Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T20:03:56.515Z Has data issue: false hasContentIssue false
  • English
  • Français

DEGREE SUPERVALUATIONAL LOGIC

Published online by Cambridge University Press:  16 August 2010

J. ROBERT G. WILLIAMS
J. ROBERT G. WILLIAMS*
Affiliation:
Department of Philosophy, University of Leeds
*
*DEPARTMENT OF PHILOSOPHY, UNIVERSITY OF LEEDS, WOODHOUSE LANE, LEEDS, WEST YORKSHIRE, LS2 9JT, UNITED KINGDOM. Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 4 , Issue 1 , March 2011 , pp. 130 - 149
Copyright
Copyright © Association for Symbolic Logic 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

Adams, E. (1996). A Primer of Probability Logic. Chicago, IL: CSLI.Google Scholar
Akiba, K. (2000). Vagueness as a modality. Philosophical Quarterly, 50, 359–370.CrossRefGoogle Scholar
Barnes, E. J., & Williams, J. R. G. (2010). A theory of metaphysical indeterminacy. Oxford Studies in Metaphysics, 6.Google Scholar
Edgington, D. (1997). Vagueness by degrees. In Keefe, R. and Smith, P., editors. Vagueness: A Reader. Cambridge, MA: MIT Press, pp. 294–316.CrossRefGoogle Scholar
Field, H. (2009). What is the normative role of logic? Proceedings of the Aristotelian Society, 83, 251–268.CrossRefGoogle Scholar
Field, H. H. (1973). Theory change and the indeterminacy of reference. Journal of Philosophy, 70, 462–481. Reprinted in Field, Truth and the Absence of Fact (Oxford University Press, 2001), pp. 177–198.CrossRefGoogle Scholar
Field, H. H. (1974). Quine and the correspondence theory. Philosophical Review, 83, 200–228. Reprinted in Field, Truth and the Absence of Fact (Oxford University Press, 2001), pp. 199–221.CrossRefGoogle Scholar
Field, H. H. (2000). Indeterminacy, degree of belief, and excluded middle. Nous, 34, 1–30. Reprinted in Field, Truth and the Absence of Fact (Oxford University Press, 2001), pp. 278–311.CrossRefGoogle Scholar
Field, H. H. (2003). Semantic paradoxes and the paradoxes of vagueness. In Beall, J. C., editor. Liars and Heaps. Oxford: Oxford University Press, pp. 262–311.Google Scholar
Fine, K. (1975). Vagueness, truth and logic. Synthese, 30, 265–300. Reprinted with corrections in Keefe and Smith, editors. Vagueness: A Reader (Cambridge, MA: MIT Press, 1997), pp. 119–150.CrossRefGoogle Scholar
Halpern, J. Y. (1995). Reasoning About Uncertainty (revised edition). Cambridge, MA: MIT Press. Revised paperback edition published 2003.CrossRefGoogle Scholar
Joyce, J. M. (1998). A non-pragmatic vindication of probabilism. Philosophy of Science, 65, 575–603.CrossRefGoogle Scholar
Joyce, J. M. (2009). Accuracy and coherence: Prospects for an alethic epistemology of partial belief. In Huber, F. and Schmidt-Petri, C., editors. Degrees of Belief. Berlin: Springer, pp. 263–297.CrossRefGoogle Scholar
Kamp, J. A. W. (1975). Two theories about adjectives. In Keenan, E., editor. Formal Semantics of Natural Language. Cambridge, MA: Cambridge University Press, pp. 123–155. Reprinted in Davis and Gillon, editors. Semantics: A Reader (Oxford: Oxford University Press, 2004), pp.541–562.CrossRefGoogle Scholar
Keefe, R. (2000). Theories of Vagueness. Cambridge, MA: Cambridge University Press.Google Scholar
Lewis, D. K. (1970). General semantics. Synthese, 22, 18–67. Reprinted with postscript in Lewis, Philosophical Papers I (Oxford University Press, 1983), pp. 189–229.CrossRefGoogle Scholar
Lewis, D. K. (1984). Putnam’s paradox. Australasian Journal of Philosophy, 62(3), 221–236. Reprinted in Lewis, Papers on Metaphysics and Epistemology (Cambridge University Press, 1999), pp. 56–77.CrossRefGoogle Scholar
Lewis, D. K. (1993). Many, but almost one. In Campbell, K., Bacon, J., and Reinhardt, L., editors. Ontology, Causality and Mind: Essays on the Philosophy of D. M. Armstrong. Cambridge, MA: Cambridge University Press. Reprinted in Lewis, Papers on Metaphysics and Epistemology (Cambridge University Press, 1999), pp. 164–182.Google Scholar
Macfarlane, J. (2003). Future contingents and relative truth. Philosophical Quarterly, 53, 321–336.CrossRefGoogle Scholar
Macfarlane, J. (2010). Fuzzy epistemicism. In Moruzzi, S. and Dietz, R., editors. Cuts and Clouds. Oxford: Oxford University Press, pp. 438–463.CrossRefGoogle Scholar
Machina, K. F. (1976). Truth, belief and vagueness. Journal of Philosophical Logic, 5, 47–78. Reprinted in Keefe and Smith, editors. Vagueness: A Reader (MIT Press, 1997), pp. 174–204.CrossRefGoogle Scholar
Paris, J. (2001). A note on the Dutch Book method. In Proceedings of the Second International Symposium on Imprecise Probabilities and Their Applications, ISIPTA, Ithaca, NY: Shaker, pp. 301–306.Google Scholar
Restall, G. (2005). Multiple conclusions. In Hajek, P., Valdes-Villanueva, L., and Westerstahl, D., editors. Logic, Methodology and Philosophy of Science: Proceedings of the Twelfth International Congress. London: King’s College Publications, pp. 189–205. Available from: http://consequently.org/writing/multipleconclusions/.Google Scholar
Smith, N. J. J. (2008). Vagueness and Degrees of Truth. Oxford: Oxford University Press.CrossRefGoogle Scholar
Smith, N. J. J. (2010). Degrees of truth, degrees of belief and subjective probabilities. In Moruzzi, S., and Dietz, R., editors. Cuts and Clouds. Oxford: Oxford University Press, pp. 491–506.CrossRefGoogle Scholar
Stalnaker, R. (1980). A defense of conditional excluded middle. In Harper, R., Stalnaker, W. L., and Pearce, G., editors. Ifs: Conditionals, Belief, Decision, Chance and Time. Dordrecht, Holland: Kluwer Academic Publishers, pp. 87–106.CrossRefGoogle Scholar
Thomason, R. H. (1970). Indeterminist time and truth-value gaps. Theoria, 3, 264–281.CrossRefGoogle Scholar
Varzi, A. (2007). Supervaluationism and its logics. Mind, 116(463), 633–676.CrossRefGoogle Scholar
Weatherson, B. (2003). From classical to constructive probability. Notre Dame Journal of Formal Logic, 44, 111–123.CrossRefGoogle Scholar
Williams, J. R. G. (2007). Eligibility and inscrutability. Philosophical Review, 116(3), 361–399.CrossRefGoogle Scholar
Williams, J. R. G. (2008). Supervaluations and logical revisionism. The Journal of Philosophy, 105, 192–212.CrossRefGoogle Scholar
Williams, J. R. G. (manuscript). Gradational accuracy and non-classical logic.Google Scholar
Williamson, T. (1994). Vagueness. London: Routledge.Google Scholar