Abstract
It is often assumed that the supervaluationist theory of vagueness is committed to a global notion of logical consequence, in contrast with the local notion characteristic of modal logics. There are, at least, two problems related to the global notion of consequence. First, it brings some counterexamples to classically valid patterns of inference. Second, it is subject to an objection related to higher-order vagueness. This paper explores a third notion of logical consequence, and discusses its adequacy for the supervaluationist theory. The paper proceeds in two steps. In the first step, the paper provides a deductive notion of consequence for global validity using the tableaux method. In the second step, the paper provides a notion of logical consequence which is an alternative to global validity, and discusses i) whether it is acceptable to the supervaluationist and ii) whether it plays a better role in a theory of vagueness in the face of the problems related to the global notion.
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References
Fara D.G., ‘Gap principles, penumbral consequence, and infinitely higher-order vagueness’, Liars and Heaps: New Essays on Paradox, (2003), 195–221. Originally published under the name ‘Delia Graff’.
Fine K.: ‘Vagueness, truth and logic’. Synthese 30, 265–300 (1975)
Heck R.: ‘A note on the logic of (higher-order) vagueness’. Analysis 53, 201–208 (1993)
Hyde, D., ‘The prospects of a paraconsistent approach to vagueness’, Unpublished manuscript, (2005).
Keefe R.: ‘Supervaluationism and validity’. Philosophical Topics 28, 93–106 (2000)
Keefe, R., Theories of Vagueness, Cambridge University Press, 2000.
Kremer P., Kremer M.: ‘Some supervaluation-based consequence relations’. Journal of Philosophical Logic 32, 225–244 (2003)
McGee V., McLaughlin B.: ‘Review of Vagueness’. Linguistics and Philosophy 21, 221–235 (1998)
Priest, G., An Introduction to Non-Classical Logic, Cambridge Univerisity Press, 2001.
Smullyan, R., First Order Logic, Dover, 1995.
Williamson, T., Vagueness, Routledge, 1994.
Williamson T.: ‘On the structure of higher-order vagueness’. Mind 108, 127–143 (1999)
Williamson, T., ‘Reply to McGee and McLaughlin’, Linguistics and Philosophy, 27 (2004).
Wright C.: ‘Further reflections on the sorites paradox’. Philosophical Topics 15, 227–290 (1987)
Wright C.: ‘Is higher-order vagueness coherent?’. Analysis 52, 129–139 (1992)
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Cobreros, P. Supervaluationism and Logical Consequence: A Third Way. Stud Logica 90, 291–312 (2008). https://doi.org/10.1007/s11225-008-9154-1
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DOI: https://doi.org/10.1007/s11225-008-9154-1