Modality and Paradox

Abstract

Philosophers often explain what could be the case in terms of what is, in fact, the case at one possible world or another. They may di↵er in what they take possible worlds to be or in their gloss of what is for something to be the case at a possible world. Still, they stand united by the threat of paradox. A family of paradoxes akin to the set-theoretic antinomies seem to allow one to derive a contradiction from apparently plausible principles. Some of them concern the interaction between propositions and worlds, and they appear to a↵ord the means to map classes of propositions into propositions-or, likewise, classes of worlds into worlds-in a one-to-one fashion that leads to contradiction. Yet another family of paradoxes threaten the view that whatever could exist does, in fact, exist, which is in line with modal realism, for example. This article aims to survey and identify the source of each family of paradoxes as well as to outline some responses to them.

A Purely Recombinatorial Puzzle

“…Sider () and Hawthorne and Uzquiano () pose such puzzles as problems for particular metaphysical views, such as necessitism; Uzquiano () uses such a puzzle to argue, tentatively, against conceiving of propositions as objects. See also Uzquiano () for an overview of related arguments.…”