Degree supervaluational logic

Review of Symbolic Logic 4 (1):130-149 (2011)
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Abstract

Supervaluationism is often described as the most popular semantic treatment of indeterminacy. There’s little consensus, however, about how to fill out the bare-bones idea to include a characterization of logical consequence. The paper explores one methodology for choosing between the logics: pick a logic thatnorms beliefas classical consequence is standardly thought to do. The main focus of the paper considers a variant of standard supervaluational, on which we can characterizedegrees of determinacy. It applies the methodology above to focus ondegree logic. This is developed first in a basic, single-premise case; and then extended to the multipremise case, and to allowdegreesof consequence. The metatheoretic properties of degree logic are set out. On the positive side, the logic is supraclassical—all classical valid sequents are degree logic valid. Strikingly, metarules such as cut and conjunction introduction fail.

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Robert Williams
University of Leeds

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References found in this work

Vagueness.Timothy Williamson - 1996 - New York: Routledge.
General semantics.David K. Lewis - 1970 - Synthese 22 (1-2):18--67.
Vagueness, truth and logic.Kit Fine - 1975 - Synthese 30 (3-4):265-300.
Putnam’s paradox.David Lewis - 1984 - Australasian Journal of Philosophy 62 (3):221 – 236.
A nonpragmatic vindication of probabilism.James M. Joyce - 1998 - Philosophy of Science 65 (4):575-603.

View all 29 references / Add more references