Inconsistency without Contradiction

Notre Dame Journal of Formal Logic 38 (4):621-639 (1997)
David Lewis has argued that impossible worlds are nonsense: if there were such worlds, one would have to distinguish between the truths about their contradictory goings-on and contradictory falsehoods about them; and this--Lewis argues--is preposterous. In this paper I examine a way of resisting this argument by giving up the assumption that ‘in so-and-so world’ is a restricting modifier which passes through the truth-functional connectives The outcome is a sort of subvaluational semantics which makes a contradiction ‘A & ~A’ false even when both ‘A’ and ‘~A’ are true, just as supervaluational semantics makes a tautology ‘A v ~A’ true even when neither ‘A’ nor ‘~A’ are. Connections with discussive logics and complications of the account are discussed, and some general morals are drawn.
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DOI 10.1305/ndjfl/1039540773
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Pablo Cobreros (2013). Vagueness: Subvaluationism. Philosophy Compass 8 (5):472-485.
Achille C. Varzi (2002). On Logical Relativity. Philosophical Issues 12 (1):197-219.
David Ripley (forthcoming). Paraconsistent Logic. Journal of Philosophical Logic:1-10.

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Achille C. Varzi (2004). Conjunction and Contradiction. In Graham Priest, J. C. Beall & Bradley Armour-Garb (eds.), The Law of Non-Contradiction: New Philosophical Essays. Clarendon Press. pp. 93–110.
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