Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-25T08:14:56.850Z Has data issue: false hasContentIssue false

Milne's Argument for the Log-Ratio Measure

Published online by Cambridge University Press:  01 January 2022

Abstract

This article shows that a slight variation of the argument in Milne 1996 yields the log-likelihood ratio l rather than the log-ratio measure r as “the one true measure of confirmation.”

Type
Research Article
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 grateful to Jiji Zhang for pointing out an error in a previous version of this paper, and to Branden Fitelson, Chris Hitchcock, and two anonymous referees for helpful comments and suggestions. My research was supported by the Ahmanson Foundation and the German Research Foundation through its Emmy Noether Program.

References

János, Aczél (1966), Lectures on Functional Equations and Their Applications. New York: Academic Press.Google Scholar
Cox, Richard T. (1946), “Probability, Frequency, and Reasonable Expectation”, Probability, Frequency, and Reasonable Expectation 14:113.Google Scholar
Fitelson, Branden (2001), Studies in Bayesian Confirmation Theory. PhD dissertation. Madison: University of Wisconsin–Madison.Google Scholar
Fitelson, Branden (2007), “Likelihoodism, Bayesianism, and Relational Confirmation”, Likelihoodism, Bayesianism, and Relational Confirmation 156:473489.Google Scholar
Halpern, Joseph Y. (1999a), “A Counterexample to Theorems of Cox and Fine”, A Counterexample to Theorems of Cox and Fine 10:6785.Google Scholar
Halpern, Joseph Y. (1999b), “Cox's Theorem Revisited”, Cox's Theorem Revisited 11:429435.Google Scholar
Huber, Franz (2005), “What Is the Point of Confirmation?”, What Is the Point of Confirmation? 72:11461159.Google Scholar
Joyce, James M. (1998), “A Nonpragmatic Vindication of Probabilism”, A Nonpragmatic Vindication of Probabilism 65:575603.Google Scholar
Joyce, James M. (2003), “Bayes’ Theorem”, in E. N. Zalta (ed.), Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/bayes-theorem/.Google Scholar
Milne, Peter (1996), “ $\mathrm{log}\,[ \mathrm{Pr}\,( H\vert E\cap B) / \mathrm{Pr}\,( H\vert B) ] $ Is the One True Measure of Confirmation”, Philosophy of Science 63:2126.CrossRefGoogle Scholar
Percival, Philip (2002), “Epistemic Consequentialism”, Epistemic Consequentialism 76:121151.Google Scholar
Stalnaker, Robert C. (2002), “Epistemic Consequentialism”, Epistemic Consequentialism 76:153168.Google Scholar