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Higher-order free logic and the Prior-Kaplan paradox

Published online by Cambridge University Press:  01 January 2020

Andrew Bacon ,
John Hawthorne  and
Gabriel Uzquiano
Andrew Bacon*
Affiliation:
Philosophy, University of Southern California, Los Angeles, CA, USA.
John Hawthorne
Affiliation:
Philosophy, University of Southern California, Los Angeles, CA, USA.
Gabriel Uzquiano
Affiliation:
Philosophy, University of Southern California, Los Angeles, CA, USA.
*
Email: abacon@usc.edu
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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.

Keywords

Modal logic as metaphysicsPrior's paradoxKaplan's paradoxhigher-order modal logicfree logic
Type
Articles
Information
Canadian Journal of Philosophy , Volume 46 , Issue 4-5: Special Issue: Williamson on Modality , August 2016 , pp. 493 - 541
Copyright
Copyright © Canadian Journal of Philosophy 2016

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