Ways Things Can't Be

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