Journal of Philosophical Logic 48 (6):1003-1016 (2019)

Authors
Weng Kin San
University of Southern California
Abstract
Augment the propositional language with two modal operators: □ and ■. Define ⧫ to be the dual of ■, i.e. ⧫=¬■¬. Whenever (X) is of the form φ → ψ, let (X⧫) be φ→⧫ψ . (X⧫) can be thought of as the modally qualified counterpart of (X)—for instance, under the metaphysical interpretation of ⧫, where (X) says φ implies ψ, (X⧫) says φ implies possibly ψ. This paper shows that for various interesting instances of (X), fairly weak assumptions suffice for (X⧫) to imply (X)—so, the modally qualified principle is as strong as its unqualified counterpart. These results have surprising and interesting implications for issues spanning many areas of philosophy.
Keywords Fitch's Paradox  Paradox of Knowability  S5  Moorean sentences  Bimodal Logic  KK
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DOI 10.1007/s10992-019-09504-0
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References found in this work BETA

Modal Logic: An Introduction.Brian F. Chellas - 1980 - Cambridge University Press.
Ceteris Paribus Conditionals and Comparative Normalcy.Martin Smith - 2007 - Journal of Philosophical Logic 36 (1):97-121.
A Logical Analysis of Some Value Concepts.Frederic Fitch - 1963 - Journal of Symbolic Logic 28 (2):135-142.
The Logic of What Might Have Been.Nathan Salmon - 1989 - Philosophical Review 98 (1):3-34.
Referee Reports on Fitch's "Definition of Value".Alonzo Church - 2009 - In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press. pp. 13--20.

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Citations of this work BETA

Fitch's Paradox and Level-Bridging Principles.Weng Kin San - 2020 - Journal of Philosophy 117 (1):5-29.

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