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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: [email protected]
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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 

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