This paper examines how coherence of the contents of evidence affects the transmission of probabilistic support from the evidence to the hypothesis. It is argued that coherence of the contents in the sense of the ratio of the positive intersection reduces the transmission of probabilistic support, though this negative impact of coherence may be offset by other aspects of the relations among the contents. It is argued further that there is no broader conception of coherence whose impact on the transmission (...) of probabilistic support is never offset by other aspects of the relations among the contents. The paper also examines reasons for the contrary impression that coherence of the contents increases the transmission of probabilistic support, especially in the special case where the hypothesis to evaluate is the conjunction of the contents of evidence. (shrink)

Focused correlation compares the degree of association within an evidence set to the degree of association in that evidence set given that some hypothesis is true. A difference between the confirmation lent to a hypothesis by one evidence set and the confirmation lent to that hypothesis by another evidence set is robustly tracked by a difference in focused correlations of those evidence sets on that hypothesis, provided that all the individual pieces of evidence are equally, positively relevant to that hypothesis. (...) However, that result depends on a very strong equal relevance condition on individual pieces of evidence. In this essay, we prove tracking results for focused correlation analogous to Wheeler and Scheines’s results but for cases involving unequal relevance. Our result is robust as well, and we retain conditions for bidirectional tracking between incremental confirmation measures and focused correlation. (shrink)

This chapter contains sections titled: Introduction Goal and Scope of the Argument The Concept of a Miracle Textual Assumptions Background Facts: Death and Burial The Salient Facts: W, D, and P Probabilistic Cumulative Case Arguments: Nature and Structure The Testimony of the Women: Bayes Factor Analysis The Testimony of the Disciples: Bayes Factor Analysis The Conversion of Paul: Bayes Factor Analysis The Collective Force of the Salient Facts Independence Hume's Maxim and Worldview Worries Plantinga's Principle of Dwindling Probabilities Knavery, Folly, (...) and the Love of Wonder Conclusion References. (shrink)

This essay presents results about a deviation from independence measure called focused correlation . This measure explicates the formal relationship between probabilistic dependence of an evidence set and the incremental confirmation of a hypothesis, resolves a basic question underlying Peter Klein and Ted Warfield's ‘truth-conduciveness’ problem for Bayesian coherentism, and provides a qualified rebuttal to Erik Olsson's claim that there is no informative link between correlation and confirmation. The generality of the result is compared to recent programs in Bayesian epistemology (...) that attempt to link correlation and confirmation by utilizing a conditional evidential independence condition. Several properties of focused correlation are also highlighted. Introduction Correlation Measures 2.1 Standard covariance and correlation measures 2.2 The Wayne–Shogenji measure 2.3 Interpreting correlation measures 2.4 Correlation and evidential independence Focused Correlation Conclusion Appendix CiteULike Connotea Del.icio.us What's this? (shrink)

outlined. This account is partly inspired by the work of C.S. Peirce. When we want to consider how degree of confirmation varies with changing I show that a large class of quantitative Bayesian measures of con-.

In three recent papers, Wayne Myrvold and Timothy McGrew have developed Bayesian accounts of the virtue of unification. In his account, McGrew demonstrates that, ceteris paribus, a hypothesis that unifies its evidence will have a higher posterior probability than a hypothesis that does not. Myrvold, on the other hand, offers a specific measure of unification that can be applied to individual hypotheses. He argues that one must account for this measure in order to calculate correctly the degree of confirmation that (...) a hypothesis receives from its evidence. Using the probability calculus, I prove that the two accounts of unification require the same underlying inequality; thus, McGrew and Myrvold have accounted for unification in fundamentally identical probabilistic terms. I then evaluate five putative counterexamples to this account and show that these examples, far from disqualifying it, serve to clarify our notion of unification by disentangling it from a host of other concepts. (shrink)

Recent work on inference to the best explanation has come to an impasse regarding the proper way to coordinate the theoretical virtues in explanatory inference with probabilistic confirmation theory, and in particular with aspects of Bayes's Theorem. I argue that the theoretical virtues are best conceived heuristically and that such a conception gives us the resources to explicate the virtues in terms of ceteris paribus theorems. Contrary to some Bayesians, this is not equivalent to identifying the virtues with likelihoods or (...) priors per se; the virtues may be more accessible epistemically than likelihoods or priors. I then prove a ceteris paribus theorem regarding theoretical consilience, use it to correct a recent application of Reichenbach's common cause principle, and apply it to a test case of scientific reasoning. Explanation and confirmation The heuristic conception of theoretical virtues Abduction and the accessibility of explanatory power Evidential and theoretical consilience A test case: gravitational lensing Conclusion Thus natural science appears completely to lose from sight the large and general questions; but all the more splendid is the success when, groping in the thicket of special questions, we suddenly find a small opening that allows a hitherto undreamt of outlook on the whole. (L. Boltzmann, Theoretical Physics and Philosophical Problems). (shrink)

