Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T12:02:49.275Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bacon, Andrew. 2014.“Radical Anti-Disquotationalism.” MS.Google Scholar
Bacon, Andrew. 2011. “Vagueness at Every Order.” MS.Google Scholar
Bradwardine, Thomas. 2010. Insolubilia. Leuven: Peeters.Google Scholar
Church, Alonzo. 1976. “Comparison of Russell's Resolution of the Semantical Antinomies with that of Tarski.” Journal of Symbolic Logic 41(4): 747–760.CrossRefGoogle Scholar
Davies, Martin. 1981. Meaning, Quantification, Necessity: Themes in Philosophical Logic. Routledge & Kegan Paul.Google Scholar
Divers, John. 2006. Possible Worlds. Routledge.CrossRefGoogle Scholar
Dorr, Cian. 2012. “Propositional Profusion and the Liar.” MS.Google Scholar
Glanzberg, Michael. 2001. “The Liar in Context.” Philosophical Studies 103(3): 217–251.CrossRefGoogle Scholar
Harris, J. H. 1982. “What's So Logical about the ‘logical’ axioms?” Studia Logica 41(2–3): 159–171.CrossRefGoogle Scholar
Kaplan, David. 1977. “Demonstratives.” In Themes from Kaplan, edited by Almog, Joseph, Perry, John, and Wettstein, Howard, 481–563. Oxford University Press.Google Scholar
Kaplan, David. 1995. “A Problem in Possible Worlds Semantics.” In Modality, Morality and Belief: Essays in Honor of Ruth Barcan Marcus, edited by Sinnott-Armstrong, Walter, Raffman, Diana, and Asher, Nicholas, 41–52. Cambridge University Press.Google Scholar
Kripke, Saul A. 2011. “A Puzzle about Time and Thought.” In Philosophical Troubles. Collected Papers Vol I, edited by Kripke, Saul A..Oxford University Press.CrossRefGoogle Scholar
Lewis, David K. 1986. On the Plurality of Worlds. Blackwell Publishers.Google Scholar
McDaniel, Kris. 2009. “Ways of Being.” In Metametaphysics: New Essays on the Foundations of Ontology, edited by Chalmers, David John, Manley, David, and Wasserman, Ryan, Oxford University Press.Google Scholar
McGee, Vann. 2000. “Everything.” In Between Logic and Intuition: Essays in Honor of Charles Parsons, edited by Sher, Gila and Tieszen, Richard L., 54–78. Cambridge University Press.CrossRefGoogle Scholar
Myhill, John. 1979. “A Refutation of an Unjustified Attack on the Axiom of Reducibility.” In Bertrand Russell Memorial Volume, edited by Russell, Bertrand and Roberts, G. W., 81–90. Humanities Press.Google Scholar
Parsons, Charles. 1974. “The Liar Paradox.” Journal of Philosophical Logic 3(4): 381–412.CrossRefGoogle Scholar
Prior, A. N. 1956. “Modality and Quantification in S5.” Journal of Symbolic Logic 21(1): 60–62.CrossRefGoogle Scholar
Prior, A. N. 1961. “On a Family of Paradoxes.” Notre Dame Journal of Formal Logic 2(1): 16–32.CrossRefGoogle Scholar
Prior, A. N. 1977. Worlds, Times, and Selves. Duckworth.Google Scholar
Ramsey, Frank Plumpton. 1960. The Foundations of Mathematics and Other Logical Essays. Paterson, NJ: Littlefield, Adams.Google Scholar
Rayo, Agustín, and Uzquiano, Gabriel. 1999. “Toward a Theory of Second-Order Consequence.” Notre Dame Journal of Formal Logic 40(3): 315–325.CrossRefGoogle Scholar
Rayo, Agustín, and Williamson, Timothy. 2003. “A Completeness Theorem for Unrestricted First-Order Languages.” In Liars and Heaps, edited by Beall, J. C..Oxford University Press.Google Scholar
Russell, Bertrand. 1908. “Mathematical Logic as Based on the Theory of Types.” American Journal of Mathematics 30(3): 222–262.CrossRefGoogle Scholar
Sher, Gilar, and Tieszen, Richard L.. eds. 2000. Between Logic and Intuition: Essays in Honor of Charles Parsons. Cambridge University Press.CrossRefGoogle Scholar
Slater, B. H. 1986. “Prior's Analytic.” Analysis 46(2): 76–81.CrossRefGoogle Scholar
Smith, Nicholas J. J. 2006. “Semantic Regularity and the Liar Paradox.” The Monist 89(1): 178–202.CrossRefGoogle Scholar
Tarski, Alfred. 1936. “The Concept of Truth in Formalized Languages.” In Logic, Semantics, Metamathematics, edited by Tarski, A., 152–278. Oxford University Press.Google Scholar
Tucker, Dustin, and Thomason, Richmond H.. 2011. “Paradoxes of Intensionality.” Review of Symbolic Logic 4(3): 394–411.CrossRefGoogle Scholar
Uzquiano, Gabriel. 2015. “A Neglected Resolution of Russell's Paradox of Propositions.” Review of Symbolic Logic 8(2): 328–344.CrossRefGoogle Scholar
Williamson, Timothy. 1988. “Equivocation and Existence.” Proceedings of the Aristotelian Society 88 (n/a): 109–127.CrossRefGoogle Scholar
Williamson, Timothy. 1998. “Bare Possibilia.” Erkenntnis 48(2/3): 257–273.CrossRefGoogle Scholar
Williamson, Timothy. 2003. “Everything.” Philosophical Perspectives 17(1): 415–465.CrossRefGoogle Scholar
Williamson, Timothy. 2013. Modal Logic as Metaphysics. Oxford University Press.CrossRefGoogle Scholar