Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-26T22:07:12.288Z Has data issue: false hasContentIssue false
  • English
  • Français

GRADATIONAL ACCURACY AND NONCLASSICAL SEMANTICS

Published online by Cambridge University Press:  03 October 2012

J. ROBERT G. WILLIAMS
J. ROBERT G. WILLIAMS*
Affiliation:
University of Leads
*
*DEPARTMENT OF PHILOSOPHY, UNIVERSITY OF LEEDS, WOODHOUSE LANE, LEEDS, LS2 9JT, UK. E-mail: j.r.g.williams@leeds.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper gives a generalization of Jim Joyce’s 1998 argument for probabilism, dropping his background assumption that logic and semantics are classical. Given a wide variety of nonclassical truth-value assignments, Joyce-style arguments go through, allowing us to identify in each case a class of “nonclassically coherent” belief states. To give a local characterization of coherence, we need to identify a notion of logical consequence to use in an axiomatization. There is a very general, ‘no drop in truth-value’ characterization that will do the job. The result complements Paris’s 2001discussion of generalized forms of Dutch books appropriate to nonclassical settings.

Type
Research Articles
Information
The Review of Symbolic Logic , Volume 5 , Issue 4 , December 2012 , pp. 513 - 537
Copyright
Copyright © Association for Symbolic Logic 2012

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

Broome, J. (2005). Does rationality give us reasons? Philosophical Issues, 15(1), 321–337.Google Scholar
Choquet, G. (1953). Theory of capacities. Annales d’Institute Fourier, V, 131–295.Google Scholar
De Finetti, B. (1974). Theory of Probability, Vol. 1. New York: Wiley.Google Scholar
Di Nola, A., Georgescu, G., & Lettieri, A. (1999). Conditional states in finite-valued logic. In Dubois, D., Henri, P., and Klement, E., editors. Fuzzy Sets, Logics, and Reasoning about Knowledge. Dordrecht, The Netherlands: Kluwer, pp. 161–174.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.Google 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. (2003). Semantic paradoxes and the paradoxes of vagueness. In Beall, J. C., editor. Liars and Heaps. Oxford, UK: Oxford University Press, pp. 262–311.Google Scholar
Field, H. H. (2008). Saving Truth from Paradox. Oxford, UK: Oxford University Press.CrossRefGoogle Scholar
Fine, K. (1975). Vagueness, truth and logic. Synthese, 30, 265–300. Reprinted with corrections in Keefe and Smith (eds) Vagueness: A reader (MIT Press, Cambridge, MA: 1997) pp. 119–150.Google Scholar
Gerla, B. (2000). MV-algebras, multiple bets and subjective states. International Journal of Approximate Reasoning, 25(1), 1–13.Google Scholar
Gibbard, A. (2008). Rational credence and the value of truth. Oxford Studies in Epistemology, 2, 143.Google Scholar
Hájek, A. (2008). Arguments for—or against—probablism? British Journal for the Philosophy of Science, 59, 793–819.Google Scholar
Jaffray, J.-Y. (1989). Coherent bets under partially resolving uncertainty and belief functions. Theory and decision, 26, 90–105.Google Scholar
Joyce, J. M. (1998). A non-pragmatic vindication of probabilism. Philosophy of Science, 65, 575–603.CrossRefGoogle Scholar
Joyce, J. M. (2004). The accuracy of partial beliefs i and ii. Lecture notes. Unpublished Manuscript.Google 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.Google Scholar
Kamp, J. A. W. (1975). Two theories about adjectives. In Keenan, E., editor. Formal Semantics of Natural Language. Cambridge: Cambridge University Press, pp. 123–155. Reprinted in Davis and Gillon (eds) Semantics: A reader (Oxford University Press, Oxford, 2004) pp. 541–562.Google Scholar
Keefe, R. (2000). Theories of Vagueness. Cambridge, UK: Cambridge University Press.Google Scholar
Kolodny, N. (2007). How does coherence matter? Proceedings of the Aristotelian Society, 107, 229.Google Scholar
Leitgeb, H., & Pettigrew, R. (2010a). An objective justification of bayesianism i: Measuring inaccuracy. Philosophy of Science, 77(2), 201–235.Google Scholar
Leitgeb, H., & Pettigrew, R. (2010b). An objective justification of bayesianism ii: The consequences of minimizing inaccuracy. Philosophy of Science, 77(2), 236–272.Google Scholar
Lewis, D. K. (1970). General semantics. Synthese, 22, 18–67. Reprinted with postscript in Lewis, Philosophical Papers I (Oxford University Press, 1983) 189–229.CrossRefGoogle Scholar
Machina, K. F. (1976). Truth, belief and vagueness. Journal of Philosophical Logic, 5, 47–78. Reprinted in Keefe and Smith (eds) Vagueness: A reader (MIT Press, 1997) pp. 174–204.Google Scholar
Maher, P. (2002). Joyce’s argument for probabilism. Philosophy of Science, 69, 73–81.Google Scholar
Maudlin, T. (2004). Truth and Paradox: Solving the Riddles. Oxford, UK: Oxford University Press.Google Scholar
McGee, V., & McLaughlin, B. (1994). Distinctions without a difference. Southern Journal of Philosophy, Suppl. XXXII, 203–251.Google Scholar
Mundici, D. (2006). Bookmaking over infinite-valued events. International Journal of Approximate Reasoning, 43(3), 223–240.Google 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. Oxford, UK: Shaker, pp.301–306.Google Scholar
Pettigrew, R. (2012). Accuracy, chance and the principal principle. Philosophical Review, 121(2): 241–275.Google Scholar
Priest, G. (2001). An Introduction to Non-classical Logics. Cambridge, UK: Cambridge University Press.Google Scholar
Priest, G. (2006). In Contradiction: A Study of the Transconsistent. New York: Oxford University Press.CrossRefGoogle Scholar
Shafer, G. (1976). A Mathematical Theory of Evidence. Princeton, NJ: Princeton University Press.Google Scholar
Smith, N. J. J. (2008). Vagueness and Degrees of Truth. Oxford, UK: Oxford University Press.Google Scholar
van Fraassen, B. (1984). Belief and the will. The Journal of Philosophy, 81(5), 235–256.Google Scholar
Varzi, A. (2007). Supervaluationism and its logics. Mind, 116(463), 633–676.Google Scholar
Weatherson, B. (2003). From classical to constructive probability. Notre Dame Journal of Formal Logic, 44, 111–123.Google Scholar
Williams, J. R. G. (2011a). Degree supervaluational logic. Review of Symbolic Logic, 4(1), 130–149.Google Scholar
Williams, J. R. G. (2011b). Generalized probabilism: Dutch books and accuracy domination. Journal of Philosophical Logic, 1–30.Google Scholar
Williamson, T. (1994). Vagueness. London: Routledge.Google Scholar
Williamson, T. (2000). Knowledge and Its Limits. Oxford, UK: Oxford University Press.Google Scholar
Williamson, T. (2006). Must do better. In Greenough, P., and Lynch, M., editors. Truth and Realism. Oxford, UK: Oxford University Press.Google Scholar
Williamson, J. (2010). In Defence of Objective Bayesianism. Oxford, UK: Oxford University Press.Google Scholar
Wright, C. (1992). Truth and Objectivity. Cambridge, MA: Harvard University Press.Google Scholar
Wright, C. (2001). On being in a quandry. Mind, 110, 45–98.Google Scholar
Wright, C. (2003). Vagueness: A fifth column approach. In Beall, J. C., editor. Liars and Heaps: New Essays on Paradox. Oxford, UK: Oxford University Press, pp. 84–105.Google Scholar