Advertisement

Erkenntnis

, Volume 79, Issue 5, pp 1027–1044 | Cite as

Vagueness, Uncertainty and Degrees of Belief: Two Kinds of Indeterminacy—One Kind of Credence

  • Nicholas J. J. Smith
Original Article

Abstract

If we think, as Ramsey did, that a degree of belief that P is a stronger or weaker tendency to act as if P, then it is clear that not only uncertainty, but also vagueness, gives rise to degrees of belief. If I like hot coffee and do not know whether the coffee is hot or cold, I will have some tendency to reach for a cup; if I like hot coffee and know that the coffee is borderline hot, I will have some tendency to reach for a cup. Suppose that we take degrees of belief arising from uncertainty to obey the laws of probability and that we model vagueness using degrees of truth. We then encounter a problem: it does not look as though degrees of belief arising from vagueness should obey the laws of probability. One response would be to countenance two different sorts of degrees of belief: degrees of belief arising from uncertainty, which obey the laws of probability; and degrees of belief arising from vagueness, which obey a different set of laws. I argue, however, that if a degree of belief that P is a stronger or weaker tendency to act as if P, then this option is not open. Instead, I propose an account of the behaviour of degrees of belief that integrates subjective probabilities and degrees of truth. On this account, degrees of belief are expectations of degrees of truth. The account explains why degrees of belief behave in accordance with the laws of probability in cases involving only uncertainty, while also allowing degrees of belief to behave differently in cases involving only vagueness, and in mixed cases involving both uncertainty and vagueness. Justifications of the account are given both via Dutch books and in terms of epistemic accuracy.

Keywords

Probability Measure Actual World Subjective Probability Epistemic State Belief Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Campbell, R. (1974). The sorites paradox. Philosophical Studies, 26, 175–191.CrossRefGoogle Scholar
  2. Cargile, J. (1969). The sorites paradox. In R. Keefe & P. Smith (Eds.), Vagueness: A reader (pp. 89–98). Cambridge, MA: MIT Press.Google Scholar
  3. Chisholm, R. M. (1957). Perceiving: A philosophical study. Ithaca: Cornell University Press.Google Scholar
  4. de Finetti, B. (1931). Sul significato soggettivo della probabilità. Fundamenta Mathematicae, 17, 298–329.Google Scholar
  5. de Finetti, B. (1937). La prévision: ses lois logiques, ses sources subjectives. Annales De l’Institute Henri Poincaré, 7, 1–68.Google Scholar
  6. de Finetti, B. (1974). Theory of probability: A critical introductory treatment, Vol. 1. Chichester: Wiley.Google Scholar
  7. Dempster, A. P. (1968). A generalization of Bayesian inference. Journal of the Royal Statistical Society, Series B (Methodological), 30, 205–247.Google Scholar
  8. Dubois, D., & Prade, H. (1988). Possibility theory: An approach to computerized processing of uncertainty. New York: Plenum.CrossRefGoogle Scholar
  9. Field, H. (2000). Indeterminacy, degree of belief, and excluded middle. Noûs, 34, 1–30.CrossRefGoogle Scholar
  10. Geach, P. (1957). Mental acts: Their content and their objects. London: Routledge & Kegan Paul.Google Scholar
  11. Horwich, P. (1998). Truth, second revised edition. Oxford: Clarendon Press.Google Scholar
  12. Joyce, J. M. (1998). A nonpragmatic vindication of probabilism. Philosophy of Science, 65, 575–603.CrossRefGoogle Scholar
  13. Keefe, R., & Smith, P. (Eds). (1997). Vagueness: A reader. Cambridge, MA: MIT Press. Google Scholar
  14. Lewis, D. (1986). A subjectivist’s guide to objective chance. In Philosophical papers, Vol. II (pp. 83–132). New York: Oxford University Press.Google Scholar
  15. Mundici, D. (2006). Bookmaking over infinite-valued events. International Journal of Approximate Reasoning, 43, 223–240.CrossRefGoogle Scholar
  16. Paris, J. B. (2005). A note on the dutch book method. Revised version of a paper in the proceedings of the 2nd international symposium on imprecise probabilities and their applications, Ithaca, New York, 2001. http://www.maths.manchester.ac.uk/~jeff/papers/15.ps.
  17. Ramsey, F. P. (1926). Truth and probability. In Philosophical papers (pp. 52–94). Cambridge: Cambridge University Press.Google Scholar
  18. Ramsey, F. P. (1990). Philosophical papers. Cambridge: Cambridge University Press (Edited by D. H. Mellor).Google Scholar
  19. Rosenkrantz, R. D. (1981). Foundations and applications of inductive probability. Atascadero, CA: Ridgeview.Google Scholar
  20. Schiffer, S. (2000). Vagueness and partial belief. Philosophical Issues, 10, 220–257.CrossRefGoogle Scholar
  21. Shafer, G. (1976). A mathematical theory of evidence. Princeton: Princeton University Press.Google Scholar
  22. Skyrms, B. (1984). Pragmatics and empiricism. New Haven: Yale University Press.Google Scholar
  23. Smets, P. (1981). The degree of belief in a fuzzy event. Information Sciences, 25, 1–19.CrossRefGoogle Scholar
  24. Smith, N. J. J. (2008). Vagueness and degrees of truth. Oxford: Oxford University Press. Paperback 2013.Google Scholar
  25. Smith, N. J. J. (2010). Degree of belief is expected truth value. In R. Dietz & S. Moruzzi (Eds.), Cuts and clouds: Vagueness, its nature, and its logic (pp. 491–506). Oxford: Oxford University Press.Google Scholar
  26. Smith, N. J. J. (2012). Many-valued logics. In G. Russell & D. Graff Fara (Eds.), The Routledge companion to philosophy of language (pp. 636–651). London: Routledge.Google Scholar
  27. Sorensen, R. (1988). Blindspots. Oxford: Clarendon Press.Google Scholar
  28. Sorensen, R. (2001). Vagueness and contradiction. Oxford: Clarendon Press.Google Scholar
  29. van Fraassen, B. C. (1983). Calibration: A frequency justification for personal probability. In R. S. Cohen & L. Laudan (Eds.), Physics, philosophy, and psychoanalysis (pp. 295–319). Dordrecht: D. Reidel.Google Scholar
  30. Williamson, T. (1992). Vagueness and ignorance. In R. Keefe & P. Smith (Eds.), Vagueness: A reader (pp. 265–280). Cambridge, MA: MIT Press.Google Scholar
  31. Williamson, T. (1994). Vagueness. London: Routledge.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of SydneySydneyAustralia

Personalised recommendations