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Dwindling Confirmation

Published online by Cambridge University Press:  01 January 2022

William Roche  and
Tomoji Shogenji
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Abstract

We show that as a chain of confirmation becomes longer, confirmation dwindles under screening-off. For example, if E confirms H1, H1 confirms H2, and H1 screens off E from H2, then the degree to which E confirms H2 is less than the degree to which E confirms H1. Although there are many measures of confirmation, our result holds on any measure that satisfies the Weak Law of Likelihood. We apply our result to testimony cases, relate it to the Data-Processing Inequality in information theory, and extend it in two respects so that it covers a broader range of cases.

Type
Research Article
Information
Philosophy of Science , Volume 81 , Issue 1 , January 2014 , pp. 114 - 137
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

We wish to thank Elliott Sober and Le Zhang for helpful discussion and three anonymous reviewers for detailed and extremely helpful comments.

References

Brossel, Peter. 2013. “The Problem of Measure Sensitivity Redux.” Philosophy of Science 80:378–97.CrossRefGoogle Scholar
Carnap, Rudolf. 1962. Logical Foundations of Probability. 2nd ed. Chicago: University of Chicago Press.Google Scholar
Cover, Thomas, and Thomas, Joy. 2006. Elements of Information Theory. 2nd ed. Hoboken, NJ: Wiley.Google Scholar
Crupi, Vincenzo, Festa, Roberto, and Buttasi, Carlo. 2010. “Towards a Grammar of Bayesian Confirmation.” In Epistemology and Philosophy of Science, ed. Suarez, Mauricio, Dorato, Mauro, and Redei, Miklos, 73–93. Dordrecht: Springer.Google 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
Douven, Igor. 2011. “Further Results on the Intransitivity of Evidential Support.” Review of Symbolic Logic 4:487–97.CrossRefGoogle Scholar
Eells, Ellery, and Fitelson, Branden. 2002. “Symmetries and Asymmetries in Evidential Support.” Philosophical Studies 107:129–42.CrossRefGoogle Scholar
Fano, Robert. 1961. Transmission of Information: A Statistical Theory of Communications. Cambridge, MA: MIT Press.CrossRefGoogle Scholar
Festa, Roberto. 1999. “Bayesian Confirmation.” In Experience, Reality, and Scientific Explanation, ed. Galavotti, Maria and Pagnini, Alessandro, 55–87. Dordrecht: Kluwer.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 2007. “Likelihoodism, Bayesianism, and Relational Confirmation.” Synthese 156:473–89.CrossRefGoogle Scholar
Fitelson, Branden 2011. “Favoring, Likelihoodism, and Bayesianism.” Philosophy and Phenomenological Research 83:666–72.CrossRefGoogle Scholar
Joyce, James. 2008. “Bayes’ Theorem.” In Stanford Encyclopedia of Philosophy, ed. Zalta, Edward. Stanford, CA: Stanford University. http://plato.stanford.edu/archives/fall2008/entries/bayes-theorem/.Google Scholar
McGrew, Timothy. 2004. “Has Plantinga Refuted the Historical Argument?” Philosophia Christi 6:7–26.CrossRefGoogle Scholar
Plantinga, Alvin. 2000. Warranted Christian Belief. New York: Oxford University Press.CrossRefGoogle Scholar
Plantinga, Alvin 2006. “Historical Arguments and Dwindling Probabilities.” Philosophia Christi 8:7–22.CrossRefGoogle Scholar
Roche, William. 2012a. “Transitivity and Intransitivity in Evidential Support: Some Further Results.” Review of Symbolic Logic 5:259–68.CrossRefGoogle Scholar
Roche, William 2012b. “A Weaker Condition for Transitivity in Probabilistic Support.” European Journal for Philosophy of Science 2:111–18.CrossRefGoogle Scholar
Roche, William, and Shogenji, Tomoji. 2013. “Confirmation, Transitivity, and Moore: The Screening-Off Approach.” Philosophical Studies. doi:10.1007/s11098-013-0161-3.CrossRefGoogle Scholar
Shogenji, Tomoji. 2003. “A Condition for Transitivity in Probabilistic Support.” British Journal for the Philosophy of Science 54:613–16.CrossRefGoogle Scholar
Shogenji, Tomoji 2012. “The Degree of Epistemic Justification and the Conjunction Fallacy.” Synthese 184:29–48.CrossRefGoogle Scholar
Sober, Elliott. 2009. “Absence of Evidence and Evidence of Absence: Evidential Transitivity in Connection with Fossils, Fishing, Fine-Tuning, and Firing Squads.” Philosophical Studies 143:63–90.CrossRefGoogle Scholar
Sober, Elliott 2011. “Responses to Fitelson, Sansom, and Sarkar.” Philosophy and Phenomenological Research 83:692–704.CrossRefGoogle Scholar
Sober, Elliott, and Steel, Mike. 2013. “Time and Knowability in Evolutionary Processes.” Unpublished manuscript, arXiv.org. http://arxiv-web3.library.cornell.edu/abs/1301.6470.Google Scholar
Swinburne, Richard. 2004. “Natural Theology, Its ‘Dwindling Probabilities’ and ‘Lack of Rapport.’” Faith and Philosophy 21:533–46.CrossRefGoogle Scholar
Tornebohm, Hakan. 1966. “Two Measures of Evidential Strength.” In Aspects of Inductive Logic, ed. Hintikka, Jaakko and Suppes, Patrick, 81–95. Amsterdam: North-Holland.CrossRefGoogle Scholar