Degree supervaluational logic

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

Authors
Robert Williams
University of Leeds
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 that norms belief as classical consequence is standardly thought to do. The main focus of the paper considers a variant of standard supervaluational, on which we can characterize degrees of determinacy. It applies the methodology above to focus on degree logic. This is developed first in a basic, single-premise case; and then extended to the multipremise case, and to allow degrees of 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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DOI 10.1017/s1755020310000237
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References found in this work BETA

Vagueness.Timothy Williamson - 1994 - Routledge.
A Nonpragmatic Vindication of Probabilism.James Joyce - 1998 - Philosophy of Science 65 (4):575-603.
Many, but Almost One.David K. Lewis - 1993 - In Keith Cambell, John Bacon & Lloyd Reinhardt (eds.), Ontology, Causality and Mind: Essays on the Philosophy of D. M. Armstrong. Cambridge University Press. pp. 23-38.
Future Contingents and Relative Truth.John MacFarlane - 2003 - Philosophical Quarterly 53 (212):321–336.
Vagueness, Truth and Logic.Kit Fine - 1975 - Synthese 30 (3-4):265-300.

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Citations of this work BETA

Gradational Accuracy and Nonclassical Semantics.J. Robert G. Williams - 2012 - Review of Symbolic Logic 5 (4):513-537.
Nonclassical Minds and Indeterminate Survival.J. Robert G. Williams - 2014 - Philosophical Review 123 (4):379-428.
Vagueness as Indecision.J. Robert G. Williams - 2016 - Aristotelian Society Supplementary Volume 90 (1):285-309.
Must Good Reasoning Satisfy Cumulative Transitivity?Shyam Nair - 2019 - Philosophy and Phenomenological Research 98 (1):123-146.

View all 7 citations / Add more citations

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