Abstract
A simple rule of probability revision ensures that the final result ofa sequence of probability revisions is undisturbed by an alterationin the temporal order of the learning prompting those revisions.This Uniformity Rule dictates that identical learning be reflectedin identical ratios of certain new-to-old odds, and is grounded in the oldBayesian idea that such ratios represent what is learned from new experiencealone, with prior probabilities factored out. The main theorem of this paperincludes as special cases (i) Field's theorem on commuting probability-kinematical revisions and (ii) the equivalence of two strategiesfor generalizing Jeffrey's solution to the old evidence problem tothe case of uncertain old evidence and probabilistic new explanation.
Similar content being viewed by others
REFERENCES
Eells, E.: 1990, 'Bayesian Problems of Old Evidence', in C. Savage (ed.), Scientific Theories, Minnesota Studies in the Philosophy of Science XIV, University of Minnesota Press, Minneapolis, pp. 205-223.
Eells, E. and B. Fitelson: 2000, 'Measuring Confirmation and Evidence', The Journal of Philosophy 97, 663-672.
Field, H.: 1978, 'A Note on Jeffrey Conditionalization', Philosophy of Science 45, 361-367.
Garber, D.: 1980, 'Field and Jeffrey Conditionalization', Philosophy of Science 47, 142-145.
Garber, D.: 1983, 'Old Evidence and Logical Omniscience in Bayesian Confirmation Theory', in J. Earman (ed.), Testing Scientific Theories, Minnesota Studies in the Philosophy of Science X, University of Minnesota Press, Minneapolis, pp. 99-131.
Good, I.: 1985, 'Weight of Evidence: A Brief Survey', in J. Bernardo et al. (eds), Bayesian Statistics 2, North-Holland, pp. 249-370.
Glymour, C.: 1980, Theory and Evidence, Princeton University Press, Princeton.
Jeffrey, R.: 1965, The Logic of Decision, McGraw-Hill, New York, University of Chicago Press, Chicago.
Jeffrey, R.: 1991, 'Postscript 1991: New Explanation Revisited', in Jeffrey 1992, 103-107.
Jeffrey, R.: 1992, Probability and the Art of Judgement, Cambridge University Press, Cambridge.
Jeffrey, R.: 1995, 'Probability Reparation: The Problem of New Explanation', Philosophical Studies 77, 97-102.
Joyce, J.: 1999, The Foundations of Casual Decision Theory, Cambridge University Press, Cambridge, pp. 200-215.
Renyi, A.: 1970, Foundations of Probability, Holden-Day, San Francisco.
Skyrms, B.: 1983, 'ThreeWays to Give a Probability Assignment a Memory', in J. Earman (ed.), Testing Scientific Theories, Minnesota Studies in the Philosophy of Science X, University of Minnesota Press, Minneapolis, pp. 157-161.
Spohn, W.: 1988, 'Ordinal Conditional Functions: A Dynamic Theory of Epistemic States', in W. Harper and B. Skyrms (eds.), Causation, Belief Change, and Statistics II, Kluwer, Dordrecht, pp. 105-134.
Wagner, C.: 1997, 'Old Evidence and New Explanation', Philosophy of Science 64, 677-691.
Wagner, C.: 1999, 'Old Evidence and New Explanation II', Philosophy of Science 66, 283-288.
Wagner, C.: 2001, 'Old Evidence and New Explanation III', Philosophy of Science 68 (Proceedings): S165-S175.
Wagner, C.: 2002, 'Probability Kinematics and Commutativity', Philosophy of Science 69, 266-278
Weinberg, S.: 1992, Dreams of a Final Theory, Pantheon Press, New York.
Zynda, L.: 1995, 'Old Evidence and New Theories', Philosophical Studies 77, 67-96.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wagner, C.G. Commuting Probability Revisions: The Uniformity Rule. Erkenntnis 59, 349–364 (2003). https://doi.org/10.1023/A:1026077603719
Issue Date:
DOI: https://doi.org/10.1023/A:1026077603719