## Notre Dame Journal of Formal Logic

### Ways Things Can't Be

Greg Restall

#### 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.

#### Article information

Source
Notre Dame J. Formal Logic Volume 38, Number 4 (1997), 583-596.

Dates
First available in Project Euclid: 10 December 2002

https://projecteuclid.org/euclid.ndjfl/1039540771

Digital Object Identifier
doi:10.1305/ndjfl/1039540771

Mathematical Reviews number (MathSciNet)
MR1648854

Zentralblatt MATH identifier
0916.03015

#### Citation

Restall, Greg. Ways Things Can't Be. Notre Dame J. Formal Logic 38 (1997), no. 4, 583--596. doi:10.1305/ndjfl/1039540771. https://projecteuclid.org/euclid.ndjfl/1039540771.

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