NICHOLAS D. SMITHMathematicians and Knowledge
The problem we encountered in the last section was that Plato criti-
cizes the imitators as engaging in image-making without knowledge.
And yet it would appear that the same objection can be made against
those whose creation of images Plato seems to endorse. In this section,
however, I deny this comparison. The imitators, I claim, do what they do
without knowledge, whereas the mathematicians (and Socrates) do what
they do with knowledge. I recognize that in saying this, I appear to con-
tradict the very passages in which Plato has Socrates compare the cog-
nitive states of the mathematicians unfavorably with the dialecticians,
on the one hand, and also those in which Socrates himself disclaims
knowledge, on the other. So in order to secure my claim, I must explain
how my reading actually does not violate the sense of these texts.
Given the way contemporary philosophers approach epistemol-
ogy, it might seem as if the only question we must settle here is whether
or not the mathematicians generate warranted true beliefs in regard to
the subjects they pursue by their use of images, or perhaps alternatively,
whether their use of images is conditioned upon or derives from such
cognitive states. But just to put the question this way already creates
a diffi culty for the Plato scholar, for the epistemology of the Republic,
especially as it is most carefully articulated in book 5, makes it plain
that unlike contemporary epistemologists, Plato does not provide an
analysis of knowledge as a species of belief. In contemporary epistemol-
ogy, knowledge is generally treated as a species of belief, of course—as
justifi ed or warranted true belief. Justifi cation or warrant, we are often
told, is that additional feature of knowledge that is lacking in other sorts
of true belief.^7 But in Plato’s account, not only is knowledge not some
special kind of belief, but in fact it is not any kind of belief at all, but is
instead an entirely different cognitive power altogether. So if we are go-
ing to make much headway in discovering how Plato makes assessments
of knowledge, we w ill need to leave our modern epistemological presup -
positions “at the door,” as it were.
Plato introduces his notion of cognitive powers by likening them to
our sensory capacities, such as sight and hearing. Such powers, he says,
are to be distinguished by what they are naturally related to as object,
and by what they produce from their activity. Knowledge (ejpisthvmh),
Plato argues, is a distinct cognitive power from belief (or opinion—
dovxa) because knowledge is naturally related to what is, whereas belief
is naturally related to particular sensible things.
Plato’s epistemic complaint about the imitators—and his qualifi ed