William Roche

Information and Inaccuracy

This article proposes a new interpretation of mutual information (MI). We examine three extant interpretations of MI by reduction in doubt, by reduction in uncertainty, and by divergence. We argue that the first two are inconsistent with the epistemic value of information (EVI) assumed in many applications of MI: the greater is the amount of information we acquire, the better is our epistemic position, other things being equal. The third interpretation is consistent with EVI, but it is faced with the problem of measure sensitivity and fails to justify the use of MI in giving definitive answers to questions of information. We propose a fourth interpretation of MI by reduction in expected inaccuracy, where inaccuracy is measured by a strictly proper monotonic scoring rule. It is shown that the answers to questions of information given by MI are definitive whenever this interpretation is appropriate, and that it is appropriate in a wide range of applications with epistemic implications. 1 Introduction 2 Formal Analyses of the Three Interpretations    2.1 Reduction in doubt   2.2 Reduction in uncertainty   2.3 Divergence 3 Inconsistency with Epistemic Value of Information 4 Problem of Measure Sensitivity 5 Reduction in Expected Inaccuracy 6 Resolution of the Problem of Measure Sensitivity    6.1 Alternative measures of inaccuracy   6.2 Resolution by strict propriety   6.3 Range of applications 7 Global Scoring Rules 8 Conclusion 1 Introduction 2 Formal Analyses of the Three Interpretations    2.1 Reduction in doubt   2.2 Reduction in uncertainty   2.3 Divergence   2.1 Reduction in doubt   2.2 Reduction in uncertainty   2.3 Divergence 3 Inconsistency with Epistemic Value of Information 4 Problem of Measure Sensitivity 5 Reduction in Expected Inaccuracy 6 Resolution of the Problem of Measure Sensitivity    6.1 Alternative measures of inaccuracy   6.2 Resolution by strict propriety   6.3 Range of applications   6.1 Alternative measures of inaccuracy   6.2 Resolution by strict propriety   6.3 Range of applications 7 Global Scoring Rules 8 Conclusion

Foundationalism with infinite regresses of probabilistic support

There is a long-standing debate in epistemology on the structure of justification. Some recent work in formal epistemology promises to shed some new light on that debate. I have in mind here some recent work by David Atkinson and Jeanne Peijnenburg, hereafter “A&P”, on infinite regresses of probabilistic support. A&P show that there are probability distributions defined over an infinite set of propositions {

Explanation = Unification? A New Criticism of Friedman’s Theory and a Reply to an Old One

p_{1}, p_{2}, p_{3}, {\ldots }, p_{n}, {\ldots }\}

Confirmation, transitivity, and Moore: the Screening-Off Approach

p1,p2,p3,…,pn,…} such that (i)

Transitivity and Intransitivity in Evidential Support: Some Further Results

p_{i}

Coherentism, Truth, and Witness Agreement

pi is probabilistically supported by