Supervaluationism and Logical Consequence: A Third Way
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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.
KeywordsSupervaluationism Vagueness Logical Consequence Truth
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- 1.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’.Google Scholar
- 4.Hyde, D., ‘The prospects of a paraconsistent approach to vagueness’, Unpublished manuscript, (2005).Google Scholar
- 5.Keefe R.: ‘Supervaluationism and validity’. Philosophical Topics 28, 93–106 (2000)Google Scholar
- 6.Keefe, R., Theories of Vagueness, Cambridge University Press, 2000.Google Scholar
- 9.Priest, G., An Introduction to Non-Classical Logic, Cambridge Univerisity Press, 2001.Google Scholar
- 10.Smullyan, R., First Order Logic, Dover, 1995.Google Scholar
- 11.Williamson, T., Vagueness, Routledge, 1994.Google Scholar
- 13.Williamson, T., ‘Reply to McGee and McLaughlin’, Linguistics and Philosophy, 27 (2004).Google Scholar
- 14.Wright C.: ‘Further reflections on the sorites paradox’. Philosophical Topics 15, 227–290 (1987)Google Scholar