Synthese

, Volume 178, Issue 1, pp 67–85 | Cite as

Objective Bayesianism, Bayesian conditionalisation and voluntarism

Article

Abstract

Objective Bayesianism has been criticised on the grounds that objective Bayesian updating, which on a finite outcome space appeals to the maximum entropy principle, differs from Bayesian conditionalisation. The main task of this paper is to show that this objection backfires: the difference between the two forms of updating reflects negatively on Bayesian conditionalisation rather than on objective Bayesian updating. The paper also reviews some existing criticisms and justifications of conditionalisation, arguing in particular that the diachronic Dutch book justification fails because diachronic Dutch book arguments are subject to a reductio: in certain circumstances one can Dutch book an agent however she changes her degrees of belief. One may also criticise objective Bayesianism on the grounds that its norms are not compulsory but voluntary, the result of a stance. It is argued that this second objection also misses the mark, since objective Bayesian norms are tied up in the very notion of degrees of belief.

Keywords

Objective Bayesianism Bayesian epistemology Formal epistemology Maximum entropy Maxent Conditionalisation 

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References

  1. Bacchus F., Kyburg H.E. Jr., Thalos M. (1990) Against conditionalization. Synthese 84(3): 475–506CrossRefGoogle Scholar
  2. Bayes T. (1764) An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London 53: 370–418CrossRefGoogle Scholar
  3. Bernoulli, J. (1713). Ars Conjectandi (E. D. Sylla, Trans., 2006). Baltimore: The Johns Hopkins University Press.Google Scholar
  4. Dias P.M.C., Shimony A. (1981) A critique of Jaynes’ maximum entropy principle. Advances in Applied Mathematics 2(2): 172–211CrossRefGoogle Scholar
  5. Earman J. (1992) Bayes or bust?. MIT Press, Cambridge MAGoogle Scholar
  6. Foley R. (1993) Working without a net. Oxford University Press, New YorkGoogle Scholar
  7. Friedman K., Shimony A. (1971) Jaynes’s maximum entropy prescription and probability theory. Journal of Statistical Physics 3(4): 381–384CrossRefGoogle Scholar
  8. Gillies D. (2000) Philosophical theories of probability. London and New York, RoutledgeGoogle Scholar
  9. Grove, A. J., & Halpern, J. Y. (1997). Probability update: Conditioning vs. cross-entropy. In Proceedings of the 13th annual conference on uncertainty in artificial intelligence (pp. 208–214). San Francisco, CA: Morgan Kaufmann.Google Scholar
  10. Howson C. (1997) Bayesian rules of updating. Erkenntnis 45: 195–208Google Scholar
  11. Howson C. (2000) Hume’s problem: Induction and the justification of belief. Clarendon Press, OxfordGoogle Scholar
  12. Jaynes E.T. (2003) Probability theory: The logic of science. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  13. Keynes J.M. (1921/1948). A treatise on probability. London, MacmillanGoogle Scholar
  14. Lange M. (1999) Calibration and the epistemological role of Bayesian conditionalization. The Journal of Philosophy 96: 294–324CrossRefGoogle Scholar
  15. Ramsey, F. P. (1926). Truth and probability. In H. E. Kyburg & H. E. Smokler (Eds.), Studies in subjective probability (2nd ed., 1980, pp. 23–52). Huntington, New York: Robert E. Krieger Publishing Company.Google Scholar
  16. Rosenkrantz R.D. (1977) Inference, method and decision: Towards a Bayesian philosophy of science. Reidel, DordrechtGoogle Scholar
  17. Rowbottom D.P. (2007) The insufficiency of the Dutch Book argument. Studia Logica 87: 65–71CrossRefGoogle Scholar
  18. Rowbottom, D. P., & Bueno, O. (2009). How to change it: modes of engagement, rationality, and stance voluntarism. Synthese. doi:10.1007/s11229-009-9521-0.
  19. Seidenfeld T. (1979) Why I am not an objective Bayesian. Theory and Decision 11: 413–440CrossRefGoogle Scholar
  20. Seidenfeld T. (1986) Entropy and uncertainty. Philosophy of Science 53(4): 467–491CrossRefGoogle Scholar
  21. Shimony A. (1973) Comment on the interpretation of inductive probabilities. Journal of Statistical Physics 9(2): 187–191CrossRefGoogle Scholar
  22. Shimony A. (1985) The status of the principle of maximum entropy. Synthese 63: 35–53CrossRefGoogle Scholar
  23. Skyrms B. (1985) Maximum entropy inference as a special case of conditionalization. Synthese 63: 55–74CrossRefGoogle Scholar
  24. Skyrms B. (1987) Coherence. In: Rescher N. (eds) Scientific inquiry in philosophical perspective. University Press of America, Lanham, Maryland, pp 225–242Google Scholar
  25. Teller P. (1973) Conditionalisation and observation. Synthese 26: 218–258CrossRefGoogle Scholar
  26. Uffink J. (1996) The constraint rule of the maximum entropy principle. Studies in History and Philosophy of Modern Physics 27: 47–79CrossRefGoogle Scholar
  27. van Fraassen B.C. (1981) A problem for relative information minimizers in probability kinematics. British Journal for the Philosophy of Science 32: 375–379CrossRefGoogle Scholar
  28. van Fraassen B.C. (1984) Belief and the will. Journal of Philosophy 81(5): 235–256CrossRefGoogle Scholar
  29. van Fraassen B.C. (1987) Symmetries of personal probability kinematics. In: Rescher N. (eds) Scientific inquiry in philosophical perspective. University Press of America, Lanham, Maryland, pp 183–223Google Scholar
  30. van Fraassen B.C. (1989) Laws and symmetry. Clarendon Press, OxfordCrossRefGoogle Scholar
  31. van Fraassen B.C. (2002) The empirical stance. Yale University Press, New HavenGoogle Scholar
  32. van Fraassen B., Hughes R., Harman G. (1986) A problem for relative information minimisers, continued. British Journal for the Philosophy of Science 37: 453–475Google Scholar
  33. Williams P.M. (1980) Bayesian conditionalisation and the principle of minimum information. British Journal for the Philosophy of Science 31: 131–144CrossRefGoogle Scholar
  34. Williamson J. (2005) Bayesian nets and causality: philosophical and computational foundations. Oxford University Press, OxfordGoogle Scholar
  35. Williamson J. (2007a) Inductive influence. British Journal for the Philosophy of Science 58(4): 689–708CrossRefGoogle Scholar
  36. Williamson J. (2007b) Motivating objective Bayesianism: From empirical constraints to objective probabilities. In: Harper W.L. (eds) Probability and inference: Essays in honour of Henry E. Kyburg Jr.. College Publications, London, pp 151–179Google Scholar
  37. Williamson J. (2008a) Objective Bayesian probabilistic logic. Journal of Algorithms in Cognition, Informatics and Logic 63: 167–183Google Scholar
  38. Williamson J. (2008b) Objective Bayesianism with predicate languages. Synthese 163(3): 341–356CrossRefGoogle Scholar
  39. Williamson, J. (2008c). Philosophies of probability. In A. Irvine (Ed.), Handbook of the philosophy of mathematics. Handbook of the philosophy of science (Vol. 4). Amsterdam: Elsevier.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of Philosophy, SECLUniversity of KentCanterburyUK

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