Actuality, Tableaux, and Two-Dimensional Modal Logics

Erkenntnis 83 (3):403-443 (2018)
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Abstract

In this paper we present tableau methods for two-dimensional modal logics. Although models for such logics are well known, proof systems remain rather unexplored as most of their developments have been purely axiomatic. The logics herein considered contain first-order quantifiers with identity, and all the formulas in the language are doubly-indexed in the proof systems, with the upper indices intuitively representing the actual or reference worlds, and the lower indices representing worlds of evaluation—first and second dimensions, respectively. The tableaux modulate over different notions of validity such as local, general, and diagonal, besides being general enough for several two-dimensional logics proposed in the literature. We also motivate the introduction of a new operator into two-dimensional languages and explore some of the philosophical questions raised by it concerning the relations there are between actuality, necessity, and the a priori, that seem to undermine traditional intuitive interpretations of two-dimensional operators.

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Fabio Lampert
University of Vienna

Citations of this work

Actual Issues for Relevant Logics.Shawn Standefer - 2020 - Ergo: An Open Access Journal of Philosophy 7.
Actuality and the a priori.Fabio Lampert - 2018 - Philosophical Studies 175 (3):809-830.
The Logic of Sequence Frames.Fabio Lampert - 2022 - Review of Symbolic Logic 15 (1):101-132.

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References found in this work

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.
Naming and Necessity.Saul Kripke - 1980 - Critica 17 (49):69-71.
Counterfactuals.David Lewis - 1973 - Tijdschrift Voor Filosofie 36 (3):602-605.
Epistemic Two-Dimensional Semantics.David J. Chalmers - 2004 - Philosophical Studies 118 (1-2):153-226.

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