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Bayesian confirmation theory is rife with confirmation measures. Many of them differ from each other in important respects. It turns out, though, that all the standard confirmation measures in the literature run counter to the socalled “Reverse Matthew Effect” (“RME” for short). Suppose, to illustrate, that H1 and H2 are equally successful in predicting E in that p(E  H1)/p(E) = p(E  H2)/p(E) > 1. Suppose, further, that initially H1 is less probable than H2 in that p(H1) < p(H2). (...) 

Is evidential support transitive? The answer is negative when evidential support is understood as confirmation so that X evidentially supports Y if and only if p(Y  X) > p(Y). I call evidential support so understood “support” (for short) and set out three alternative ways of understanding evidential support: supportt (support plus a sufficiently high probability), supportt* (support plus a substantial degree of support), and supporttt* (support plus both a sufficiently high probability and a substantial degree of support). I also (...) 

Hempel’s Converse Consequence Condition (CCC), Entailment Condition (EC), and Special Consequence Condition (SCC) have some prima facie plausibility when taken individually. Hempel, though, shows that they have no plausibility when taken together, for together they entail that E confirms H for any propositions E and H. This is “Hempel’s paradox”. It turns out that Hempel’s argument would fail if one or more of CCC, EC, and SCC were modified in terms of explanation. This opens up the possibility that Hempel’s paradox (...) 

There is a longstanding 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 {\ such that \ is probabilistically supported by \ for all i and \ has a high probability. (...) 

I argue elsewhere (Roche 2014) that evidence of evidence is evidence under screeningoff. Tal and Comesaña (2017) argue that my appeal to screeningoff is subject to two objections. They then propose an evidence of evidence thesis involving the notion of a defeater. There is much to learn from their very careful discussion. I argue, though, that their objections fail and that their evidence of evidence thesis is open to counterexample. 

There are many scientific and everyday cases where each of Pr and Pr is high and it seems that Pr is high. But high probability is not transitive and so it might be in such cases that each of Pr and Pr is high and in fact Pr is not high. There is no issue in the special case where the following condition, which I call “C1”, holds: H 1 entails H 2. This condition is sufficient for transitivity in high (...) 

We examine whether the "evidence of evidence is evidence" principle is true. We distinguish several different versions of the principle and evaluate recent attacks on some of those versions. We argue that, whatever the merits of those attacks, they leave the more important rendition of the principle untouched. That version is, however, also subject to new kinds of counterexamples. We end by suggesting how to formulate a better version of the principle that takes into account those new counterexamples. 