Lydia McGrew

I propose a measure of dependence that relates a set of items of evidence to an hypothesis H and to H's negation. I dub this measure relative consilience and propose a method for using it as a correction factor for dependence among items of evidence. Using RC, I examine collusion and testimonial independence, the value of diverse evidence, and the strengthening of otherwise weak or non-existent cases. RC provides a valuable tool for formal epistemologists interested in analyzing cumulative case arguments.

In the debate over testimony to miracles, a common Humean move is to emphasize the prior improbability of miracles as the most important epistemic factor. Robert Fogelin uses the example of Henry, who tells multiple tall tales about meeting celebrities, to argue that low prior probabilities alone can render testimony unbelievable, with obvious implications for testimony to miracles. A detailed Bayesian analysis of Henry’s stories shows instead that the fact that Henry tells multiple stories about events that occurred independently if they occurred at all is crucial to his loss of credibility. The epistemic structure is similar to that of a case of multiple lottery wins by the same person. Each of Henry’s stories can confirm only one event, but all the stories confirm the hypothesis that Henry is a liar. This structure does not apply to testimony to just one event, however antecedently improbable. Such examples therefore do nothing to undermine a standard Bayesian analysis involving both priors and likelihoods in evaluating testimony to an improbable event.

Jonathan Weisberg has argued that Jeffrey Conditioning is inherently “anti-holistic” By this he means, inter alia, that JC does not allow us to take proper account of after-the-fact defeaters for our beliefs. His central example concerns the discovery that the lighting in a room is red-tinted and the relationship of that discovery to the belief that a jelly bean in the room is red. Weisberg’s argument that the rigidity required for JC blocks the defeating role of the red-tinted light rests on the strong assumption that all posteriors within the distribution in this example are rigid on a partition over the proposition that the jelly bean is actually red. But individual JC updates of propositions do not require such a broad rigidity assumption. Jeffrey conditionalizers should consider the advantages of a modest project of targeted updating focused on particular propositions rather than seeking to update the entire distribution using one obvious partition. Although Weisberg’s example fails to show JC to be irrelevant or useless, other problems he raises for JC (the commutativity and inputs problems) remain and actually become more pressing when we recognize the important role of background information.

Richard Jeffrey developed the formula for probability kinematics with the intent that it would show that strong foundations are epistemologically unnecessary. But the reasons that support strong foundationalism are considerations of dynamics rather than kinematics. The strong foundationalist is concerned with the origin of epistemic force; showing how epistemic force is propagated therefore cannot undermine his position. The weakness of personalism is evident in the difficulty the personalist has in giving a principled answer to the question of when the conditions for the application of the kinematic formula—the rigidity of the posteriors—are fulfilled, a problem made intractable by the personalist commitment to treating changes in intermediate probability as unexplained surds. Because the strong foundationalist admits changes in the intermediate probability of propositions only when there is some change in the foundations, he can avail himself of ananswer to the problem of the rigidity of the posteriors which the personalist cannot regard as complete. While probability kinematics does not make certain foundations unnecessary, the possession of certain foundations also does not make the probability kinematics formula superfluous. The formula allowsus to model the indirect routes by which the foundations influence various non-foundational propositions in the probability distribution.

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.

Both advocates and opponents of the fine-tuning argument treat multiple universes with a selection effect as a legitimate hypothesis to explain the life-permitting values of the constants in our universe. I argue that, except where there is specific relevant prior information, the occurrence of multiple instances of a low-likelihood causal process should not be treated as an alternative hypothesis to a higher-likelihood causal process. Since an ’ad hoc’ hypothesis can be invented to give high likelihood to any evidence, we must provide some epistemic rationale other than similar likelihood for comparing two hypotheses

Two different types of objections to the historical investigation of miracles imply that such investigation is inappropriate or can never lead to rational belief that a historical miracle has occurred. The first objection concerns the alleged chasm between the rational realm of history and the realm of faith. The second objection alleges that God is, or would be if he existed, too much unlike ourselves for us reasonably to use Divine action as an explanatory hypothesis. Both objections involve a tacit question-begging move against the traditional theistic hypothesis that a God exists who is capable of revealing himself to man by public signs. The theist should be free to test the hypothesis of a God who speaks rather than a God who is necessarily separated from his creatures.