On propensity-frequentist models for stochastic phenomena; with applications to Bell's theorem

The paper develops models of statistical experiments that combine propensities with frequencies, the underlying theory being the branching space-times (BST) of Belnap (1992). The models are then applied to analyze Bell's theorem. We prove the so-called Bell-CH inequality via the assumptions of a BST version of Outcome Independence and of (non-probabilistic) No Conspiracy. Notably, neither the condition of probabilistic No Conspiracy nor the condition of Parameter Independence is needed in the proof. As the Bell-CH inequality is most likely experimentally falsified, the choice is this: contrary to the appearances, experimenters cannot choose some measurement settings, or some transitions, with spacelike related initial events, are correlated; or both

Models of scientific explanation

Ever since Hempel and Oppenheim's development of the Deductive Nomological model of scientific explanation in 1948, a great deal of philosophical energy has been dedicated to constructing a viable model of explanation that concurs both with our intuitions and with the general project of science. Here I critically examine the developments in this field of study over the last half century, and conclude that Humphreys' aleatory model is superior to its competitors. There are, however, some problems with Humphreys' account of the relative quality of an explanation, so in the end I develop and defend a modified version of the aleatory account

Philosophy of Probability and Statistical Modeling

This book has two main aims. The first one (chapters 1-7) is an historically informed review of the philosophy of probability. It describes recent historiography, lays out the distinction between subjective and objective notions, and concludes by applying the historical lessons to the main interpretations of probability. The second aim (chapters 8-13) focuses entirely on objective probability, and advances a number of novel theses regarding its role in scientific practice. A distinction is drawn between traditional attempts to interpret chance, and a novel methodological study of its application. A radical form of pluralism is then introduced, advocating a tripartite distinction between propensities, probabilities and frequencies. Finally, a distinction is drawn between two different applications of chance in statistical modelling which, it is argued, vindicates the overall methodological approach. The ensuing conception of objective probability in practice is the ‘complex nexus of chance’