreaming or a waking state? Consider: Isn’t
dreaming, whether asleep or awake, taking the likeness not as a like-
ness, but as the thing itself that it is like?
I most certainly take such a one to be dreaming.
Well, then; to take up the opposite of this: someone who recognizes
The Beautiful Itself and is able to distinguish both it and the things
that participate in it, and does not take the participants to be it, or
take it to be the participants—is such a one living in a waking or a
dreaming state?
Very much, he said, a waking state. (476c2– d4)The distinction Plato has Socrates make here is not made between those
who recognize only images and those who recognize only their origi-
nals; rather, the difference between the believer and the knower is that
the knower recognizes both sorts of entities, whereas the believer rec-
ognizes only images. It would obviously appear to follow that one who
understands that images actually are only images of higher realities em-
ploys images in a way that engages the cognitive power of knowledge,
rather than mere belief. Precisely because this use of images character-
izes the mathematician, I count the distinction in book 5 between the
dreamer and the non-dreamer as support for my earlier claim that the
mathematicians use images with knowledge. Their cognitive disadvan-
tage relative to the dialecticians must not, accordingly, be understood
as the disadvantage of those who do not engage the power of knowledge
relative to those who do.
The actual disadvantage between these two groups is explored and
described in the famous Divided Line passage of book 6. The proper
interpretation of this passage is anything but uncontroversial,^8 but hap-
pily my argument here does not have to make any signifi cant effort to
interpret this image in detail. Instead, the way in which Plato character-
izes the relationship between the top two subsections of the line and the
lower two is suffi cient for my present purposes. After fi rst dividing the
line into two unequal segments, and then subdividing each segment in
the same proportion as the segments of original division, Socrates then
associates the lowest subsection with shadows and refl ections, and the