Notre Dame Journal of Formal Logic

Inconsistency without Contradiction

Achille C. Varzi

Abstract

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.

Article information

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

Dates
First available: 10 December 2002

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1039540773

Mathematical Reviews number (MathSciNet)
MR1648856

Digital Object Identifier
doi:10.1305/ndjfl/1039540773

Zentralblatt MATH identifier
0916.03016

Subjects
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}

Citation

Varzi, Achille C. Inconsistency without Contradiction. Notre Dame Journal of Formal Logic 38 (1997), no. 4, 621--639. doi:10.1305/ndjfl/1039540773. http://projecteuclid.org/euclid.ndjfl/1039540773.


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