The Broadest Necessity

Journal of Philosophical Logic 47 (5):733-783 (2018)
Authors
Andrew Bacon
University of Southern California
Abstract
In this paper the logic of broad necessity is explored. Definitions of what it means for one modality to be broader than another are formulated, and it is proven, in the context of higher-order logic, that there is a broadest necessity, settling one of the central questions of this investigation. It is shown, moreover, that it is possible to give a reductive analysis of this necessity in extensional language. This relates more generally to a conjecture that it is not possible to define intensional connectives from extensional notions. This conjecture is formulated precisely in higher-order logic, and concrete cases in which it fails are examined. The paper ends with a discussion of the logic of broad necessity. It is shown that the logic of broad necessity is a normal modal logic between S4 and Triv, and that it is consistent with a natural axiomatic system of higher-order logic that it is exactly S4. Some philosophical reasons to think that the logic of broad necessity does not include the S5 principle are given.
Keywords Logical necessity  Modality  Higher-order logic  Higher-order metaphysics
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DOI 10.1007/s10992-017-9447-9
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References found in this work BETA

On the Plurality of Worlds.David Lewis - 1986 - Journal of Philosophy 85 (1):42-47.
Vagueness, Truth and Logic.Kit Fine - 1975 - Synthese 30 (3-4):265-300.
Remarks on Counterpossibles.Berit Brogaard & Joe Salerno - 2013 - Synthese 190 (4):639-660.

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Citations of this work BETA

Modality as a Subject for Science.Timothy Williamson - 2017 - Res Philosophica 94 (3):415-436.
Is Reality Fundamentally Qualitative?Andrew Bacon - forthcoming - Philosophical Studies:1-37.

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