From the Beginning to Plato

334 PLATO: METAPHYSICS AND EPISTEMOLOGY
Knowledge exists, and its object must plainly be what is, reality. And here all
the aspects of being noted above coalesce: truth, essence, eternity,
changelessness, stability and intrinsic intelligibility. For Plato, a paradigm case
of knowledge would be expressed in the definition of the being or nature of
triangularity. Since in knowing that the triangle is a three-sided plane figure one
has knowledge of reality, what reality precisely is it that is known? Not a
sensible triangle for, as we saw, the changeable character of sensible objects
exposes their lack of the being demanded of an object of knowledge: they are
not anything but only appear to be and imitate reality. The nature and being of a
triangle is not present in but beyond the sensible object and there is nothing there
in the sensible to be known. Since sensibles have no natures to be known, the
objects of knowledge must be different: the Forms.
Nevertheless, we do have mental states related to sensible objects. These,
however, are perceptions and opinions or judgements (doxai) based on
perception, not knowledge. Lacking any notion of a proposition or sense that could
serve as the content of a cognitive mental state, Plato identifies this content with
the being in the world that the mental state is about. Since judgement or opinion
differs from knowledge—it can be correct or incorrect, it is not based on an
account of its object—the entity that is its content, Plato argues, can no more be
identical with the being grasped by knowledge (namely, the Forms) than a colour
can be what we hear. Still, since opinion does have a content it cannot be
directed toward sheer nothingness. So the objects of opinion fall between being
and not being. Sensible objects, appearing both to be F and not to be F for many
properties, must be the entities that furnish opinions with their content. 8
Again, the Forms must be changeless and eternal, and as objects of knowledge
they must be the natures expressed in definitions.
For Plato, even if there were (or are) eternal triangles in the sensible world,
there would be a distinct Form of Triangularity because we could not otherwise
explain why the triangles have something in common, share one general feature.
If it is by reference to the Form of Triangularity that we explain why particular
triangles have something in common, then (Republic 597b–c; cf. Timaeus 31a)
there must be only one Form of Triangularity. An individual’s being F is
explained by its participation in F. If, per impossible, we had two Forms of
triangularity, T 1 and T 2, then if object a were a triangle because it participated in
T 1 and b were a triangle because it participated in T 2, we could not explain why a
and b have something in common. To do that we must relate them both to one
and the same entity, one and the same Form.
To explain how things have features in common, then, we must suppose that
for each property there is one and only one Form.
We have, Plato believes, the ability to think of ideal standards such as perfect
equality, for when we judge that sensible objects are equal we may judge at the
same time that they fall short of perfect equality. So to judge is to compare the
sensible objects with another entity. For to think about perfect equality—to have
that as a content of thought— is for the mind to stand in a relation to a reality