Higher-order free logic and the Prior-Kaplan paradox

Canadian Journal of Philosophy 46 (4-5):493-541 (2016)
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Abstract

The principle of universal instantiation plays a pivotal role both in the derivation of intensional paradoxes such as Prior’s paradox and Kaplan’s paradox and the debate between necessitism and contingentism. We outline a distinctively free logical approach to the intensional paradoxes and note how the free logical outlook allows one to distinguish two different, though allied themes in higher-order necessitism. We examine the costs of this solution and compare it with the more familiar ramificationist approaches to higher-order logic. Our assessment of both approaches is largely pessimistic, and we remain reluctantly inclined to take Prior’s and Kaplan’s derivations at face value.

Author Profiles

John Hawthorne
Australian Catholic University
Gabriel Uzquiano
University of Southern California
Andrew Bacon
University of Southern California

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