Review of Symbolic Logic 7 (3):385-414 (2014)

Authors
Peter Fritz
Australian Catholic University
Abstract
This paper is concerned with a propositional modal logic with operators for necessity, actuality and apriority. The logic is characterized by a class of relational structures defined according to ideas of epistemic two-dimensional semantics, and can therefore be seen as formalizing the relations between necessity, actuality and apriority according to epistemic two-dimensional semantics. We can ask whether this logic is correct, in the sense that its theorems are all and only the informally valid formulas. This paper gives outlines of two arguments that jointly show that this is the case. The first is intended to show that the logic is informally sound, in the sense that all of its theorems are informally valid. The second is intended to show that it is informally complete, in the sense that all informal validities are among its theorems. In order to give these arguments, a number of independently interesting results concerning the logic are proven. In particular, the soundness and completeness of two proof systems with respect to the semantics is proven (Theorems 2.11 and 2.15), as well as a normal form theorem (Theorem 3.2), an elimination theorem for the actuality operator (Corollary 3.6), and the decidability of the logic (Corollary 3.7). It turns out that the logic invalidates a plausible principle concerning the interaction of apriority and necessity; consequently, a variant semantics is briefly explored on which this principle is valid. The paper concludes by assessing the implications of these results for epistemic two-dimensional semantics.
Keywords Modal logic  Necessity  Apriority  Actuality  Two-Dimensional Semantics  Nesting Problem
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Reprint years 2014
DOI 10.1017/s1755020314000136
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References found in this work BETA

Demonstratives: An Essay on the Semantics, Logic, Metaphysics and Epistemology of Demonstratives and Other Indexicals.David Kaplan - 1989 - In Joseph Almog, John Perry & Howard Wettstein (eds.), Themes From Kaplan. Oxford University Press. pp. 481-563.
Modal Logic as Metaphysics.Timothy Williamson - 2013 - Oxford, England: Oxford University Press.
Naming and Necessity.S. Kripke - 1972 - Tijdschrift Voor Filosofie 45 (4):665-666.

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Citations of this work BETA

Ground and Grain.Peter Fritz - forthcoming - Philosophy and Phenomenological Research.
Counterfactuals, counteractuals, and free choice.Fabio Lampert & Pedro Merlussi - 2021 - Philosophical Studies 178 (2):445-469.
Actuality and the a Priori.Fabio Lampert - 2018 - Philosophical Studies 175 (3):809-830.

View all 14 citations / Add more citations

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