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.

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)

Epistemologists routinely distinguish between two kinds of justification or rationality – the propositional and the doxastic kind – in order to characterize importantly different ways in which an attitude can be justified or rational for a person. I argue that these notions, as they are commonly understood, are well suited to capture rationality judgments about the attitudes that agents reach as conclusions of their reasoning. Yet, these notions are ill-suited to capture rationality judgments about attitudes that agents form while their (...) reasoning is still in progress. In fact, we currently lack any suitable theory of rationality that lets us capture the ways in which we evaluate the rationality of such transitional attitudes, even though they are ubiquitous. I propose to capture these rationality judgments by introducing a new notion of rationality that is orthogonal to the propositional/doxastic distinction, which I call pro tem rationality. This new notion can be integrated with both traditional and formal ways of characterizing rationality or justification. It can be used to enlighten debates about logical and empirical learning, higher-order evidence, and the epistemology of philosophy, among others. (shrink)

This chapter contains sections titled: Highlights of Past Literature Current Work Future Work.

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. (shrink)

Science depends on judgments of the bearing of evidence on theory. Scientists must judge whether an observation or the result of an experiment supports, disconfirms, or is simply irrelevant to a given hypothesis. Similarly, scientists may judge that, given all the available evidence, a hypothesis ought to be accepted as correct or nearly so, rejected as false, or neither. Occasionally, these evidential judgments can be made on deductive grounds. If an experimental result strictly contradicts a hypothesis, then the truth of (...) the data deductively entails the falsity of the hypothesis. In the great majority of cases, however, the connection between evidence and hypothesis is non-demonstrative, or inductive. In particular, this is so whenever a general hypothesis is inferred to be correct on the basis of the available data, since the truth of the data will not deductively entail the truth of the hypothesis. It always remains possible that the hypothesis is false even though the data are correct. (shrink)

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

Jessica Brown argues against infallibilist views of knowledge as follows. (1) Infallibilism is committed to the sufficiency of knowledge for self-support: if one knows that p, then p is part of one's evidence for p. (2) This commitment is false: often one knows that p, but p isn't part of one's evidence for p. So (3) infallibilism about knowledge is false. I’ll respond by questioning the motivation for (2). Brown’s main line of argument in defense of (2) concerns the awkwardness (...) of citing a proposition as evidence in support of itself. I’ll argue that this infelicity, while genuine, stem not from any particular view about knowledge, but from a probabilistic conception of evidential support. Given such a conception of evidential support, whenever E is part of someone’s evidence, E is evidence for E. This is no less awkward for the fallibilist than the infallibilist. I’ll argue that if we adopt a contextualist view of evidence, we can hold on to the independently attractive probabilistic conception of evidential support, while respecting the idea that there's something wrong with citing a proposition as evidence for itself. -/- . (shrink)

Awareness growth—coming to entertain propositions of which one was previously unaware—is a crucial aspect of epistemic thriving. And yet, it is widely believed that orthodox Bayesianism cannot accommodate this phenomenon, since that would require employing supposedly defective catch-all propositions. Orthodox Bayesianism, it is concluded, must be amended. In this paper, I show that this argument fails, and that, on the contrary, the orthodox version of Bayesianism is particularly well-suited to accommodate awareness growth. For it entails what I call the refinement (...) view, which allows us to capture that awareness growth consists in the increase of one’s capacity of discernment. (shrink)