Supervaluations debugged

Mind 118 (472):901-933 (2009)
Supervaluational accounts of vagueness have come under assault from Timothy Williamson for failing to provide either a sufficiently classical logic or a disquotational notion of truth, and from Crispin Wright and others for incorporating a notion of higher-order vagueness, via the determinacy operator, which leads to contradiction when combined with intuitively appealing ‘gap principles’. We argue that these criticisms of supervaluation theory depend on giving supertruth an unnecessarily central role in that theory as the sole notion of truth, rather than as one mode of truth. Allowing for the co-existence of supertruth and local truth, we define a notion of local entailment in supervaluation theory, and show that the resulting logic is fully classical and allows for the truth of the gap principles. Finally, we argue that both supertruth and local truth are disquotational, when disquotational principles are properly understood.
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DOI 10.1093/mind/fzp107
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References found in this work BETA
Anil Gupta (1982). Truth and Paradox. Journal of Philosophical Logic 11 (1):1-60.
Hans G. Herzberger (1982). Notes on Naive Semantics. Journal of Philosophical Logic 11 (1):61 - 102.

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Elia Zardini (2013). Higher-Order Sorites Paradox. Journal of Philosophical Logic 42 (1):25-48.

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