Abstract

The ontological pictures underpinning David Lewis's Parts of Classes and On the Plurality of Worlds are in some tension. One tension concerns whether the sets and classes of Parts of Classes can be found in Lewis's modal space, since they cannot in general be parts of any possible world. The second is that the atoms that are the mathematical ontology of Parts of Classes seem to meet the criteria for being possible worlds themselves, and so fail to be the material Parts of Classes needs. Two different responses to these tensions are discussed: one is unappealing in several ways but keeps more of Lewis's doctrines, while the other requires some modifications to the system of Parts of Classes.