Successful development of the theory of forms depended upon the
development of a distinction between two kinds of predication. Plato held that
a sentence making a predication about a sensible particular, “A is B,” must be
understood as stating that the particular in question, A, displays a certain
property, B. There are ordinary predications about the forms, which also state
that the forms in question display properties. Crucially, however, there is
also a special kind of predication that can be used to express a form’s nature.
Since Plato envisaged that these natures could be given in terms of
genus-species trees, a special predication about a form, “A is B,” is true if B
appears above A in its correct tree as a differentia or genus. Equivalently, “A
is B” has the force that being a B is (part of) what it is to be an A. This
special predication is closely approximated in modern classifications of
animals and plants according to a biological taxonomy. “The wolf is a canis,”
for example, states that “wolf” appears below “canis” in a genus-species
classification of the animals, or equivalently that being a canis is part of
what it is to be a wolf (Canis lupus).
Plato’s distinction can be illustrated by examples such as the
following. The ordinary predication “Socrates is just” is true, because the
individual in question displays the property of being just. Understood as a
special predication, however, the assertion is false, because it is false that
being just is part of what it is to be Socrates (there is no such thing as what
it is to be Socrates). “Man is a vertebrate,” understood as an ordinary
predication, is false, since the form Man does not have a backbone. But when
treated as a special predication it is true, since part of what it is to be a
human is to be a vertebrate. Self-predication sentences are now revealed as
trivial but true: “the Beautiful is beautiful” asserts only that being
beautiful is (part of) what it is to be beautiful. In general one must be
careful not to assume that Plato’s self-predication sentences involve ordinary
predication, which would in many cases involve problematic self-exemplification
issues.
Plato was interested in special predication as a vehicle for providing
the real definitions that he had been seeking in earlier dialogues. When one
knows in this way what Justice itself really is, one can appreciate its
relation to other entities of the same kind, including how it differs from the
other virtues, such as Bravery, and whether it is really the whole of Virtue or
only a part of it.
By means of special predication it is possible to provide an account of
each fundamental nature. Such accounts, moreover, provide a way of
understanding the “pure being” of the forms: it consists of the fact that there
cannot be a true special predication of the form “A is both B and not-B.” In
other words, special predication sentences do not exhibit the phenomenon of
rolling around between being and not being. This is because it must be the case
that either B appears above A in a correct genus-species classification or it
does not. Moreover, since forms do not function by being exemplars of
themselves only, there is nothing to prevent their having other properties,
such as being and unity, as appropriate. As Plato expresses it, all forms must
participate in Being and Unity.
Because the special predications serve to give (in whole or in part) the
real definitions that Socrates had been searching for, this interpretation of
the forms connects Plato’s most technical dialogues to the literary masterpieces
and to the earlier Socratic dialogues. The technical works stress and develop
the idea (which is hinted at in the early Euthyphro) that forms should be
understood in terms of a genus-species classification. They develop a schema
that, with modifications of course, went on to be productive in the work of
Aristotle and many later researchers. In this way, Plato’s late theory of the
forms grows out of the program of his teacher and leads forward to the research
of his students and well beyond.
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