Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T03:36:47.916Z Has data issue: false hasContentIssue false
  • English
  • Français

LOGICS FOR PROPOSITIONAL CONTINGENTISM

Published online by Cambridge University Press:  20 March 2017

PETER FRITZ
PETER FRITZ*
Affiliation:
Department of Philosophy, Classics, History of Art and Ideas, University of Oslo
*
*DEPARTMENT OF PHILOSOPHY, CLASSICS, HISTORY OF ART AND IDEAS UNIVERSITY OF OSLO POSTBOKS 1020 BLINDERN 0315 OSLO, NORWAY E-mail: peter.fritz@ifikk.uio.no
Get access Rights & Permissions [Opens in a new window]

Abstract

Robert Stalnaker has recently advocated propositional contingentism, the claim that it is contingent what propositions there are. He has proposed a philosophical theory of contingency in what propositions there are and sketched a possible worlds model theory for it. In this paper, such models are used to interpret two propositional modal languages: one containing an existential propositional quantifier, and one containing an existential propositional operator. It is shown that the resulting logic containing an existential quantifier is not recursively axiomatizable, as it is recursively isomorphic to second-order logic, and a natural candidate axiomatization for the resulting logic containing an existential operator is shown to be incomplete.

Keywords

03B45contingentismpropositionsmodal logicpropositional quantifiers
Type
Research Article
Information
The Review of Symbolic Logic , Volume 10 , Issue 2 , June 2017 , pp. 203 - 236
Copyright
Copyright © Association for Symbolic Logic 2017 

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

BIBLIOGRAPHY

Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal Logic. Cambridge Tracts in Theoretical Computer Science, Vol. 53. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Chellas, B. F. (1980). Modal Logic: An Introduction. Cambridge: Cambridge University Press.Google Scholar
Davey, B. A. & Priestley, H. A. (2002). Introduction to Lattices and Order (second edition). Cambridge: Cambridge University Press.Google Scholar
Fine, K. (1970). Propositional quantifiers in modal logic. Theoria, 36(3), 336–346.Google Scholar
Fine, K. (1974a). An ascending chain of S4 logics. Theoria, 40(2), 110–116.Google Scholar
Fine, K. (1974b). An incomplete logic containing S4. Theoria, 40(1), 23–29.Google Scholar
Fine, K. (1977). Properties, propositions and sets. Journal of Philosophical Logic, 6(1), 135–191.CrossRefGoogle Scholar
Fine, K. (1980). First-order modal theories II – Propositions. Studia Logica, 39(2), 159–202.CrossRefGoogle Scholar
Fritz, P. (2013). Modal ontology and generalized quantifiers. Journal of Philosophical Logic, 42(4), 643–678.Google Scholar
Fritz, P. (2016). Propositional contingentism. The Review of Symbolic Logic, 9(1), 123–142.Google Scholar
Fritz, P. (unpublished). Higher-order contingentism, part 3: Expressive limitations.Google Scholar
Fritz, P. & Goodman, J. (2016). Higher-order contingentism, part 1: Closure and generation. Journal of Philosophical Logic, 45(6), 645–695.Google Scholar
Fritz, P. & Lederman, H. (2015). Standard state space models of unawareness. In Ramanujam, R., editor. Proceedings of the 15th Conference on Theoretical Aspects of Rationality and Knowledge. Pittsburgh: Carnegie Mellon University, pp. 163–172.Google Scholar
Gallin, D. (1975). Intensional and Higher-Order Modal Logic. Amsterdam: North-Holland.Google Scholar
Givant, S. & Halmos, P. (2009). Introduction to Boolean Algebras. New York: Springer.Google Scholar
Goranko, V. & Passy, S. (1992). Using the universal modality: Gains and questions. Journal of Logic and Computation, 2(1), 5–30.Google Scholar
Hodges, W. (1997). A Shorter Model Theory. Cambridge: Cambridge University Press.Google Scholar
Humberstone, L. (2002). The modal logic of agreement and noncontingency. Notre Dame Journal of Formal Logic, 43(2), 95–127.CrossRefGoogle Scholar
Jónsson, B. & Tarski, A. (1951). Boolean algebras with operators. Part I. American Journal of Mathematics, 73(4), 891–939.Google Scholar
Kaminski, M. & Tiomkin, M. (1996). The expressive power of second-order propositional modal logic. Notre Dame Journal of Formal Logic, 37(1), 35–43.Google Scholar
Kaplan, D. (1970). S5 with quantifiable propositional variables. Journal of Symbolic Logic, 35(2), 355.Google Scholar
Kremer, P. (1993). Quantifying over propositions in relevance logic: Nonaxiomatizability of primary interpretations of ∀p and ∃p . Journal of Symbolic Logic, 58(1), 334–349.Google Scholar
Kremer, P. (1997). On the complexity of propositional quantification in intuitionistic logic. Journal of Symbolic Logic, 62(2), 529–544.Google Scholar
Lewis, C. I. & Langford, C. H. (1932). Symbolic Logic. London: Century.Google Scholar
Lewis, D. (1988a). Relevant implication. Theoria, 54(1), 161–174.Google Scholar
Lewis, D. (1988b). Statements partly about observation. Philosophical Papers, 17(1), 1–31.Google Scholar
Makinson, D. (1969). On the number of ultrafilters of an infinite boolean algebra. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 15(7–12), 121–122.Google Scholar
Makinson, D. (1971). Some embedding theorems for modal logic. Notre Dame Journal of Formal Logic, 12(2), 252–254.Google Scholar
Nerode, A. & Shore, R. A. (1980). Second order logic and first-order theories of reducibility orderings. In Barwise, J., Keisler, H. J., and Kunen, K., editors. The Kleene Symposium. Amsterdam: North Holland, pp. 181–200.Google Scholar
Segerberg, K. (1971). An Essay in Classical Modal Logic. Filosofiska Studier, Vol. 13. Uppsala: Uppsala Universitet.Google Scholar
Stalnaker, R. (2012). Mere Possibilities. Princeton: Princeton University Press.Google Scholar
Thomason, S. K. (1972). Semantic analysis of tense logic. The Journal of Symbolic Logic, 37(1), 150–158.CrossRefGoogle Scholar
Thomason, S. K. (1974). An incompleteness theorem in modal logic. Theoria, 40(1), 30–34.Google Scholar
von Kutschera, F. (1994). Global supervenience and belief. Journal of Philosophical Logic, 23(1), 103–110.Google Scholar
Williamson, T. (2013). Modal Logic as Metaphysics. Oxford: Oxford University Press.Google Scholar