Why Must Incompatibility Be Symmetric?

Philosophical Quarterly 74 (2):658-682 (2024)
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Abstract

Why must incompatibility be symmetric? An odd question, but recent work in the semantics of non-classical logic, which appeals to the notion of incompatibility as a primitive and defines negation in terms of it, has brought this question to the fore. Francesco Berto proposes such a semantics for negation argues that, since incompatibility must be symmetric, double negation introduction must be a law of negation. However, he offers no argument for the claim that incompatibility really must be symmetric. Here, I provide such an argument, showing that, insofar as we think of incompatibility in normative pragmatic terms, it can play its basic pragmatic function only if it is symmetric. The upshot is that we can vindicate Berto’s claim about the symmetry of incompatibility but only if we, pace Berto, think about incompatibility, in the first instance, as a pragmatic relation between acts rather than a semantic relation between contents.

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Ryan Simonelli
University of Chicago

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References found in this work

Accuracy and the Laws of Credence.Richard Pettigrew - 2016 - New York, NY.: Oxford University Press UK.
On the Plurality of Worlds.David Lewis - 1986 - Revue Philosophique de la France Et de l'Etranger 178 (3):388-390.
Impossible Worlds.Francesco Berto & Mark Jago - 2019 - Oxford: Oxford University Press. Edited by Mark Jago.
A Spirit of Trust: A Reading of Hegel’s phenomenology.Robert Brandom - 2019 - Cambridge, Massachusetts: Harvard University Press.
Making it Explicit.Isaac Levi & Robert B. Brandom - 1996 - Journal of Philosophy 93 (3):145.

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