Can the axioms of probability theory and the classical patterns of statistical inference ever be falsified by observation? Various possible answers to this question are examined in a set theoretical context and in relation to the findings of microphysics.

A comparison of Neyman's theory of interval estimation with the corresponding subjective Bayesian theory of credible intervals shows that the Bayesian approach to the estimation of statistical parameters allows experimental procedures which, from the orthodox objective viewpoint, are clearly biased and clearly inadmissible. This demonstrated methodological difference focuses attention on the key difference in the two general theories, namely, that the orthodox theory is supposed to provide a known average frequency of successful estimates, whereas the Bayesian account provides only a (...) coherent ordering of degrees of belief and a subsequent maximization of subjective expected utilities. To rebut the charge of allowing biased procedures, the Bayesian must attack the foundations of orthodox, objectivist methods. Two apparently popular avenues of attack are briefly considered and found wanting. The first is that orthodox methods fail to apply to the single case. The second is that orthodox methods are subject to a typical Humean regress. The conclusion is that orthodox objectivist methods remain viable in the face of the subjective Bayesian alternative — at least with respect to the problem of statistical estimation. (shrink)

An approach to inference to the best explanation integrating a Popperianconception of natural laws together with a modified Hempelian account of explanation, one the one hand, and Hacking's law of likelihood (in its nomicguise), on the other, which provides a robust abductivist model of sciencethat appears to overcome the obstacles that confront its inductivist,deductivist, and hypothetico-deductivist alternatives.This philosophy of scienceclarifies and illuminates some fundamental aspects of ontology and epistemology, especially concerning the relations between frequencies and propensities. Among the most important (...) elements of this conception is thecentral role of degrees of nomic expectability in explanation, prediction,and inference, for which this investigation provides a theoretical defense. (shrink)

I argue that to the extent to which philosophical theories of objective probability have offered theoretically adequateconceptions of objective probability (in connection with such desiderata as causal and explanatory significance, applicability to single cases, etc.), they have failed to satisfy amethodological standard — roughly, a requirement to the effect that the conception offered be specified with the precision appropriate for a physical interpretation of an abstract formal calculus and be fully explicated in terms of concepts, objects or phenomena understood independently (...) of the idea of physical probability. The significance of this, and of the suggested methodological standard, is then briefly discussed. (shrink)