Probabilistic models have much to offer to philosophy. We continually receive information from a variety of sources: from our senses, from witnesses, from scientific instruments. When considering whether we should believe this information, we assess whether the sources are independent, how reliable they are, and how plausible and coherent the information is. Bovens and Hartmann provide a systematic Bayesian account of these features of reasoning. Simple Bayesian Networks allow us to model alternative assumptions about the nature of the information sources. (...) Measurement of the coherence of information is a controversial matter: arguably, the more coherent a set of information is, the more confident we may be that its content is true, other things being equal. The authors offer a new treatment of coherence which respects this claim and shows its relevance to scientific theory choice. Bovens and Hartmann apply this methodology to a wide range of much discussed issues regarding evidence, testimony, scientific theories, and voting. Bayesian Epistemology is an essential tool for anyone working on probabilistic methods in philosophy, and has broad implications for many other disciplines. (shrink)

From Descartes to Popper, philosophers have criticized and tried to improve the strategies of reasoning invoked in science and in everyday life. In recent years leading cognitive psychologists have painted a detailed, controversial, and highly critical portrait of common sense reasoning. Stephen Stich begins with a spirited defense of this work and a critique of those writers who argue that widespread irrationality is a biological or conceptual impossibility.Stich then explores the nature of rationality and irrationality: What is it that distinguishes (...) good reasoning from bad? He rejects the most widely accepted approaches to this question approaches which unpack rationality by appeal to truth, to reflective equilibrium or conceptual analysis. The alternative he defends grows out of the pragmatic tradition in which reasoning is viewed as a cognitive tool. Stich's version of pragmatism leads to a radical epistemic relativism and he argues that the widespread abhorrence of relativism is ill founded. (shrink)

It is easy to construct pairs of sentences X, Y that lead many people to ascribe higher probability to the conjunction X-and-Y than to the conjuncts X, Y. Whether an error is thereby committed depends on reasoners’ interpretation of the expressions “probability” and “and.” We report two experiments designed to clarify the normative status of typical responses to conjunction problems. © 2004 Cognitive Science Society, Inc. All rights reserved.

Because the conjunction pandq implies p, the value of a bet on pandq cannot exceed the value of a bet on p at the same stakes. We tested recognition of this principle in a betting paradigm that (a) discouraged misreading p as pandnotq, and (b) encouraged genuinely conjunctive reading of pandq. Frequent violations were nonetheless observed. The findings appear to discredit the idea that most people spontaneously integrate the logic of conjunction into their assessments of chance.

This article described three heuristics that are employed in making judgements under uncertainty: representativeness, which is usually employed when people are asked to judge the probability that an object or event A belongs to class or process B; availability of instances or scenarios, which is often employed when people are asked to assess the frequency of a class or the plausibility of a particular development; and adjustment from an anchor, which is usually employed in numerical prediction when a relevant value (...) is available. These heuristics are highly economical and usually effective, but they lead to systematic and predictable errors. A better understanding of these heuristics and of the biases to which they lead could improve judgements and decisions in situations of uncertainty. (shrink)

It is easy to construct pairs of sentences X, Y that lead many people to ascribe higher probability to the conjunction X‐and‐Y than to the conjuncts X, Y. Whether an error is thereby committed depends on reasoners' interpretation of the expressions “probability” and “and.” We report two experiments designed to clarify the normative status of typical responses to conjunction problems.

Plausibly, when we adopt a probabilistic standpoint any measure Cb of the degree to which evidence e confirms hypothesis h relative to background knowledge b should meet these five desiderata: Cb > 0 when P > P < 0 when P < P; Cb = 0 when P = P. Cb is some function of the values P and P assume on the at most sixteen truth-functional combinations of e and h. If P < P and P = P then (...) Cb ≤ Cb; if P = P and P < P then Cb ≥ Cb. Cb – Cb is fully determined by Cb and Cbe – Cbe; if Cb = 0 then Cb + Cbe = 0. If P = P then Cb = Cb. (shrink)

A familiar adage in the philosophy of science is that general hypotheses are better supported by varied evidence than by uniform evidence. Several studies suggest that young children do not respect this principle, and thus suffer from a defect in their inductive methodology. We argue that the diversity principle does not have the normative status that psychologists attribute to it, and should be replaced by a simple rule of probability. We then report experiments designed to detect conformity to the latter (...) rule in children's inductive judgment. The results suggest that young children in both the United States and Taiwan are sensitive to the constraints imposed by the rule on judgments of probability and evidential strength. We conclude with a suggested reinterpretation of the thesis that children's inductive methodology qualifies them as “little scientists.”. (shrink)

This book defends the view that any adequate account of rational decision making must take a decision maker's beliefs about causal relations into account. The early chapters of the book introduce the non-specialist to the rudiments of expected utility theory. The major technical advance offered by the book is a 'representation theorem' that shows that both causal decision theory and its main rival, Richard Jeffrey's logic of decision, are both instances of a more general conditional decision theory. The book solves (...) a long-standing problem for Jeffrey's theory by showing for the first time how to obtain a unique utility and probability representation for preferences and judgements of comparative likelihood. The book also contains a major new discussion of what it means to suppose that some event occurs or that some proposition is true. The most complete and robust defence of causal decision theory available. (shrink)

