William Roche

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: support-t (support plus a sufficiently high probability), support-t* (support plus a substantial degree of support), and support-tt* (support plus both a sufficiently high probability and a substantial degree of support). I also set out two screening-off conditions (under which support is transitive): SOC1 and SOC2. It has already been shown that support-t is non-transitive in the general case (where it is not required that SOC1 holds and it is not required that SOC2 holds), in the special case where SOC1 holds, and in the special case where SOC2 holds. I introduce two rather weak adequacy conditions on support measures and argue that on any support measure meeting those conditions it follows that neither support-t* nor support-tt* is transitive in the general case, in the special case where SOC1 holds, or in the special case where SOC2 holds. I then relate some of the results to Douven’s evidential support theory of conditionals along with a few rival theories.

It is standard practice, when distinguishing between the foundationalist and the coherentist, to construe the coherentist as an internalist. The coherentist, the construal goes, says that justification is solely a matter of coherence, and that coherence, in turn, is solely a matter of internal relations between beliefs. The coherentist, so construed, is an internalist (in the sense I have in mind) in that the coherentist, so construed, says that whether a belief is justified hinges solely on what the subject is like mentally. I argue that this practice is fundamentally misguided, by arguing that the foundationalism / coherentism debate and the internalism / externalism debate are about two very different things, so that there is nothing, qua coherentist, precluding the coherentist from siding with the externalist. I then argue that this spells trouble for two of the three most pressing and widely known objections to coherentism: the Alternative-Systems Objection and the Isolation Objection.

According to Michael Friedman’s theory of explanation, a law X explains laws Y1, Y2, …, Yn precisely when X unifies the Y’s, where unification is understood in terms of reducing the number of independently acceptable laws. Philip Kitcher criticized Friedman’s theory but did not analyze the concept of independent acceptability. Here we show that Kitcher’s objection can be met by modifying an element in Friedman’s account. In addition, we argue that there are serious objections to the use that Friedman makes of the concept of independent acceptability.

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 the Screening-Off Condition is the most important condition for transitivity in confirmation because of its generality and ease of application. We illustrate our point with the example of Moore’s “proof” of the existence of a material world, where H1 logically entails H2, the Screening-Off Condition holds, and confirmation in all four senses turns out to be transitive

Ted Poston's book Reason and Explanation: A Defense of Explanatory Coherentism is a book worthy of careful study. Poston develops and defends an explanationist theory of (epistemic) justification on which justification is a matter of explanatory coherence which in turn is a matter of conservativeness, explanatory power, and simplicity. He argues that his theory is consistent with Bayesianism. He argues, moreover, that his theory is needed as a supplement to Bayesianism. There are seven chapters. I provide a chapter-by-chapter summary along with some substantive concerns.

There are numerous (Bayesian) confirmation measures in the literature. Festa provides a formal characterization of a certain class of such measures. He calls the members of this class “incremental measures”. Festa then introduces six rather interesting properties called “Matthew properties” and puts forward two theses, hereafter “T1” and “T2”, concerning which of the various extant incremental measures have which of the various Matthew properties. Festa’s discussion is potentially helpful with the problem of measure sensitivity. I argue, that, while Festa’s discussion is illuminating on the whole and worthy of careful study, T1 and T2 are strictly speaking incorrect (though on the right track) and should be rejected in favor of two similar but distinct theses.

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 {\ such that \ is probabilistically supported by \ for all i and \ has a high probability. Let this result be “APR”. A&P oftentimes write as though they believe that APR runs counter to foundationalism. This makes sense, since there is some prima facie plausibility in the idea that APR runs counter to foundationalism, and since some prominent foundationalists argue for theses inconsistent with APR. I argue, though, that in fact APR does not run counter to foundationalism. I further argue that there is a place in foundationalism for infinite regresses of probabilistic support.

Can a perceptual experience justify (epistemically) a belief? More generally, can a nonbelief justify a belief? Coherentists answer in the negative: Only a belief can justify a belief. A perceptual experience can cause a belief but cannot justify a belief. Coherentists eschew all noninferential justification—justification independent of evidential support from beliefs—and, with it, the idea that justification has a foundation. Instead, justification is holistic in structure. Beliefs are justified together, not in isolation, as members of a coherent belief system. The main question of the paper is whether coherentism is consistent. I set out an apparent inconsistency in coherentism and then give a resolution to that apparent inconsistency.

Recently there have been several attempts in formal epistemology to develop an adequate probabilistic measure of coherence. There is much to recommend probabilistic measures of coherence. They are quantitative and render formally precise a notion—coherence—notorious for its elusiveness. Further, some of them do very well, intuitively, on a variety of test cases. Siebel, however, argues that there can be no adequate probabilistic measure of coherence. Take some set of propositions A, some probabilistic measure of coherence, and a probability distribution such that all the probabilities on which A’s degree of coherence depends (according to the measure in question) are defined. Then, the argument goes, the degree to which A is coherent depends solely on the details of the distribution in question and not at all on the explanatory relations, if any, standing between the propositions in A. This is problematic, the argument continues, because, first, explanation matters for coherence, and, second, explanation cannot be adequately captured solely in terms of probability. We argue that Siebel’s argument falls short

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.

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 probability. But many of the scientific and everyday cases referred to above are cases where it is not the case that H 1 entails H 2. I consider whether there are additional conditions sufficient for transitivity in high probability. I consider three candidate conditions. I call them “C2”, “C3”, and “C2&3”. I argue that C2&3, but neither C2 nor C3, is sufficient for transitivity in high probability. I then set out some further results and relate the discussion to the Bayesian requirement of coherence.