  David Lewis (1979a) and Roderick Chisholm (1981) independently developed theories of indexical belief according to which the things that agents believe are properties rather than propositions. The primary differences between Lewis’s view and Chisholm’s view are ontological. Chisholm’s primitive ontology includes properties and relations. Lewis’s does not. It instead includes sets of possible objects, such as possible worlds and other individuals. Lewis reduces properties to sets of possible objects and relations to sets of \(n\)-tuples of possible objects. Lewis’s variant has been more influential, and so we concentrate on his theory below.