Donald Gillies - An Objective Theory of Probability

The aim of this book is to present a philosophical theory of probability which can best be considered as a development of von Mises views. I am entirely in agreement with von Mises in regarding probability theory as a mathematical science similar to mechanics or electrodynamics, and probability itself as an objective measurable concept similar to mass or charge. In this sense I am presenting an objective theory of probability - as opposed to subjective or logical accounts.

The point where I differ from von Mises is often, though wrongly in my opinion, taken as the essential feature of his theory: namely the definition of probability as limiting frequency. This definition, as is well-known, leads to mathematical complexities, and, generally speaking, does not harmonize at all well with the measure-theoretic approach to probability theory introduced by Kolmogorov and almost universally accepted among mathematicians. At the same time it is often felt that some kind of definition of probability in terms of frequency is needed in order to establish the connection between the abstract calculus of probability and the world of actual experiments. My suggested resolution of this difficulty is that the link between theory and experience should be established not by a definition but rather by an application of Popper's concept of falsifiability.

In the Introduction I give a critical account of the various current standpoints in the philosophy of probability. Against this background, it is possible to give a more detailed sketch of my own theory, and to explain where it stands in the spectrum of competing views. The remainder of the book is then devoted to developing the theory in detail. Throughout I make free use of the standard terminology of probability theory, but for the benefit of the reader unacquainted with the mathematical theory an appendix is included which explains the meanings of all the technical terms. Any such reader who goes through this appendix first, and then, if necessary, refers back to the technicalterms when they occur, should have no difficulty in following the text. In this way I hope the book will prove interesting and comprehensible both to mathematicians interested in the foundations of probability and statistics, and to philosophers who have not studied the mathematical theory.

Extracts from the Introduction and in Synthese. I would like to thank the publishers of these journals, that is the Cambridge University Press and the D. Reidel Publishing Company, for permission to reprint these passages.

It remains only to express my thanks to the many friends and colleagues who have helped me in writing this book. Much of the book is a revised version of parts of my Ph.D. thesis, and my greatest debt of gratitude is thus to my supervisor Imre Lakatos for all his help and encouragement, as well as for introducing me to the Popperian standpoint in philosophy which has very deeply influenced the whole work. Previous versions of many parts of the book were circulated among my friends or read at various seminars in London and Cambridge and I would like to thank all those who offered very valuable comments and criticisms, and especially to mention in this connection Allan Birnbaum, Richard Braithwaite, Jon Dorling, Bruno de Finetti, Ian Hacking, Mary Hesse, Mark Hill, Colin Howson, John Lucas, Hugh Mellor, Sir Karl Popper, Heinz Post, Quentin Rappoport, Alan Stuart, Aidan Sudbury, John Watkins, John Worrall and Elie Zahar. Some particular debts are mentioned in footnotes. The book was mainly written while I was holding a research fellowship at King's College, Cambridge, and I should like to thank all those who made my stay there a most agreeable one.