Logics for propositional contingentism

Journal article


Fritz, Peter. (2017). Logics for propositional contingentism. The Review of Symbolic Logic. 10(2), pp. 203 - 236. https://doi.org/10.1017/S1755020317000028
AuthorsFritz, Peter
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.

Keywords03B45; contingentism; propositions; modal logic; propositional quantifiers
Year2017
JournalThe Review of Symbolic Logic
Journal citation10 (2), pp. 203 - 236
PublisherCambridge University Press
ISSN1755-0203
Digital Object Identifier (DOI)https://doi.org/10.1017/S1755020317000028
Scopus EID2-s2.0-85015629993
Page range203 - 236
Research GroupDianoia Institute of Philosophy
Publisher's version
File Access Level
Controlled
Place of publicationUnited Kingdom
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