Ways Things Can't Be

Notre Dame Journal of Formal Logic 38 (4):583-596 (1997)
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Abstract

Paraconsistent logics are often semantically motivated by considering "impossible worlds." Lewis, in "Logic for equivocators," has shown how we can understand paraconsistent logics by attributing equivocation of meanings to inconsistent believers. In this paper I show that we can understand paraconsistent logics without attributing such equivocation. Impossible worlds are simply sets of possible worlds, and inconsistent believers (inconsistently) believe that things are like each of the worlds in the set. I show that this account gives a sound and complete semantics for Priest's paraconsistent logic LP, which uses materials any modal logician has at hand

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Greg Restall
University of Melbourne

Citations of this work

Impossible Worlds.Daniel Nolan - 2013 - Philosophy Compass 8 (4):360-372.
Grounding Entails Counterpossible Non‐Triviality.Alastair Wilson - 2018 - Philosophy and Phenomenological Research 96 (3):716-728.
Granularity problems.Jens Christian Bjerring & Wolfgang Schwarz - 2017 - Philosophical Quarterly 67 (266):22-37.

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References found in this work

The logic of paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Logic for equivocators.David Lewis - 1982 - Noûs 16 (3):431-441.
Truthmakers, entailment and necessity.Greg Restall - 1996 - Australasian Journal of Philosophy 74 (2):331 – 340.
On Inferences from Inconsistent Premises.Nicholas Rescher & Ruth Manor - 1970 - Theory and Decision 1 (2):179-217, 1970-1971.

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