Jeffrey has devised a probability revision method that increases the probability of hypothesis H when it is discovered that H implies previously known evidence E. A natural extension of Jeffrey's method likewise increases the probability of H when E has been established with sufficiently high probability and it is then discovered, quite apart from this, that H confers sufficiently higher probability on E than does its logical negation H̄.

Additional results are reported on the author's earlier generalization of Richard Jeffrey's solution to the problem of old evidence and new explanation.

Suppose that several individuals who have separately assessed prior probability distributions over a set of possible states of the world wish to pool their individual distributions into a single group distribution, while taking into account jointly perceived new evidence. They have the option of first updating their individual priors and then pooling the resulting posteriors or first pooling their priors and then updating the resulting group prior. If the pooling method that they employ is such that they arrive at the (...) same final distribution in both cases, the method is said to be externally Bayesian, a property first studied by Madansky . We show that a pooling method for discrete distributions is externally Bayesian if and only if it commutes with Jeffrey conditioning, parameterized in terms of certain ratios of new to old odds, as in Wagner , rather than in terms of the posterior probabilities of members of the disjoint family of events on which such conditioning originates. (shrink)

Jonathan Weisberg claims that certain probability assessments constructed by Jeffrey conditioning resist subsequent revision by a certain type of after-the-fact defeater of the reasons supporting those assessments, and that such conditioning is thus “inherently anti-holistic.” His analysis founders, however, in applying Jeffrey conditioning to a partition for which an essential rigidity condition clearly fails. Applied to an appropriate partition, Jeffrey conditioning is amenable to revision by the sort of after-the-fact defeaters considered by Weisberg in precisely the way that he demands.

A simple rule of probability revision ensures that the final result ofa sequence of probability revisions is undisturbed by an alterationin the temporal order of the learning prompting those revisions.This Uniformity Rule dictates that identical learning be reflectedin identical ratios of certain new-to-old odds, and is grounded in the oldBayesian idea that such ratios represent what is learned from new experiencealone, with prior probabilities factored out. The main theorem of this paperincludes as special cases (i) Field's theorem on commuting probability-kinematical (...) revisions and (ii) the equivalence of two strategiesfor generalizing Jeffrey's solution to the old evidence problem tothe case of uncertain old evidence and probabilistic new explanation. (shrink)

The fundamental constants that are involved in the laws of physics which describe our universe are finely-tuned for life, in the sense that if some of the constants had slightly different values life could not exist. Some people hold that this provides evidence for the existence of God. I will present a probabilistic version of this fine-tuning argument which is stronger than all other versions in the literature. Nevertheless, I will show that one can have reasonable opinions such that the (...) fine-tuning argument doesn’t lead to an increase in one’s probability for the existence of God. (shrink)

I maintain, in defending “thirdism,” that Sleeping Beauty should do Bayesian updating after assigning the “preliminary probability” 1/4 to the statement S: “Today is Tuesday and the coin flip is heads.” (This preliminary probability obtains relative to a specific proper subset I of her available information.) Pust objects that her preliminary probability for S is really zero, because she could not be in an epistemic situation in which S is true. I reply that the impossibility of being in such an (...) epistemic situation is irrelevant, because relative to I, statement S nonetheless has degree of evidential support 1/4. (shrink)

In the 1970’s, a controversy arose about a probability problem posed by Irving Copi. One side argued that a common spontaneous intuition about the problem is correct; the other side argued that this intuition is mistaken. Here, I argue (1) that the naïve intuition yields the correct answer, but accidentally and for a wrong reason; (2) that a more reflective intuition yields a wrong answer, and hence, is also mistaken; and (3) that an even more reflective intuition yields the correct (...) answer for a correct reason. This warrants what I call optimistic fallibilism concerning intuitions about probability: although intuition is certainly prone to error in this domain, intuition has the capacity for self-correction. A naïve intuition that is mistaken can be replaced by a distinct, reflective intuition; and a reflective intuition that is mistaken can be replaced by another reflective intuition – with the process ultimately yielding a sound intuition. (shrink)

We present a new argument for the claim that in the Sleeping Beauty problem, the probability that the coin comes up heads is 1/3. Our argument depends on a principle for the updating of probabilities that we call ‘generalized conditionalization’, and on a species of generalized conditionalization we call ‘synchronic conditionalization on old information’. We set forth a rationale for the legitimacy of generalized conditionalization, and we explain why our new argument for thirdism is immune to two attacks that Pust (...) (Synthese 160:97–101, 2008) has leveled at other arguments for thirdism. (shrink)

Garber (1983) and Jeffrey (1991, 1995) have both proposed solutions to the old evidence problem. Jeffrey's solution, based on a new probability revision method called reparation, has been generalized to the case of uncertain old evidence and probabilistic new explanation in Wagner 1997, 1999. The present paper reformulates some of the latter work, highlighting the central role of Bayes factors and their associated uniformity principle, and extending the analysis to the case in which an hypothesis bears on a countable family (...) of evidentiary propositions. This extension shows that no Garber-type approach is capable of reproducing the results of generalized reparation. (shrink)

It seems improbable that life would exist in a naturalistic universe. But if the universe were spatially infinite, then seemingly improbable events would be expected to happen; life would be expected to exist. It follows that the existence of life provides evidence that the universe is spatially infinite.