Ways Things Can't Be

Notre Dame Journal of Formal Logic 38 (4):583-596 (1997)
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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DOI 10.1305/ndjfl/1039540771
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Martin A. Lipman (2015). On Fine’s Fragmentalism. Philosophical Studies 172 (12):3119-3133.
Barak Krakauer (2013). What Are Impossible Worlds? Philosophical Studies 165 (3):989-1007.
Daniel P. Nolan (2013). Impossible Worlds. Philosophy Compass 8 (4):360-372.

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