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LOGICS FOR PROPOSITIONAL CONTINGENTISM

  • PETER FRITZ (a1)
Abstract
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.

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*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
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P. Blackburn , M. de Rijke , & Y Venema . (2001). Modal Logic. Cambridge Tracts in Theoretical Computer Science, Vol. 53. Cambridge: Cambridge University Press.

B. F Chellas . (1980). Modal Logic: An Introduction. Cambridge: Cambridge University Press.

B. A. Davey & H. A Priestley . (2002). Introduction to Lattices and Order (second edition). Cambridge: Cambridge University Press.

K Fine . (1970). Propositional quantifiers in modal logic. Theoria, 36(3), 336346.

K Fine . (1974a). An ascending chain of S4 logics. Theoria, 40(2), 110116.

K Fine . (1974b). An incomplete logic containing S4. Theoria, 40(1), 2329.

K Fine . (1977). Properties, propositions and sets. Journal of Philosophical Logic, 6(1), 135191.

K Fine . (1980). First-order modal theories II – Propositions. Studia Logica, 39(2), 159202.

P Fritz . (2016). Propositional contingentism. The Review of Symbolic Logic, 9(1), 123142.

P. Fritz & J Goodman . (2016). Higher-order contingentism, part 1: Closure and generation. Journal of Philosophical Logic, 45(6), 645695.

D Gallin . (1975). Intensional and Higher-Order Modal Logic. Amsterdam: North-Holland.

S. Givant & P Halmos . (2009). Introduction to Boolean Algebras. New York: Springer.

V. Goranko & S Passy . (1992). Using the universal modality: Gains and questions. Journal of Logic and Computation, 2(1), 530.

L Humberstone . (2002). The modal logic of agreement and noncontingency. Notre Dame Journal of Formal Logic, 43(2), 95127.

B. Jónsson & A Tarski . (1951). Boolean algebras with operators. Part I. American Journal of Mathematics, 73(4), 891939.

P Kremer . (1993). Quantifying over propositions in relevance logic: Nonaxiomatizability of primary interpretations of ∀p and ∃p . Journal of Symbolic Logic, 58(1), 334349.

P Kremer . (1997). On the complexity of propositional quantification in intuitionistic logic. Journal of Symbolic Logic, 62(2), 529544.

D Lewis . (1988a). Relevant implication. Theoria, 54(1), 161174.

D Lewis . (1988b). Statements partly about observation. Philosophical Papers, 17(1), 131.

D Makinson . (1969). On the number of ultrafilters of an infinite boolean algebra. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 15(7–12), 121122.

D Makinson . (1971). Some embedding theorems for modal logic. Notre Dame Journal of Formal Logic, 12(2), 252254.

A. Nerode & R. A Shore . (1980). Second order logic and first-order theories of reducibility orderings. In J. Barwise , H. J. Keisler , and K. Kunen , editors. The Kleene Symposium. Amsterdam: North Holland, pp. 181200.

S. K Thomason . (1972). Semantic analysis of tense logic. The Journal of Symbolic Logic, 37(1), 150158.

S. K Thomason . (1974). An incompleteness theorem in modal logic. Theoria, 40(1), 3034.

F von Kutschera . (1994). Global supervenience and belief. Journal of Philosophical Logic, 23(1), 103110.

T Williamson . (2013). Modal Logic as Metaphysics. Oxford: Oxford University Press.

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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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