A Two-Dimensional Logic for Two Paradoxes of Deontic Modality

Review of Symbolic Logic 15 (4):991-1022 (2022)
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Abstract

In this paper, we axiomatize the deontic logic in Fusco (2015), which uses a Stalnaker-inspired account of diagonal acceptance and a two-dimensional account of disjunction to treat Ross’s Paradox and the Puzzle of Free Choice Permission. On this account, disjunction-involving validities are a priori rather than necessary. We show how to axiomatize two-dimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as one-dimensional projections of more general two-dimensional rules. These completeness results help make explicit the restrictions Fusco’s account must place on free-choice inferences. They are also of independent interest, as they raise difficult questions about how to “lift” a Kripke frame for a one-dimensional modal logic into two dimensions.

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Author Profiles

Melissa Fusco
Columbia University
Alexander W. Kocurek
Cornell University

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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.
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Naming and Necessity.Saul A. Kripke - 1985 - Critica 17 (49):69-71.
Counterfactuals.David Lewis - 1973 - Foundations of Language 13 (1):145-151.
Epistemic Modals.Seth Yalcin - 2007 - Mind 116 (464):983-1026.

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