Contemporary epistemology has been moving away from classical foundationalism—the thesis that our empirical knowledge is grounded in perceptual beliefs we know with certainty. McGrew reexamines classical foundationalism and offers a compelling reconstruction and defense of empirical knowledge grounded in perceptual certainty. He articulates and defends a new version of foundationalism and demonstrates how it meets all the standard criticisms. The book offers substantial rebuttals of the arguments of Kuhn and Rorty and demonstrates the value of the classical analytic approach to (...) philosophy. 'Foundations' will interest philosophers of science, language, and the mind. (shrink)

This chapter discusses the Bayesian analysis of miracles. It is set in the context of the eighteenth-century debate on miracles. The discussion is focused on the probable response of Thomas Bayes to David Hume's celebrated argument against miracles. The chapter presents the claim that the criticisms Richard Price made against Hume's argument against miracles were largely solid.

The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.

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.

Garber (1983) and Jeffrey (1991, 1995) have both proposed solutions to the old evidence problem. Jeffrey's solution, based on a new probability revision method called reparation, has been generalized to the case of uncertain old evidence and probabilistic new explanation in Wagner 1997, 1999. The present paper reformulates some of the latter work, highlighting the central role of Bayes factors and their associated uniformity principle, and extending the analysis to the case in which an hypothesis bears on a countable family (...) of evidentiary propositions. This extension shows that no Garber-type approach is capable of reproducing the results of generalized reparation. (shrink)