Notre Dame Journal of Formal Logic

Inconsistency without Contradiction

Achille C. Varzi


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 and not-A' false even when both 'A' and 'not-A' are true, just as supervaluational semantics makes a tautology 'A and not-A' true even when neither 'A' and 'not-A' are.

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Notre Dame J. Formal Logic Volume 38, Number 4 (1997), 621-639.

First available in Project Euclid: 10 December 2002

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Primary: 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30}
Secondary: 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}


Varzi, Achille C. Inconsistency without Contradiction. Notre Dame J. Formal Logic 38 (1997), no. 4, 621--639. doi:10.1305/ndjfl/1039540773.

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