Review of Symbolic Logic 10 (2):203-236 (2017)

Authors
Peter Fritz
Australian Catholic University
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 contingentism  propositions  modal logic  propositional quantifiers
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DOI 10.1017/S1755020317000028
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References found in this work BETA

Symbolic Logic.C. I. Lewis & C. H. Langford - 1934 - Erkenntnis 4 (1):65-66.
Higher-Order Contingentism, Part 1: Closure and Generation.Peter Fritz & Jeremy Goodman - 2016 - Journal of Philosophical Logic 45 (6):645-695.
Relevant Implication.David Lewis - 1988 - Theoria 54 (3):161-174.
A Shorter Model Theory.Wilfrid Hodges - 1997 - Studia Logica 64 (1):133-134.
Statements Partly About Observation.David Lewis - 1988 - Philosophical Papers 17 (1):1-31.

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Citations of this work BETA

Counterfactuals and Propositional Contingentism.Peter Fritz & Jeremy Goodman - 2017 - Review of Symbolic Logic 10 (3):509-529.
Standard State Space Models of Unawareness.Peter Fritz & Harvey Lederman - 2015 - Theoretical Aspects of Rationality and Knowledge 15.

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