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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 that coherence is truthconducive in that coherence implies an increase in the probability of truth. Central to my argument is a certain principle for transitivity in probabilistic support. I then address a question concerning the truthconduciveness of coherence as it relates to (something else I argue for) the truthconduciveness of consistency, and consider how the truthconduciveness of coherence bears on coherentist theories of justification. 

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 (...) 

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). (...) 

We show that as a chain of confirmation becomes longer, confirmation dwindles under screeningoff. 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 DataProcessing Inequality (...) 

It is well known that the probabilistic relation of confirmation is not transitive in that even if E confirms H1 and H1 confirms H2, E may not confirm H2. In this paper we distinguish four senses of confirmation and examine additional conditions under which confirmation in different senses becomes transitive. We conduct this examination both in the general case where H1 confirms H2 and in the special case where H1 also logically entails H2. Based on these analyses, we argue that (...) 

An important question in the current debate on the epistemic significance of peer disagreement is whether evidence of evidence is evidence. Fitelson argues that, at least on some renderings of the thesis that evidence of evidence is evidence, there are cases where evidence of evidence is not evidence. I introduce a condition and show that under this condition evidence of evidence is evidence. 

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. 

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 (...) 



