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A TWO-DIMENSIONAL LOGIC FOR TWO PARADOXES OF DEONTIC MODALITY

Part of: Other social and behavioral sciences (mathematical treatment) General logic

Published online by Cambridge University Press:  25 August 2020

MELISSA FUSCO  and
ALEXANDER W. KOCUREK
MELISSA FUSCO
Affiliation:
DEPARTMENT OF PHILOSOPHY COLUMBIA UNIVERSITY NEW YORK, NY, USA E-mail: mf3095@columbia.edu
ALEXANDER W. KOCUREK
Affiliation:
SAGE SCHOOL OF PHILOSOPHY CORNELL UNIVERSITY ITHACA, NY, USA E-mail: awk78@cornell.edu
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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.

Keywords

deontic logicRoss's puzzlefree-choice permissiontwo-dimensional logicdiagonalization

MSC classification

Primary: 91F20: Linguistics 03B65: Logic of natural languages 03B45: Modal logic (including the logic of norms)
Type
Research Article
Information
The Review of Symbolic Logic , Volume 15 , Issue 4 , December 2022 , pp. 991 - 1022
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Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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