A Bayesian account of independent evidential support is outlined. This account is partly inspired by the work of C. S. Peirce. I show that a large class of quantitative Bayesian measures of confirmation satisfy some basic desiderata suggested by Peirce for adequate accounts of independent evidence. I argue that, by considering further natural constraints on a probabilistic account of independent evidence, all but a very small class of Bayesian measures of confirmation can be ruled out. In closing, another application of (...) my account to the problem of evidential diversity is also discussed. (shrink)

It is tempting to think that, if a person's beliefs are coherent, they are also likely to be true. This truth conduciveness claim is the cornerstone of the popular coherence theory of knowledge and justification. Erik Olsson's new book is the most extensive and detailed study of coherence and probable truth to date. Setting new standards of precision and clarity, Olsson argues that the value of coherence has been widely overestimated. Provocative and readable, Against Coherence will make stimulating reading for (...) epistemologists and anyone with a serious interest in truth. (shrink)

Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...

Andrew Wayne discusses some recent attempts to account, within a Bayesian framework, for the "common methodological adage" that "diverse evidence better confirms a hypothesis than does the same amount of similar evidence". One of the approaches considered by Wayne is that suggested by Howson and Urbach and dubbed the "correlation approach" by Wayne. This approach is, indeed, incomplete, in that it neglects the role of the hypothesis under consideration in determining what diversity in a body of evidence is relevant diversity. (...) In this paper, it is shown how this gap can be filled, resulting in a more satisfactory account of the evidential role of diversity of evidence. In addition, it is argued that Wayne's criticism of the correlation approach does not indicate a serious flaw in the approach. (shrink)

Recent results in probability theory have cast doubt on coherentism, purportedly showing (a) that coherence among a set of beliefs cannot raise their probability unless individual beliefs have some independent credibility, and (b) that no possible measure of coherence makes coherence generally probability-enhancing. I argue that coherentists can reject assumptions on which these theorems depend, and I derive a general condition under which the concurrence of two information sources lacking individual credibility can raise the probability of what they report.

This vital study offers a new interpretation of Hume's famous "Of Miracles," which notoriously argues against the possibility of miracles. By situating Hume's popular argument in the context of the 18th century debate on miracles, Earman shows Hume's argument to be largely unoriginal and chiefly without merit where it is original. Yet Earman constructively conceives how progress can be made on the issues that Hume's essay so provocatively posed about the ability of eyewitness testimony to establish the credibility of marvelous (...) and miraculous events. (shrink)

In his groundbreaking book, Against Coherence (2005), Erik Olsson presents an ingenious impossibility theorem that appears to show that there is no informative relationship between probabilistic measures of coherence and higher likelihood of truth. Although Olsson's result provides an important insight into probabilistic models of epistemological coherence, the scope of his negative result is more limited than generally appreciated. The key issue is the role conditional independence conditions play within the witness testimony model Olsson uses to establish his result. Olsson (...) maintains that his witness model yields charitable ceteris paribus conditions for any theory of probabilistic coherence. Not so. In fact, Olsson's model, like Bayesian witness models in general, selects a peculiar class of models that are in no way representative of the range of options available to coherence theorists. Recent positive results suggest that there is a way to develop a formal theory of coherence after all. Further, although Bayesian witness models are not conducive to the truth, they are conducive to reliability. (shrink)

A focus on the conjunction of the contents of witness reports and on the coherence of their contents has had negative effects on the epistemic clarity of the Bayesian coherence literature. Whether or not increased coherence of witness reports is correlated with higher confirmation for some H depends upon the hypothesis in question and upon factors concerning the confirmation and independence of the reports, not directly on the positive relevance of the contents to each other. I suggest that Bayesians should (...) shift focus to “coherence for” an hypothesis – that is, to the definition and analysis of cumulative case arguments in which a body of evidence supports some hypothesis that is not restricted to the conjunction of the contents of reports. Such a shift of focus will be valuable for approaching issues such as the problem of the external world which have interested Bayesian coherentists all along. (shrink)

A Bayesian account of the virtue of unification is given. On this account, the ability of a theory to unify disparate phenomena consists in the ability of the theory to render such phenomena informationally relevant to each other. It is shown that such ability contributes to the evidential support of the theory, and hence that preference for theories that unify the phenomena need not, on a Bayesian account, be built into the prior probabilities of theories.

The value of varied evidence, I propose, lies in the fact that more varied evidence is less coherent on the assumption of the negation of the hypothesis under consideration than less varied evidence. I contrast my own analysis with several other Bayesian analyses of the value of evidential diversity and show how my account explains cases where it seems intuitively that evidential variety is valuable for confirmation.