Contemporary Bayesian confirmation theorists measure degree of (incremental) confirmation using a variety of non-equivalent relevance measures. As a result, a great many of the arguments surrounding quantitative Bayesian confirmation theory are implicitly sensitive to choice of measure of confirmation. Such arguments are enthymematic, since they tacitly presuppose that certain relevance measures should be used (for various purposes) rather than other relevance measures that have been proposed and defended in the philosophical literature. I present a survey of this pervasive class of (...) Bayesian confirmation-theoretic enthymemes, and a brief analysis of some recent attempts to resolve the problem of measure sensitivity. (shrink)

Likelihoodists and Bayesians seem to have a fundamental disagreement about the proper probabilistic explication of relational (or contrastive) conceptions of evidential support (or confirmation). In this paper, I will survey some recent arguments and results in this area, with an eye toward pinpointing the nexus of the dispute. This will lead, first, to an important shift in the way the debate has been couched, and, second, to an alternative explication of relational support, which is in some sense a "middle way" (...) between Likelihoodism and Bayesianism. In the process, I will propose some new work for an old probability puzzle: the "Monty Hall" problem. (shrink)

outlined. This account is partly inspired by the work of C.S. Peirce. When we want to consider how degree of confirmation varies with changing I show that a large class of quantitative Bayesian measures of con-.

A Bayesian account of independent evidential support is outlined. This account is partly inspired by the work of C. S. Peirce. I show that a large class of quantitative Bayesian measures of confirmation satisfy some basic desiderata suggested by Peirce for adequate accounts of independent evidence. I argue that, by considering further natural constraints on a probabilistic account of independent evidence, all but a very small class of Bayesian measures of confirmation can be ruled out. In closing, another application of (...) my account to the problem of evidential diversity is also discussed. (shrink)

Several forms of symmetry in degrees of evidential support areconsidered. Some of these symmetries are shown not to hold in general. This has implications for the adequacy of many measures of degree ofevidential support that have been proposed and defended in the philosophical literature.

First published in 1982, Ellery Eells' original work on rational decision making had extensive implications for probability theorists, economists, statisticians and psychologists concerned with decision making and the employment of Bayesian principles. His analysis of the philosophical and psychological significance of Bayesian decision theories, causal decision theories and Newcomb's paradox continues to be influential in philosophy of science. His book is now revived for a new generation of readers and presented in a fresh twenty-first-century series livery, including a specially commissioned (...) preface written by Brian Skyrms, illuminating its continuing importance and relevance to philosophical enquiry. (shrink)

Epistemologists and philosophers of science have often attempted to express formally the impact of a piece of evidence on the credibility of a hypothesis. In this paper we will focus on the Bayesian approach to evidential support. We will propose a new formal treatment of the notion of degree of confirmation and we will argue that it overcomes some limitations of the currently available approaches on two grounds: (i) a theoretical analysis of the confirmation relation seen as an extension of (...) logical deduction and (ii) an empirical comparison of competing measures in an experimental inquiry concerning inductive reasoning in a probabilistic setting. (shrink)

... Press for their editorial perspicacity, to the National Institutes of Health for the partial financial support they gave me while I was writing some of the chapters, and to Donald Michie for suggesting the title Good Thinking.

The old evidence problem affects any probabilistic confirmation measure based on comparing pr(H/E) and pr(H). The article argues for the following points: (1) measures based on likelihood ratios also suffer old evidence difficulties; (2) the less-discussed synchronic old evidence problem is, in an important sense, the most acute; (3) prominent attempts to solve or dissolve the synchronic problem fail; (4) a little-discussed variant of the standard measure avoids the problem, in an appealing way; and (5) this measure nevertheless reveals a (...) different problem for probabilistic confirmation measures, a problem that is unlikely to lend itself to formal solution. (shrink)

Bayesian epistemology addresses epistemological problems with the help of the mathematical theory of probability. It turns out that the probability calculus is especially suited to represent degrees of belief (credences) and to deal with questions of belief change, confirmation, evidence, justification, and coherence. Compared to the informal discussions in traditional epistemology, Bayesian epis- temology allows for a more precise and fine-grained analysis which takes the gradual aspects of these central epistemological notions into account. Bayesian epistemology therefore complements traditional epistemology; it (...) does not re- place it or aim at replacing it. (shrink)

The first section introduces a distinction between 2 families of cognitive operations, called System 1 and System 2. The second section presents an attribute-substitution model of heuristic judgment, which elaborates and extends earlier treatments of the topic. The third section introduces a research design for studying attribute substitution. The fourth section discusses the controversy over the representativeness heuristic. The last section situates representativeness within a broad family of prototype heuristics, in which properties of a prototypical exemplar dominate global judgments concerning (...) an entire set. (shrink)

Book Review of Luc Bovens and Stephan Hartmann *Bayesian Epistemology* by Erik J. Olsson.