Philosophical Foundations Of Probability Theory

First published in 1982, Philosophical Foundations of Probability Theory starts with the uses we make of the concept in everyday life and then examines the rival theories that seek to account for these applications. It offers a critical exposition of the major philosophical theories of probability, with special attention given to the metaphysical and epistemological assumptions and implications of each. The Classical Theory suggests probability is simply the ratio of favorable cases to all equi-possible cases: it is this theory that is relied on by gamblers and by most non-specialists. The A Priori Theory, on the other hand, describes probability as a logical relation between statements based on evidence. The Relative Frequency theories locate it not in logic but among empirical rates of occurrence in the real world, while the Subjectivist Theory identifies probability with the degree of a person’s belief in a proposition. Each of these types of theory is examined in turn, and the treatment is unified by the use of running examples and parallel analyses of each theory. The final chapter includes a summary and the author’s conclusions. This book is an essential read for scholars and researchers of Philosophy.

The Twentieth Century has seen a dramatic rise in the use of probability and statistics in almost all fields of research. This has stimulated many new philosophical ideas on probability. Philosophical Theories of Probability is the first book to present a clear, comprehensive and systematic account of these various theories and to explain how they relate to one another. Gillies also offers a distinctive version of the propensity theory of probability, and the intersubjective interpretation, which develops the subjective theory.

Proceedings of an International Research Colloquium held at the University of Western Ontario, 10-13 May 1973.

A collection of papers presented at the conference on Probability Theory - Philosophy, Recent History and Relations to Science, University of Roskilde, Denmark, September 16-18, 1998. Since the measure theoretical definition of probability was proposed by Kolmogorov, probability theory has developed into a mature mathematical theory. It is today a fruitful field of mathematics that has important applications in philosophy, science, engineering, and many other areas. The measure theoretical definition of probability and its axioms, however, are not without their problems; some of them even puzzled Kolmogorov. This book sheds light on some recent discussions of the problems in probability theory and their history, analysing their philosophical and mathematical significance, and the role pf mathematical probability theory in other sciences.

This reissue of D. A. Gillies highly influential work, first published in 1973, is a philosophical theory of probability which seeks to develop von Mises’ views on the subject. In agreement with von Mises, the author regards probability theory as a mathematical science like mechanics or electrodynamics, and probability as an objective, measurable concept like force, mass or charge. On the other hand, Dr Gillies rejects von Mises’ definition of probability in terms of limiting frequency and claims that probability should be taken as a primitive or undefined term in accordance with modern axiomatic approaches. This of course raises the problem of how the abstract calculus of probability should be connected with the ‘actual world of experiments’. It is suggested that this link should be established, not by a definition of probability, but by an application of Popper’s concept of falsifiability. In addition to formulating his own interesting theory, Dr Gillies gives a detailed criticism of the generally accepted Neyman Pearson theory of testing, as well as of alternative philosophical approaches to probability theory. The reissue will be of interest both to philosophers with no previous knowledge of probability theory and to mathematicians interested in the foundations of probability theory and statistics.

The Twentieth Century has seen a dramatic rise in the use of probability and statistics in almost all fields of research. This has stimulated many new philosophical ideas on probability. Philosophical Theories of Probability is the first book to present a clear, comprehensive and systematic account of these various theories and to explain how they relate to one another. Gillies also offers a distinctive version of the propensity theory of probability, and the intersubjective interpretation, which develops the subjective theory.