Conditionalization and Jeffrey Conditionalization cannot simultaneously satisfy two widely held desiderata on rules for empirical learning. The first desideratum is confirmational holism, which says that the evidential import of an experience is always sensitive to our background assumptions. The second desideratum is commutativity, which says that the order in which one acquires evidence shouldn't affect what conclusions one draws, provided the same total evidence is gathered in the end. (Jeffrey) Conditionalization cannot satisfy either of these desiderata without violating the other. (...) This is a surprising problem, and I offer a diagnosis of its source. I argue that (Jeffrey) Conditionalization is inherently anti-holistic in a way that is just exacerbated by the requirement of commutativity. The dilemma is thus a superficial manifestation of (Jeffrey) Conditionalization's fundamentally anti-holistic nature. (shrink)

The so-called "non-commutativity" of probability kinematics has caused much unjustified concern. When identical learning is properly represented, namely, by identical Bayes factors rather than identical posterior probabilities, then sequential probability-kinematical revisions behave just as they should. Our analysis is based on a variant of Field's reformulation of probability kinematics, divested of its (inessential) physicalist gloss.

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)

According to Williamson, your evidence consists of all and only what you know (E = K). According to his critics, it doesn’t. While E = K calls for revision, the revisions it calls for are minor. E = K gets this much right. Only true propositions can constitute evidence and anything you know non-inferentially is part of your evidence. In this paper, I defend these two theses about evidence and its possession from Williamson’s critics who think we should break more (...) radically from E = K. (shrink)

We argue that if evidence were knowledge, then there wouldn’t be any Gettier cases, and justification would fail to be closed in egregious ways. But there are Gettier cases, and justification does not fail to be close in egregious ways. Therefore, evidence isn’t knowledge.

"[This book] proposes new foundations for the Bayesian principle of rational action, and goes on to develop a new logic of desirability and probabtility."—Frederic Schick, _Journal of Philosophy_.

Bayesian psychology, in what is perhaps its most familiar version, is incomplete: Jeffrey conditionalization is not a complete account of rational belief change. Jeffrey conditionalization is sensitive to the order in which the evidence arrives. This order effect can be so pronounced as to call for a belief adjustment that cannot be understood as an assimilation of incoming evidence by Jeffrey's rule. Hartry Field's reparameterization of Jeffrey's rule avoids the order effect but fails as an account of how new evidence (...) should be assimilated. (shrink)

Bayesian decision theory can be viewed as the core of psychological theory for idealized agents. To get a complete psychological theory for such agents, you have to supplement it with input and output laws. On a Bayesian theory that employs strict conditionalization, the input laws are easy to give. On a Bayesian theory that employs Jeffrey conditionalization, there appears to be a considerable problem with giving the input laws. However, Jeffrey conditionalization can be reformulated so that the problem disappears, and (...) in fact the reformulated version is more natural and easier to work with on independent grounds. (shrink)

Timothy Williamson's epistemology leads to a fairly radical version of scepticism. According to him, all knowledge is evidence. It follows that if S knows p, the evidential probability for S that p is 1. I explain Williamson's infallibilist account of perceptual knowledge, contrasting it with Peter Klein's, and argue that Klein's account leads to a certain problem which Williamson's can avoid. Williamson can allow that perceptual knowledge is possible and that all knowledge is evidence, while at the same time avoiding (...) Klein's problem. But while Williamson can allow that we know some things through experience, there are very many things he must say we cannot know. Given just how very many these are, he should be considered a sceptic. (shrink)

A wide range of prominent epistemological theories include a principle of conservatism. Such principles take the fact that an agent currently holds a certain belief to constitute at least some measure of epistemic justification for her to maintain that belief. I examine the main arguments that have been made in conservatism's behalf, and find them unsound. Most interestingly, conservatism does not fall out of confirmational holism (the view that the justification of each of our beliefs is in part determined by (...) our other beliefs). I argue that conservatism is a mild form of dogmatism, and should be abandoned. (shrink)

Evidence is often taken to be foundational, in that while other propositions may be inferred from our evidence, evidence propositions are themselves not inferred from anything. I argue that this conception is false, since the non-inferential propositions on which beliefs are ultimately founded may be forgotten or undermined in the course of enquiry.