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Confirmation Measures and Sensitivity

Published online by Cambridge University Press:  01 January 2022

Olav B. Vassend
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Abstract

Stanley Stevens draws a useful distinction among ordinal scales, interval scales, and ratio scales. Most recent discussions of confirmation measures have proceeded on the ordinal level of analysis. In this article, I give a more quantitative analysis. In particular, I show that the requirement that our desired confirmation measure be at least an interval measure naturally yields necessary conditions that jointly entail the log-likelihood measure. Thus, I conclude that the log-likelihood measure is the only good candidate interval (or ratio) measure.

Type
Confirmation Theory
Information
Philosophy of Science , Volume 82 , Issue 5 , December 2015 , pp. 892 - 904
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

Thanks to Michael Titelbaum and two anonymous reviewers for helpful feedback, and thanks to PSA participants (esp. Emi Okayasu and Greg Gandenberger) for stimulating discussion.

References

Atkinson, David. 2009. “Confirmation and Justification: A Commentary on Shogenji’s Measure.” Synthese 184:49–61.CrossRefGoogle Scholar
Carnap, Rudolph. 1962. Logical Foundations of Probability. 2nd ed. Chicago: University of Chicago Press.Google Scholar
Christensen, David. 1999. “Measuring Confirmation.” Journal of Philosophy 96:437–61.10.2307/2564707CrossRefGoogle Scholar
Crupi, Vincenzo, Chater, Nick, and Tentori, Katya. 2013. “New Axioms for Probability and Likelihood Ratio Measures.” British Journal for the Philosophy of Science 64:189–204.10.1093/bjps/axs018CrossRefGoogle Scholar
Fitelson, Branden. 2001. “Studies in Bayesian Confirmation Theory.” PhD diss., University of Wisconsin–Madison.Google Scholar
Fitelson, Branden 2006. “Logical Foundations of Evidential Support.” Philosophy of Science 73:500–512.10.1086/518320CrossRefGoogle Scholar
Good, I. J. 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
Good, I. J. 1984. “The Best Explicatum for Weight of Evidence.” Journal of Statistical Computation and Simulation 19:294–99.CrossRefGoogle Scholar
Huber, Franz. 2008. “Milne’s Argument for the Log-Ratio Measure.” Philosophy of Science 75:413–20.10.1086/595838CrossRefGoogle Scholar
Joyce, James. 1999. The Foundations of Causal Decision Theory. Cambridge: Cambridge University Press.10.1017/CBO9780511498497CrossRefGoogle Scholar
Milne, Peter. 1996. “Log[P(hleb)/P(hlb)] Is the One True Measure of Confirmation.” Philosophy of Science 63:21–26.CrossRefGoogle Scholar
Stevens, Stanley S. 1946. “On the Theory of Scales of Measurement.” Science 103:577–80.CrossRefGoogle ScholarPubMed