Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-25T17:17:49.843Z Has data issue: false hasContentIssue false
  • English
  • Français

Representation Theorems and Realism About Degrees of Belief

Published online by Cambridge University Press:  01 April 2022

Lyle Zynda
Lyle Zynda*
Affiliation:
Indiana University South Bend
Get access Rights & Permissions [Opens in a new window]

Abstract

The representation theorems of expected utility theory show that having certain types of preferences is both necessary and sufficient for being representable as having subjective probabilities. However, unless the expected utility framework is simply assumed, such preferences are also consistent with being representable as having degrees of belief that do not obey the laws of probability. This fact shows that being representable as having subjective probabilities is not necessarily the same as having subjective probabilities. Probabilism can be defended on the basis of the representation theorems only if attributions of degrees of belief are understood either antirealistically or purely qualitatively, or if the representation theorems are supplemented by arguments based on other considerations (simplicity, consilience, and so on) that single out the representation of a person as having subjective probabilities as the only true representation of the mental state of any person whose preferences conform to the axioms of expected utility theory.

Type
Research Article
Information
Philosophy of Science , Volume 67 , Issue 1 , March 2000 , pp. 45 - 69
Copyright
Copyright © 2000 by the Philosophy of Science Association

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.)

Footnotes

†

Send requests for reprints to the author, Department of Philosophy, Indiana University South Bend, 1700 Mishawaka Avenue, P.O. Box 7111, South Bend, IN, 46634.

‡

I wish to thank Alan Hájek, Michael Kinyon, J. Wesley Robbins, and the participants at the Conference on Methods (New School, New York City, May 15, 1999) for helpful discussion of this essay. Thanks also to one of the anonymous referees, whose insightful comments prompted me to clarify several points.

References

Allais, Maurice (1952), “The Foundations of a Positive Theory of Choice Involving Risk and a Criticism of the Postulate and Axioms of the American School”, in Maurice Allais and Ole Hagen (eds.) (1979), Expected Utility Hypotheses and Allais' Paradox. Dordrecht: Reidel, 27–145.Google Scholar
Broome, John (1991), Weighing Goods. Cambridge, MA: Blackwell.Google Scholar
Carnap, Rudolf (1950), “Empiricism, Semantics, and Ontology”, Revue Internationale de Philosophie 4: 20–40. Reprinted in Rudolph Carnap, Meaning and Necessity: A Study in Semantics and Modal Logic, 2nd ed., enlarged. Chicago: University of Chicago Press, 1956.Google Scholar
Chateauneuf, Alain and Jaffray, Jean-Yves (1984), “Archimedean Qualitative Probabilities”, Journal of Mathematical Psychology 28: 191–204.CrossRefGoogle Scholar
de Finetti, Bruno (1937), “Foresight: Its Logical Laws, Its Subjective Sources”, in Henry Kyburg and Howard Smokier (eds.) (1980), Studies in Subjective Probability. Huntington, NY: Krieger.Google Scholar
Dennett, Daniel (1987), The Intentional Stance. Cambridge, MA: MIT Press.Google Scholar
Dennett, Daniel. (1998), Brainchildren: Essays on Designing Minds. Cambridge, MA: MIT Press.CrossRefGoogle Scholar
Earman, John (1992), Bayes or Bust? Cambridge, MA: MIT Press.Google Scholar
Fine, Terrence (1973), Theories of Probability. New York: Academic Press.Google Scholar
Fishburn, Peter (1981), “Subjective Expected Utility: A Review of Normative Theories”, Theory and Decision 13: 139–199.CrossRefGoogle Scholar
Fishburn, Peter. (1982), The Foundations of Expected Utility. Dordrecht: Reidel.CrossRefGoogle Scholar
Fishburn, Peter. (1986), “The Axioms of Subjective Probability”, Statistical Science 1: 345–355.Google Scholar
Fishburn, Peter. (1988), Nonlinear Preference and Utility Theory. Baltimore: John Hopkins.Google Scholar
Gärdenfors, Peter and Sahlin, Nils-Eric (eds.) (1988), Decision, Probability, and Utility. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Harman, Gilbert (1986), Change in View. Cambridge, MA: MIT Press.Google Scholar
Horgan, Terrence and Woodward, James (1985), “Folk Psychology Is Here to Stay”, Philosophical Quarterly 94, no. 2.Google Scholar
Howson, Colin and Urbach, Peter (1989) Scientific Reasoning: The Bayesian Approach. La Salle, IL: Open Court.Google Scholar
Hurley, S.L. (1989), Natural Reasons: Personality and Polity. Oxford: Oxford University Press.Google Scholar
Jeffrey, Richard (1983), The Logic of Decision, 2nd ed. Chicago: University of Chicago Press. [First edition, 1965.]Google Scholar
Jeffrey, Richard (1988), “Conditioning, Kinematics and Exchangeability”, in Skyrms, Brian and Harper, William (eds.), Causation, Chance, and Credence, vol. 1. Boston: Kluwer Academic Press, 221–255.CrossRefGoogle Scholar
Kaplan, Mark (1996), Decision Theory as Philosophy. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Kraft, Charles, Pratt, John, and Seidenberg, A. (1959), “Intuitive Probability on Finite Sets”, Annals of Mathematical Statistics 30: 408–419.CrossRefGoogle Scholar
Maher, Patrick (1993), Betting on Theories. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Pearl, Judea (1988), Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. San Mateo, CA: Morgan Kaufmann Publishers.Google Scholar
Pearl, Judea and Shafer, Glenn (eds.) (1990), Readings in Uncertain Reasoning. San Mateo, CA: Morgan Kaufmann Publishers.Google Scholar
Ramsey, Frank (1926), “Truth and Probability”, in Frank Ramsey, Philosophical Papers, edited by Mellor, D. H. Cambridge: Cambridge University Press, 1990, 52–109.Google Scholar
Savage, Leonard (1954), The Foundations of Statistics. New York: Wiley and Sons. [Revised and enlarged edition, New York: Dover, 1973.]Google Scholar
Skyrms, Brian (1984), Pragmatics and Empiricism. New Haven: Yale University Press.Google Scholar
Skyrms, Brian. (1987), “Coherence”, in Rescher, Nicholas (ed.), Scientific Inquiry in Philosophical Perspective. Pittsburgh: University of Pittsburgh Press, 225–242.Google Scholar
van Fraassen, Bas (1980), The Scientific Image. New York: Oxford University Press.CrossRefGoogle Scholar
van Fraassen, Bas. (1984), “Belief and the Will”, Journal of Philosophy 81: 235–256.CrossRefGoogle Scholar
van Fraassen, Bas. (1989), Laws and Symmetry. New York: Oxford University Press.CrossRefGoogle Scholar
Zynda, Lyle (1996), “Coherence as an Ideal of Rationality”, Synthese 109: 175–216.CrossRefGoogle Scholar