A TWO-DIMENSIONAL LOGIC FOR TWO PARADOXES OF DEONTIC MODALITY
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Published:2020-08-25
Issue:
Volume:
Page:1-32
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ISSN:1755-0203
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Container-title:The Review of Symbolic Logic
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language:en
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Short-container-title:The Review of Symbolic Logic
Author:
FUSCO MELISSA,KOCUREK ALEXANDER W.
Abstract
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.
Publisher
Cambridge University Press (CUP)
Subject
Logic,Philosophy,Mathematics (miscellaneous)
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