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.

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Author Profiles

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

Citations of this work

To Be F Is To Be G.Cian Dorr - 2016 - Philosophical Perspectives 30 (1):39-134.
Higher‐order metaphysics.Lukas Skiba - 2021 - Philosophy Compass 16 (10):1-11.
Free logic.John Nolt - 2021 - Stanford Encyclopedia of Philosophy.
A Theory of Structured Propositions.Andrew Bacon - 2023 - Philosophical Review 132 (2):173-238.
Ordinal Type Theory.Jan Plate - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.

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The Foundations of Mathematics and Other Logical Essays.Frank Plumpton Ramsey - 1925 - London, England: Routledge & Kegan Paul. Edited by R. B. Braithwaite.

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