This is a high quality, concise collection of articles on the foundations of probability and statistics. Its editor, Richard Swinburne, has collected five papers by contemporary leaders in the field, written a pretty thorough and even-handed introductory essay, and placed a very clean and accessible version of Reverend Thomas Bayes’s famous essay (“An Essay Towards the Solving a Problem in the Doctrine of Chances”) at the end, as an Appendix (with a brief historical introduction by the noted statistician G.A. Barnard). (...) I will briefly discuss each of the five papers in the volume, with an emphasis on certain issues arising from the use of probability as a tool for thinking about evidence. (shrink)

It it tempting to think that if an outcome had some probability of not occurring, then we cannot explain why that outcome in fact occurred. Despite this intuition, most philosophers of science have come to admit the possibility of indeterministic explanation. Yet some of them continue to hold that if an outcome was not determined, it cannot be explained why that outcome rather than some other occurred. I argue that this is an untenable compromise: if indeterministic explanation is possible, then (...) indeterministic contrastive explanation is possible too. In order to defend this conclusion, I develop an account of contrastive explanation. (shrink)

Following Dretske (1977), there has been a considerable body of literature on the role of contrastive stress in causal claims. Following van Fraassen (1980), there has been a considerable body of literature on the role of contrastive stress in explanations and explanation-requesting why-questions. Amazingly, the two bodies of literature have remained almost entirely disjoint. With an understanding of the contrastive nature of ordinary causal claims, and of the linguistic roles of contrastive stress, it is possible to provide a unified account (...) of both phenomena. I provide such an account from within the framework of a probabilistic theory of causation. Relations of screening-off, long familiar to researchers in probabilistic causality, play a central role in this account. (shrink)

(new version: 10/30/07). Click here to download the companion Mathematica 6 notebook that goes along with this paper.

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)

One of Ian Hacking's earliest publications, this book showcases his early ideas on the central concepts and questions surrounding statistical reasoning. He explores the basic principles of statistical reasoning and tests them, both at a philosophical level and in terms of their practical consequences for statisticians. Presented in a fresh twenty-first-century series livery, and including a specially commissioned preface written by Jan-Willem Romeijn, illuminating its enduring importance and relevance to philosophical enquiry, Hacking's influential and original work has been revived for (...) a new generation of readers. (shrink)

This is a major contribution to the theory of rational choice which will be of particular interest to philosophers and economists. The author sets out the foundations of rational choice, and then sketches a dynamic choice framework in which principles of ordering and independence follow from a number of apparently plausible conditions. However, there is potential conflict among these conditions, and when they are weakened to avoid it the usual foundations of rational choice no longer prevail. The thrust of the (...) argument is to suggest that the theory of rational choice is less deterministic than many suppose. (shrink)

The traditional Bayesian qualitative account of evidential support (TB) takes assertions of the form 'E evidentially supports H' to affirm the existence of a two-place relation of evidential support between E and H. The analysans given for this relation is $C(H,E) =_{def} Pr(H\arrowvertE) \models Pr(H)$ . Now it is well known that when a hypothesis H entails evidence E, not only is it the case that C(H,E), but it is also the case that C(H&X,E) for any arbitrary X. There is (...) a widespread feeling that this is a problematic result for TB. Indeed, there are a number of cases in which many feel it is false to assert 'E evidentially supports H&X', despite H entailing E. This is known, by those who share that feeling, as the 'tacking problem' for Bayesian confirmation theory. After outlining a generalization of the problem, I argue that the Bayesian response has so far been unsatisfactory. I then argue the following: (i) There exists, either instead of, or in addition to, a two-place relation of confirmation, a three-place, 'contrastive' relation of confirmation, holding between an item of evidence E and two competing hypotheses H₁ and H₂. (ii) The correct analysans of the relation is a particular probabilistic inequality, abbreviated C(H₁, H₂, E). (iii) Those who take the putative counterexamples to TB discussed to indeed be counterexamples are interpreting the relevant utterances as implicitly contrastive, contrasting the relevant hypothesis H₁ with a particular competitor H₂. (iv) The probabilistic structure of these cases is such that ∼C(H₁, H₂, E). This solves my generalization of the tacking problem. I then conclude with some thoughts about the relationship between the traditional Bayesian account of evidential support and my proposed account of the three-place relation of confirmation. (shrink)

Classic studies of explanation, such as those of Hempel and Bromberger, took it for granted that an explanation-seeking question of the form "Why P?" should be understood as asking about the proposition P. This view has been recently challenged by Bas van Fraassen and Alan Garfinkel. They acknowledge that some questions have the surface form "Why P?", but they hold that a correct reading for why-questions should take the form "Why P (rather than Q)?", where Q is a contrasting alternative. (...) This contrast theory is discussed here. It is argued that, properly understood, the contrast theory and the propositional approach can and should give equivalent readings to why-questions. (shrink)

According to Bayesian confirmation theory, evidence E (incrementally) confirms (or supports) a hypothesis H (roughly) just in case E and H are positively probabilistically correlated (under an appropriate probability function Pr). There are many logically equivalent ways of saying that E and H are correlated under Pr. Surprisingly, this leads to a plethora of non-equivalent quantitative measures of the degree to which E confirms H (under Pr). In fact, many non-equivalent Bayesian measures of the degree to which E confirms (or (...) supports) H have been proposed and defended in the literature on inductive logic. I provide a thorough historical survey of the various proposals, and a detailed discussion of the philosophical ramifications of the differences between them. I argue that the set of candidate measures can be narrowed drastically by just a few intuitive and simple desiderata. In the end, I provide some novel and compelling reasons to think that the correct measure of degree of evidential support (within a Bayesian framework) is the (log) likelihood ratio. The central analyses of this research have had some useful and interesting byproducts, including: (i ) a new Bayesian account of (confirmationally) independent evidence, which has applications to several important problems in con- firmation theory, including the problem of the (confirmational) value of evidential diversity, and (ii ) novel resolutions of several problems in Bayesian confirmation theory, motivated by the use of the (log) likelihood ratio measure, including a reply to the Popper-Miller critique of probabilistic induction, and a new analysis and resolution of the problem of irrelevant conjunction (a.k.a., the tacking problem). (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)

‘There are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns—the ones we don’t know we don’t know.’ —Donald Rumsfeld, 2003, President George W. Bush’s Secretary of Defense, on the subject of the U.S. government’s failure to discover weapons of mass destruction in Iraq.

Are explanations contrastive? I argue that any contrastive argument and can be reduced to a non-contrastive one, and hence a theory of explanation need not treat them as an additional kind of explanation.