Relation
A relation is an attribute
that can be jointly exemplified by more than
one thing at once. By this definition, I’ve committed myself to denying the
existence of relations that cannot be exemplified. I think this is ok because I
think that candidate relations that cannot be exemplified are analyzable as relational
properties that cannot be
exemplified. For example, to the right of
and not to the right of is the relational property of being to the right of and lacking being to the right of. I see no
reason to think that there are impossible relations in addition to these
relational properties.
Relations do not seem to be quite as well understood
as properties. We don’t have entire branches of mathematics devoted to
different kinds of relations as we do for properties, such Shape
and Quantity.
Some especially important relations are these: spatial, temporal, mental, semantic, logical, parthood, and exemplification.
I presently see no reason to think that there are
any relations aren’t binary. I suspect that candidate N-ary relations, where
N>2, can always be analyzed as relational properties. If this is right, then
all relations are simple: they aren’t built up out of
other relations, properties, or anything else. This means that we cannot give
formal names for relations that display the “inner structure” of a relation as
we can for propositions, say. For example ‘The proposition that John loves Sue’
is a name that brings to mind the inner structure of a proposition by expressing
its parts, being John, being Sue, and loves, and in a certain order. But if relations are simple, then
they cannot be formally named like that. We come to grasp various relations by
coming to grasp relational parts of properties and propositions. For an
interesting discussion of the problems we face when trying to provide formal
names for relations, see van Inwagen’s Names
for Relations.