Second-Order Predication and the Metaphysics of Properties

Problems about the accidental properties of properties motivate us - force us, I think - not to identify properties with the sets of their instances. If we identify them instead with functions from worlds to extensions, we get a theory of properties that is neutral with respect to disputes over counterpart theory, and we avoid a problem for Lewis's theory of events. Similar problems about the temporary properties of properties motivate us - though this time they probably don't force us - to give up this theory as well, and to identify properties with functions from world, time pairs to extensions. Again, the replacement theory is neutral with respect to a metaphysical dispute that the old theory (arguably) forces us to take a stand on - the dispute over whether objects have temporal parts. It also allows us to give a smoother semantics for predication, to better accommodate our intuitions about which objects temporary properties are properties of, and to make temporally self-locating beliefs genuinely self -locating.