Synopses & Reviews
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.
Synopsis
This volume in the Synthese Library Series is the result of a con- ference held at the Roskilde University, Denmark, September 16- 18, 1998. The purpose of this meeting was to shed light on some of the recent issues in probability theory and track their history; to analyze their philosophical and mathematical significance, and to analyze the role of mathematical probability theory in other sciences. Hence the conference was called Probability Theory- Philosophy Recent History and Relations to Science. The editors would like to thank the invited speakers includ- ing in alphabetical order Prof. N.H. Bingham (BruneI Univer- sity), Prof. Berna KIlmc; (Bogazici University), Prof. Eberhard Knoblock (Techniche Universitat Berlin), Prof. J.B. Paris (Uni- versity of Manchester), Prof. T. Seidenfeld (Carnegie Mellon University), Prof. Glenn Shafer (Rutgers University) and Prof. Volodya Vovk (University of London) for contributing, in the most lucid and encouraging way, to the fulfillment of the con- ference aim. The editors are also grateful to the invited speakers for making their contributions available for publication. The conference was organized by the Danish Network on the History and Philosophy of Mathematics http: //mmf.ruc.dkjmathnetj The editors would like to thank the network's organizing com- mittee consisting of Prof. Kirsti Andersen (University of Aarhus), Prof. Jesper Liitzen (University of Copenhagen), Dr. Tinne Hoff Kjeldsen (Roskilde University) and the committee's secretaries Lise Mariane Jeppesen and Jesper Thrane (Roskilde University).
Table of Contents
Preface. Contributing Authors. Introduction;
V.F. Hendricks, et al. Original Abstracts.
Part 1: The Philosophy and Recent History of Probability Theory and Statistics. Probability and Statistics: Some Thoughts at the Turn of the Millennium;
N.H. Bingham. Kolmogorov's Complexity Conception of Probability;
V. Vovk. Emile Borel's View of Probability Theory;
E. Knobloch. The Reception of John Venn's Philosophy of Probability;
B.E. Kilinç. Part 2: Contemporary Issues in Probability Theory and Statistics. On the Distribution of Probability Functions in the Natural World;
J.B. Paris. Nature's Possibilities and Expectations;
G. Shafer. Remarks on the Theory of Conditional Probability: Some Issues of Finite versus Countable Additivity;
T. Seidenfeld. Index.