Higher-order free logic and the Prior-Kaplan paradox

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

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.

Similar books and articles

Epistemic Logic and Epistemology.Wesley H. Holliday - 2018 - In Sven Ove Hansson Vincent F. Hendricks (ed.), Handbook of Formal Philosophy. Springer. pp. 351-369.
I—Columnar Higher-Order Vagueness, or Vagueness is Higher-Order Vagueness.Susanne Bobzien - 2015 - Aristotelian Society Supplementary Volume 89 (1):61-87.
CERES in higher-order logic.Stefan Hetzl, Alexander Leitsch & Daniel Weller - 2011 - Annals of Pure and Applied Logic 162 (12):1001-1034.
The inconsistency of higher order extensions of Martin-löf's type theory.Bart Jacobs - 1989 - Journal of Philosophical Logic 18 (4):399 - 422.
Higher-Order Sorites Paradox.Elia Zardini - 2013 - Journal of Philosophical Logic 42 (1):25-48.
The Knowability Paradox in the light of a Logic for Pragmatics.Massimiliano Carrara & Daniele Chiffi - 2014 - In Roberto Ciuni, Heinrich Wansing & Caroline Willkommen (eds.), Recent Trends in Philosophical Logic (Proceedings of Trends in Logic XI). Cham, Switzerland: Springer. pp. 47-58.
Externalism, internalism, and logical truth.Corine Besson - 2009 - Review of Symbolic Logic 2 (1):1-29.
Self‐Knowledge, Rationality and Moore's Paradox.Jordi Fernández - 2007 - Philosophy and Phenomenological Research 71 (3):533-556.
Can the Classical Logician Avoid the Revenge Paradoxes?Andrew Bacon - 2015 - Philosophical Review 124 (3):299-352.

Analytics

Added to PP
2016-05-12

Downloads
1,606 (#6,489)

6 months
251 (#9,628)

Historical graph of downloads
How can I increase my downloads?

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.

View all 28 citations / Add more citations

References found in this work

On the Plurality of Worlds.David K. Lewis - 1986 - Malden, Mass.: Wiley-Blackwell.
Modal Logic as Metaphysics.Timothy Williamson - 2013 - Oxford, England: Oxford University Press.
Meaning.Herbert Paul Grice - 1957 - Philosophical Review 66 (3):377-388.
On the Plurality of Worlds.David Lewis - 1986 - Revue Philosophique de la France Et de l'Etranger 178 (3):388-390.
The Foundations of Mathematics and Other Logical Essays.Frank Plumpton Ramsey - 1925 - London, England: Routledge & Kegan Paul. Edited by R. B. Braithwaite.

View all 68 references / Add more references