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The Plurality of Bayesian Measures of Confirmation and the Problem of Measure Sensitivity

Published online by Cambridge University Press:  01 April 2022

Branden Fitelson
Branden Fitelson*
Affiliation:
University of Wisconsin-Madison
*
†Department of Philosophy, University of Wisconsin, 600 North Park Street, Madison, WI 53706.
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Abstract

Contemporary Bayesian confirmation theorists measure degree of (incremental) confirmation using a variety of non-equivalent relevance measures. As a result, a great many of the arguments surrounding quantitative Bayesian confirmation theory are implicitly sensitive to choice of measure of confirmation. Such arguments are enthymematic, since they tacitly presuppose that certain relevance measures should be used (for various purposes) rather than other relevance measures that have been proposed and defended in the philosophical literature. I present a survey of this pervasive class of Bayesian confirmation-theoretic enthymemes, and a brief analysis of some recent attempts to resolve the problem of measure sensitivity.

Type
Probability and Statistical Inference
Information
Philosophy of Science , Volume 66 , Issue S3: Supplement. Proceedings of the 1998 Biennial Meetings of the Philosophy of Science Association. Part I: Contributed Papers Sep., 1999 , 1999 , pp. S362 - S378
Copyright
Copyright © 1999 by the Philosophy of Science Association

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Footnotes

‡

Thanks to Marty Barrett, Ellery Eells, Malcolm Forster, Ken Harris, Mike Kruse, Elliott Sober, and, especially, Patrick Maher for useful conversations on relevant issues.

References

Carnap, R. (1962), Logical Foundations of Probability, 2nd ed. Chicago: University of Chicago Press.Google Scholar
Earman, J. (1992), Bayes or Bust: A Critical Examination of Bayesian Confirmation Theory. Cambridge, MA: MIT Press.Google Scholar
Eells, E. (1982), Rational Decision and Causality. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Fitelson, B. (1996), “Wayne, Horwich, and Evidential Diversity”, Philosophy of Science 63: 652–660.CrossRefGoogle Scholar
Fitelson, B. (1998a), “A Bayesian Account of Independent Inductive Support with an Application to Evidential Diversity”, unpublished manuscript.Google Scholar
Fitelson, B. (1998b), “Independent Inductive Support and Measures of Confirmation”, unpublished manuscript.Google Scholar
Gillies, D. (1986), “In Defense of the Popper-Miller Argument”, Philosophy of Science 53: 110–113.CrossRefGoogle Scholar
Good, I. (1984), “The Best Explicatum for Weight of Evidence”, Journal of Statistical Computation and Simulation 19: 294–299.CrossRefGoogle Scholar
Heckerman, D. (1988), “An Axiomatic Framework for Belief Updates”, in Kanal, L. and Lemmer, J. (eds.), Uncertainty in Artificial Intelligence 2. New York: Elsevier Science Publishers, 11–22.CrossRefGoogle Scholar
Horvitz, E. and Heckerman, D. (1986), “The Inconsistent Use of Certainty Measures in Artificial Intelligence Research”, in Kanal, L. and Lemmer, J. (eds.), Uncertainty in Artificial Intelligence 1. New York: Elsevier Science Publishers, 137–151.CrossRefGoogle Scholar
Horwich, P. (1982), Probability and Evidence. Cambridge: Cambridge University Press.Google Scholar
Hosiasson-Lindenbaum, J. (1940), “On Confirmation”, Journal of Symbolic Logic 5: 133–148.10.2307/2268173CrossRefGoogle Scholar
Jeffrey, R. (1992), Probability and the Art of Judgment. Cambridge: Cambridge University Press.10.1017/CBO9781139172394CrossRefGoogle Scholar
Kaplan, M. (1996), Decision Theory as Philosophy. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Keynes, J. (1921), A Treatise on Probability. London: Macmillan.Google Scholar
Krantz, D., Luce, R., Suppes, P., and Tversky, A. (1971), Foundations of Measurement, vol. 1. New York: Academic Press.Google Scholar
Kyburg, H. (1983), “Recent Work in Inductive Logic”, in Machan, T. and Lucey, K. (eds.), Recent Work in Philosophy. Lanhan: Rowman & Allanheld, 87–150.Google Scholar
Mackie, J. (1969), “The Relevance Criterion of Confirmation”, The British Journal for the Philosophy of Science 20: 27–40.10.1093/bjps/20.1.27CrossRefGoogle Scholar
Maher, P. (1996), “Subjective and Objective Confirmation”, Philosophy of Science 63: 149–174.CrossRefGoogle Scholar
Maher, P. (1999), “Inductive Logic and the Ravens Paradox”, Philosophy of Science 66: 50–70.CrossRefGoogle Scholar
Milne, P. (1996), “log[p(h/eb)/p(h/b)] is the One True Measure of Confirmation”, Philosophy of Science 63: 21–26.10.1086/289891CrossRefGoogle Scholar
Mortimer, H. (1988), The Logic of Induction. Paramus: Prentice Hall.Google Scholar
Nozick, R. (1981), Philosophical Explanations. Cambridge, MA: Harvard University Press.Google Scholar
Pearl, J. (1988), Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. San Francisco: Morgan Kauffman.Google Scholar
Popper, K. and Miller, D. (1983), “The Impossibility of Inductive Probability”, Nature 302: 687–688.10.1038/302687a0CrossRefGoogle Scholar
Redhead, M. (1985), “On the Impossibility of Inductive Probability”, The British Journal for the Philosophy of Science 36: 185–191.10.1093/bjps/36.2.185CrossRefGoogle Scholar
Rosenkrantz, R. (1981), Foundations and Applications of Inductive Probability. Atascadero, CA: Ridgeview.Google Scholar
Rosenkrantz, R. (1994), “Bayesian Confirmation: Paradise Regained”, The British Journal for the Philosophy of Science 45: 467–476.10.1093/bjps/45.2.467CrossRefGoogle Scholar
Schlesinger, G. (1995), “Measuring Degrees of Confirmation”, Analysis 55: 208–212.10.1093/analys/55.3.208CrossRefGoogle Scholar
Schum, D. (1994), The Evidential Foundations of Probabilistic Reasoning. New York: John Wiley & Sons.Google Scholar
Sober, E. (1994), “No Model, No Inference: A Bayesian Primer on the Grue Problem”, in Stalker, D. (ed.), Gruel The New Riddle of Induction. Chicago: Open Court, 225–240.Google Scholar
Wayne, A. (1995), “Bayesianism and Diverse Evidence”, Philosophy of Science 62: 111–121.CrossRefGoogle Scholar