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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.

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