This article presents an overview of the basic philosophical motivations for, and some recent work in, modal set theory.

Two uses of modal logic to explicate mathematics—due primarily to Hilary Putnam and Charles Parsons—are compared and contrasted. The approaches differ both technically and concerning ontology. Some reasons to push the former approach in the direction of the latter are articulated and discussed.

This paper develops an account of pluralities based on the following simple claim: some things are nothing over and above the individual things they comprise. For some, this may seem like a mysterious statement, perhaps even meaningless; for others, like a truism, trivial and inferentially inert. I show that neither reaction is correct: the claim is both tractable and has important consequences for a number of debates in philosophy.

ABSTRACTAccording to a famous argument by Dummett, the concept of set is indefinitely extensible, and the logic appropriate for reasoning about the instances of any such concept is intuitionistic, not classical. But Dummett's argument is widely regarded as obscure. This note explains how the final chapter of Rumfitt's important new book advances our understanding of Dummett's argument, but it also points out some problems and unanswered questions. Finally, Rumfitt's reconstruction of Dummett's argument is contrasted with my own preferred alternative.