Diversity Reading List

Abstract: This article surveys several interrelated issues in the metaphysics of chance. First, what is the relationship between the probabilities associated with types of trials (for instance, the chance that a twenty?eight?year old develops diabetes before age thirty) and the probabilities associated with individual token trials (for instance, the chance that I develop diabetes before age thirty)? Second, which features of the the world fix the chances: are there objective chances at all, and if so, are there non?chancy facts on which they supervene? Third, can chance be reconciled with determinism, and if so, how?

Publisher's Note: Not limited to merely mathematics, probability has a rich and controversial philosophical aspect. 'A Philosophical Introduction to Probability' showcases lesser-known philosophical notions of probability and explores the debate over their interpretations. Galavotti traces the history of probability and its mathematical properties and then discusses various philosophical positions on probability, from the Pierre Simon de Laplace's 'classical' interpretation of probability to the logical interpretation proposed by John Maynard Keynes. This book is a valuable resource for students in philosophy and mathematics and all readers interested in notions of probability

Introduction: The decade from the mid-twenties to the mid-thirties was undoubtedly the most crucial for the twentieth Century notion of subjective probability. It was in 1926 that Frank Ramsey wrote his essay 'Truth and probability', presented at the Moral Science Club in Cambridge and published posthumously in 1931. There he put forward for the first time a definition of probability as degree of belief, that had been anticipated only by E. Borel in 1924, in a review of J. M. Keynes' Treatise on Ten years after Ramsey's paper, namely in 1935, Bruno de Finetti gave a series of lectures at the Institut Poincare in Paris, published in 1937 under the title 'La prévision: ses lois logiques, ses sources subjectives'. In this paper subjective probability, defined in a way analogous to that adopted by Ramsey, was implemented with the notion of exchangeability, that de Finetti had already worked out in 1928- 1930. Exchangeability confers applicability to the notion of subjective probability, and fills the gap between frequency and probability as degree of belief. It was only when these two were tied together that subjectivism could become a full-fledged interpretation of probability and gain credibility among probabilists and statisticians. One can then say that with the publication of 'La prévision' the formation process of a subjective notion of probability was completed.

Abstract: There's a long history of discussion of probability in philosophy, but objective chance separated itself off and came into its own as a topic with the advent of a physical theory—quantum mechanics—in which chances play a central, and apparently ineliminable, role. In 1980 David Lewis wrote a paper pointing out that a very broad class of accounts of the nature of chance apparently lead to a contradiction when combined with a principle that expresses the role of chance in guiding belief. There is still no settled agreement on the proper response to the Lewis problem. At the time he wrote the article, Lewis despaired of a solution, but, although he never achieved one that satisfied him completely, by 1994, due to work primarily by Thau and Hall, he had come to think the problem could be disarmed if we fudged a little on the meaning of 'chance'. I'll say more about this below. What I'm going to suggest, however, is that the qualification is unnecessary. The problem depends on an assumption that should be rejected, viz., that using information about chance to guide credence requires one to conditionalize on the theory of chance that one is using. I'm going to propose a general recipe for using information about chance to guide belief that does not require conditionalization on a theory of chance at any stage. Lewis' problem doesn't arise in this setting.