Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, (...) the Theorem's central insight — that a hypothesis is confirmed by any body of data that its truth renders probable — is the cornerstone of all subjectivist methodology. (shrink)

According to Hempel's paradox, evidence (E) that an object is a nonblack nonraven confirms the hypothesis (H) that every raven is black. According to the standard Bayesian solution, E does confirm H but only to a minute degree. This solution relies on the almost never explicitly defended assumption that the probability of H should not be affected by evidence that an object is nonblack. I argue that this assumption is implausible, and I propose a way out for Bayesians. Introduction Hempel's (...) paradox, the standard Bayesian solution, and the disputed assumption Attempts to defend the disputed assumption Attempts to refute the disputed assumption A way out for Bayesians Conclusion. (shrink)

The idea that simplicity matters in science is as old as science itself, with the much cited example of Ockham's Razor, 'entia non sunt multiplicanda praeter necessitatem': entities are not to be multiplied beyond necessity. A problem with Ockham's razor is that nearly everybody seems to accept it, but few are able to define its exact meaning and to make it operational in a non-arbitrary way. Using a multidisciplinary perspective including philosophers, mathematicians, econometricians and economists, this 2002 monograph examines simplicity (...) by asking six questions: what is meant by simplicity? How is simplicity measured? Is there an optimum trade-off between simplicity and goodness-of-fit? What is the relation between simplicity and empirical modelling? What is the relation between simplicity and prediction? What is the connection between simplicity and convenience? The book concludes with reflections on simplicity by Nobel Laureates in Economics. (shrink)

The central problem with Bayesian philosophy of science is that it cannot take account of the relevance of simplicity and unification to confirmation, induction, and scientific inference. The standard Bayesian folklore about factoring simplicity into the priors, and convergence theorems as a way of grounding their objectivity are some of the myths that Earman's book does not address adequately. 1Review of John Earman: Bayes or Bust?, Cambridge, MA. MIT Press, 1992, £33.75cloth.

The philosophical significance of the procedure of applying Akaike Information Criterion (AIC) to curve-fitting problems is evaluated. The theoretical justification for using AIC (the so-called Akaike's theorem) is presented in a rigorous way, and its range of validity is assessed by presenting both instances in which it is valid and counter-examples in which it is invalid. The philosophical relevance of the justification that this result gives for making one particular choice between simple and complicated hypotheses is emphasized. In addition, recent (...) claims that the methods based on Akaike's theorem are relevant to other philosophical problems associated with the notion of simplicity are presented and evaluated. (shrink)