Studia Logica

, Volume 90, Issue 3, pp 291–312 | Cite as

Supervaluationism and Logical Consequence: A Third Way



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.


Supervaluationism Vagueness Logical Consequence Truth 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 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
  2. 2.
    Fine K.: ‘Vagueness, truth and logic’. Synthese 30, 265–300 (1975)CrossRefGoogle Scholar
  3. 3.
    Heck R.: ‘A note on the logic of (higher-order) vagueness’. Analysis 53, 201–208 (1993)CrossRefGoogle Scholar
  4. 4.
    Hyde, D., ‘The prospects of a paraconsistent approach to vagueness’, Unpublished manuscript, (2005).Google Scholar
  5. 5.
    Keefe R.: ‘Supervaluationism and validity’. Philosophical Topics 28, 93–106 (2000)Google Scholar
  6. 6.
    Keefe, R., Theories of Vagueness, Cambridge University Press, 2000.Google Scholar
  7. 7.
    Kremer P., Kremer M.: ‘Some supervaluation-based consequence relations’. Journal of Philosophical Logic 32, 225–244 (2003)CrossRefGoogle Scholar
  8. 8.
    McGee V., McLaughlin B.: ‘Review of Vagueness’. Linguistics and Philosophy 21, 221–235 (1998)CrossRefGoogle Scholar
  9. 9.
    Priest, G., An Introduction to Non-Classical Logic, Cambridge Univerisity Press, 2001.Google Scholar
  10. 10.
    Smullyan, R., First Order Logic, Dover, 1995.Google Scholar
  11. 11.
    Williamson, T., Vagueness, Routledge, 1994.Google Scholar
  12. 12.
    Williamson T.: ‘On the structure of higher-order vagueness’. Mind 108, 127–143 (1999)CrossRefGoogle Scholar
  13. 13.
    Williamson, T., ‘Reply to McGee and McLaughlin’, Linguistics and Philosophy, 27 (2004).Google Scholar
  14. 14.
    Wright C.: ‘Further reflections on the sorites paradox’. Philosophical Topics 15, 227–290 (1987)Google Scholar
  15. 15.
    Wright C.: ‘Is higher-order vagueness coherent?’. Analysis 52, 129–139 (1992)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of NavarraPamplonaSpain

Personalised recommendations