ABSTRACT
The three contributors to this symposium have some important metaphysical agreements. We uphold against nominalists the real existence of instantiated properties and relations, which we take to be universals. Perhaps Alexander and Brian would agree with me further that properties strictly so-called are, as Russell thought, simply the monadic case, with relations the dyadic, the triadic … the n-adic cases of properties in a more extended sense. Again, we all subscribe to the idea expressed with elegant succinctness by David Lewis when he spoke of a sparse theory of properties and relations. A monadic predicate, for instance, does not necessarily pick out one of these sparse properties, even in a true proposition. Still further, we agree that it is up to empirical science to tell us just what these universal properties and relations are.
