Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-22T05:15:46.120Z Has data issue: false hasContentIssue false
  • English
  • Français

The Problem of Measure Sensitivity Redux

Published online by Cambridge University Press:  01 January 2022

Peter Brössel
Get access Rights & Permissions [Opens in a new window]

Abstract

Fitelson demonstrates that the validity of various central arguments within Bayesian confirmation theory depends on which confirmation measure is adopted. This article adds to the results set out by Fitelson, expanding on them in two principal respects. First, it considers more confirmation measures. Second, it shows that there are important arguments within Bayesian confirmation theory and that there is no confirmation measure that renders them all valid. Finally, the article reviews the ramifications that this “strengthened problem of measure sensitivity” has for Bayesian confirmation theory and discusses whether it points at pluralism about notions of confirmation.

Type
Research Article
Information
Philosophy of Science , Volume 80 , Issue 3 , July 2013 , pp. 378 - 397
Copyright
Copyright © 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

†

I am very grateful to four exceedingly helpful referees of this journal, especially for spotting a mistake in one of my proofs and encouraging me to discuss, among other issues, the ramifications of the problem of measure sensitivity in more detail in section 4. In addition, I would like to thank Ralf Busse, Vincenzo Crupi, Anna-Maria A. Eder, Branden Fitelson, Franz Huber, James M. Joyce, and Hannes Leitgeb for their invaluable feedback on various versions of this article. I also want to emphasize my gratitude to James M. Joyce for the permission to cite and quote his unpublished manuscript “On the Plurality of Probabilist Measures of Evidential Relevance.” Finally, I also would like to thank Robert Lehnert and Ben Young for proofreading the manuscript.

References

Brössel, Peter. 2012. “Rethinking Bayesian Confirmation Theory.” PhD diss., University of Konstanz.Google Scholar
Carnap, Rudolf. 1962. The Logical Foundations of Probability. 2nd ed. Chicago: University of Chicago Press.Google Scholar
Carnap, Rudolf, and Bar-Hillel, Yoshua. 1952. “An Outline of a Theory of Semantic Information.” Technical Report no. 247, Research Laboratory of Electronics, MIT.Google Scholar
Christensen, David. 1999. “Measuring Confirmation.” Journal of Philosophy 96:437–61.CrossRefGoogle Scholar
Crupi, Vincenzo, Festa, Roberto, and Buttasi, Carlo. 2010. “Towards a Grammar of Bayesian Confirmation.” In Epistemology and Methodology of Science, ed. Suárez, Mauricio, Dorato, Mauro, and Rédei, Miklós, 73–93. Dordrecht: Springer.Google Scholar
Crupi, Vincenzo, and Tentori, Katya. 2010. “Irrelevant Conjunction: Statement and Solution of a New Paradox.” Philosophy of Science 77:1–13.CrossRefGoogle Scholar
Crupi, Vincenzo, Tentori, Katya, and Gonzalez, Michel. 2007. “On Bayesian Measures of Evidential Support: Theoretical and Empirical Issues.” Philosophy of Science 74:229–52.CrossRefGoogle Scholar
Earman, John. 1992. Bayes or Bust? A Critical Examination of Bayesian Confirmation Theory. Cambridge, MA: MIT Press.Google Scholar
Eells, Ellery, and Fitelson, Branden. 2002. “Symmetries and Asymmetries in Evidential Support.” Philosophical Studies 107:129–42.CrossRefGoogle Scholar
Fitelson, Branden. 1999. “The Plurality of Bayesian Measures of Confirmation and the Problem of Measure Sensitivity.” Philosophy of Science 66 (Proceedings): S362–S378.CrossRefGoogle Scholar
Fitelson, Branden 2001. “Studies in Bayesian Confirmation Theory.” PhD diss., University of Wisconsin–Madison.Google Scholar
Fitelson, Branden 2002. “Putting the Irrelevance Back into the Problem of Irrelevant Conjunction.” Philosophy of Science 69:611–22.CrossRefGoogle Scholar
Fitelson, Branden 2006. “Logical Foundations of Evidential Support.” Philosophy of Science 73:500–512.CrossRefGoogle Scholar
Glymour, Clark. 1980. Theory and Evidence. Princeton, NJ: Princeton University Press.Google Scholar
Good, Irving John. 1960. “Weight of Evidence, Corroboration, Explanatory Power, Information and the Utility of Experiments.” Journal of the Royal Statistical Society B 22:319–31.Google Scholar
Hawthorne, James, and Fitelson, Branden. 2004. “Re-solving Irrelevant Conjunction with Probabilistic Independence.” Philosophy of Science 71:505–14.CrossRefGoogle Scholar
Hempel, Carl Gustav. 1945. “Studies in the Logic of Confirmation.” Pt. 1. Mind 54:1–26.CrossRefGoogle Scholar
Hempel, Carl Gustav 1960. “Inductive Inconsistencies.” Synthese 12:439–69.CrossRefGoogle Scholar
Horwich, Paul. 1982. Probability and Evidence. Cambridge: Cambridge University Press.Google Scholar
Huber, Franz. 2005. “What Is the Point of Confirmation?” Philosophy of Science 72:1146–59.CrossRefGoogle Scholar
Huber, Franz 2007. “Confirmation and Induction.” In Internet Encyclopedia of Philosophy, ed. James Fieser and Bradley Dowden. http://www.iep.utm.edu/conf-ind/.Google Scholar
Huber, Franz 2008. “Milne’s Argument for the Log-Ratio Measure.” Philosophy of Science 75:413–20.CrossRefGoogle Scholar
Joyce, James. 1999. Foundations of Causal Decision Theory. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Joyce, James 2003a. “Bayes’ Theorem.” In Stanford Encyclopedia of Philosophy, ed. Zalta, Edward N.. Stanford, CA: Stanford University. http://plato.stanford.edu/entries/bayes-theorem/.Google Scholar
Zalta, Edward N. 2003b. “On the Plurality of Probabilist Measures of Evidential Relevance.” Paper presented at the 26th Annual International Wittgenstein Symposium of the Austrian Ludwig Wittgenstein Society, Kirchberg.Google Scholar
Kemeny, John, and Oppenheim, Paul. 1952. “Degree of Factual Support.” Philosophy of Science 19:307–24.CrossRefGoogle Scholar
Lange, Mark. 1999. “Calibration and the Epistemological Role of Bayesian Conditionalization.” Journal of Philosophy 96:294–324.CrossRefGoogle Scholar
Milne, Peter. 1996. “ Is the One True Measure of Confirmation.” Philosophy of Science 63:21–26.CrossRefGoogle Scholar
Mortimer, Halina. 1988. The Logic of Induction. Paramus, NJ: Prentice Hall.Google Scholar
Nozick, Robert. 1981. Philosophical Explanations. Oxford: Clarendon.Google Scholar
Popper, Karl. 1954. “Degree of Confirmation.” British Journal of the Philosophy of Science 5:143–49.CrossRefGoogle Scholar
Rosenkrantz, Roger. 1981. Foundations and Applications of Inductive Probability. Atascadero, CA: Ridgeview.Google Scholar
Steel, Daniel. 2007. “Bayesian Confirmation Theory and the Likelihood Principle.” Synthese 156:55–77.CrossRefGoogle Scholar

A correction has been issued for this article:

Erratum