Topic: Ontology&possible worlds
Classes, Worlds and Hypergunk
by Daniel Nolan
Source: Online Papers in Philosophy
Many people have wanted to construe possible worlds as set-theoretic objects of one sort or another. A common feature of many of these theories is that they imply that no world contains more than a set of possible objects nor more than a set of properties possessed by those objects. A.P. Hazen has defended this consequence as being positively desirable, relying on a principle about what sorts of cases we should be able to have "genuine modal intuitions" about, and an argument that any such case can be represented set-theoretically. This paper produces a specification of a certain sort of unlimited divisibility which meets Hazen's strictures about what we may expect to have represented by a possible world, is independently plausible as a metaphysical possibility, and, if accepted as a genuine metaphysical possibility, demonstrates that many theories of possible worlds as set-theoretic objects are inadequate.