A number of Bayesians claim that, if one has no evidence relevant to a proposition P, then one's credence in P should be spread over the interval [0, 1]. Against this, I argue: first, that it is inconsistent with plausible claims about comparative levels of confidence; second, that it precludes inductive learning in certain cases. Two motivations for the view are considered and rejected. A discussion of alternatives leads to the conjecture that there is an in-principle limitation on formal representations (...) of belief: they cannot be both fully accurate and maximally specific. (shrink)

The concept of evidence is central to both epistemology and the philosophy of science. Of course, ‘evidence’ is hardly a philosopher's term of art: it is not only, or even primarily, philosophers who routinely speak of evidence, but also lawyers and judges, historians and scientists, investigative journalists and reporters, as well as the members of numerous other professions and ordinary folk in the course of everyday life. The concept of evidence would thus seem to be on firmer pre-theoretical ground than (...) various other concepts which enjoy similarly central standing within philosophy. (Contrast, for example, the epistemologist's quasi-technical term ‘epistemic justification’.). (shrink)

the symmetry of our evidential situation. If our confidence is best modeled by a standard probability function this means that we are to distribute our subjective probability or credence sharply and evenly over possibilities among which our evidence does not discriminate. Once thought to be the central principle of probabilistic reasoning by great..

Richard Pettigrew offers an extended investigation into a particular way of justifying the rational principles that govern our credences. The main principles that he justifies are the central tenets of Bayesian epistemology, though many other related principles are discussed along the way. Pettigrew looks to decision theory in order to ground his argument. He treats an agent's credences as if they were a choice she makes between different options, gives an account of the purely epistemic utility enjoyed by different sets (...) of credences, and then appeals to the principles of decision theory to show that, when epistemic utility is measured in this way, the credences that violate the principles listed above are ruled out as irrational. The account of epistemic utility set out here is the veritist's: the sole fundamental source of epistemic utility for credences is their accuracy. Thus, Pettigrew conducts an investigation in the version of epistemic utility theory known as accuracy-first epistemology. (shrink)

To the extent that we have reasons to avoid these “bad B -properties”, these arguments provide reasons not to have an incoherent credence function b — and perhaps even reasons to have a coherent one. But, note that these two traditional arguments for probabilism involve what might be called “pragmatic” reasons (not) to be (in)coherent. In the case of the Dutch Book argument, the “bad” property is pragmatically bad (to the extent that one values money). But, it is not clear (...) whether the DBA pinpoints any epistemic defect of incoherent agents. The same can be said for Representation Theorem arguments, since they involve the structure of an agent’s preferences. (shrink)

‘Bayesian epistemology’ became an epistemological movement in the 20th century, though its two main features can be traced back to the eponymous Reverend Thomas Bayes (c. 1701-61). Those two features are: (1) the introduction of a formal apparatus for inductive logic; (2) the introduction of a pragmatic self-defeat test (as illustrated by Dutch Book Arguments) for epistemic rationality as a way of extending the justification of the laws of deductive logic to include a justification for the laws of inductive logic. (...) The formal apparatus itself has two main elements: the use of the laws of probability as coherence constraints on rational degrees of belief (or degrees of confidence) and the introduction of a rule of probabilistic inference, a rule or principle of conditionalization. (shrink)

This chapter explores the topic of imprecise probabilities as it relates to model validation. IP is a family of formal methods that aim to provide a better representationRepresentation of severe uncertainty than is possible with standard probabilistic methods. Among the methods discussed here are using sets of probabilities to represent uncertainty, and using functions that do not satisfy the additvity property. We discuss the basics of IP, some examples of IP in computer simulation contexts, possible interpretations of the IP framework (...) and some conceptual problems for the approach. We conclude with a discussion of IP in the context of model validation. (shrink)

In Chapter 12 of the General Theory, on “The State of Long-Term Expectation,” Keynes writes: “It would be foolish, in forming our expectations, to attach great weight to matters which are very uncertain”. In a footnote to this sentence, Keynes points out that by “very uncertain” he does not mean the same as “very improbable” and refers to the chapter on “The Weight of Arguments” in his earlier Treatise on Probability. The purpose of this article, in the first place, is (...) to provide an account of, and to sort out the relations between, Keynes's views on probability, uncertainty, and the weight of arguments. (shrink)

Since Ramsey, much discussion of the relation between probability and belief has taken for granted that there are degrees of belief, i.e., that there is a real-valued function, B, that characterizes the degree of belief that an agent has in each statement of his language. It is then supposed that B is a probability. It is then often supposed that as the agent accumulates evidence, this function should be updated by conditioning: BE(·) should be B(·E)/B(E). Probability is also important in (...) classical statistics, where it is generally supposed that probabilities are frequencies, and that inference proceeds by controlling error and not by conditioning. I will focus on the tension between these two approaches to probability, and in the main part of the paper show where and when Bayesian conditioning conflicts with error based statistics and how to resolve these conflicts. (shrink)

The dominant argument for the introduction of propensities or chances as an interpretation of probability depends on the difficulty of accounting for single case probabilities. We argue that in almost all cases, the``single case'' application of probability can be accounted for otherwise. ``Propensities'' are needed only intheoretical contexts, and even there applications of probability need only depend on propensities indirectly.

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