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

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.

In May of 1973 we organized an international research colloquium on foundations of probability, statistics, and statistical theories of science at the University of Western Ontario. During the past four decades there have been striking formal advances in our understanding of logic, semantics and algebraic structure in probabilistic and statistical theories. These advances, which include the development of the relations between semantics and metamathematics, between logics and algebras and the algebraic-geometrical foundations of statistical theories (especially in the sciences), have led to striking new insights into the formal and conceptual structure of probability and statistical theory and their scientific applications in the form of scientific theory. The foundations of statistics are in a state of profound conflict. Fisher's objections to some aspects of Neyman-Pearson statistics have long been well known. More recently the emergence of Baysian statistics as a radical alternative to standard views has made the conflict especially acute. In recent years the response of many practising statisticians to the conflict has been an eclectic approach to statistical inference. Many good statisticians have developed a kind of wisdom which enables them to know which problems are most appropriately handled by each of the methods available. The search for principles which would explain why each of the methods works where it does and fails where it does offers a fruitful approach to the controversy over foundations.

This collection of essays is dedicated to 'Joe' Karel Lambert. The contributors are all personally affected to Joe in some way or other, but they are definitely not the only ones. Whatever excuses there are - there are some -, the editors apologize to whomever they have neglected. But even so the collection displays how influential Karel Lambert has been, personally and through his teaching and his writings. The display is in alphabetical order - with one exception: Bas van Fraassen, being about the earliest student of Karel Lambert, opens the collection with some reminiscences. Naturally, one of the focal points of this volume is Lambert's logical thinking and (or: freed of) ontological thinking. Free logic is intimately connected with description theory. Bas van Fraassen gives a survey of the development of the area, and Charles Daniels points to difficulties with definite descriptions in modal contexts and stories. Peter Woodruff addresses the relation between free logic and supervaluation semantics, presenting a novel condition which recovers desirable metatheoretic properties for free logic under that semantics. Terence Parsons shows how free logic can be utilized in interpreting sentences as purporting to denote events (true ones succeed and false ones fail) and how this helps to understand natural language.

A compact survey, at the elementary level, of some of the most important concepts of mathematics. Attention is paid to their technical features, historical development and broader philosophical significance. Each of the various branches of mathematics is discussed separately, but their interdependence is emphasised throughout. Certain topics - such as Greek mathematics, abstract algebra, set theory, geometry and the philosophy of mathematics - are discussed in detail. Appendices outline from scratch the proofs of two of the most celebrated limitative results of mathematics: the insolubility of the problem of doubling the cube and trisecting an arbitrary angle, and the Gödel incompleteness theorems. Additional appendices contain brief accounts of smooth infinitesimal analysis - a new approach to the use of infinitesimals in the calculus - and of the philosophical thought of the great 20th century mathematician Hermann Weyl. Readership: Students and teachers of mathematics, science and philosophy. The greater part of the book can be read and enjoyed by anyone possessing a good high school mathematics background.

1. INTRODUCTION In the Spring of 1975 we held an international workshop on the Foundations and Application of Decision Theory at the University of Western Ontario. To help structure the workshop into ordered and manageable sessions we distri buted the following statement of our goals to all invited participants. They in turn responded with useful revisions and suggested their own areas of interest. Since this procedure provided the eventual format of the sessions, we include it here as the most appropriate introduction to these collected papers result ing from the workshop. The reader can readily gauge the approximation to our mutual goals. 2. STATEMENT or OBJECTIVES AND RATIONALE (Attached to this statement is a bibliography; names of persons cited in the statement and writing in this century will be found referenced in the biblio graphy - certain 'classics' aside. ) 2. 1. Preamble We understand in the following the Theory of Decisions in a broader sense than is presently customary, construing it to embrace a general theory of deciSion-making, induding social, political and economic theory and applica tions. Thus, we subsume the Theory of Games under the head of Decision Theory, regarding it as a particularly clearly formulated version of part of the general theory of decision-making.

The Fifth International Congress of Logic, Methodology and Philosophy of Science was held at the University of Western Ontario, London, Canada, 27 August to 2 September 1975. The Congress was held under the auspices of the International Union of History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science, and was sponsored by the National Research Council of Canada and the University of Western Ontario. As those associated closely with the work of the Division over the years know weIl, the work undertaken by its members varies greatly and spans a number of fields not always obviously related. In addition, the volume of work done by first rate scholars and scientists in the various fields of the Division has risen enormously. For these and related reasons it seemed to the editors chosen by the Divisional officers that the usual format of publishing the proceedings of the Congress be abandoned in favour of a somewhat more flexible, and hopefully acceptable, method of pre sentation. Accordingly, the work of the invited participants to the Congress has been divided into four volumes appearing in the University of Western Ontario Series in Philosophy of Science. The volumes are entitled, Logic, Foundations of Mathematics and Computability Theory, Foun dational Problems in the Special Sciences, Basic Problems in Methodol ogy and Linguistics, and Historical and Philosophical Dimensions of Logic, Methodology and Philosophy of Science.

The essays in this volume (except for the contribution of Dr. Le Grand) are extremely revised versions of papers originally delivered at a workshop on Galileo held in Blacksburg, Virginia in October, 1975. The meeting was organized by Professor Joseph Pitt and sponsored by the Department of Philosophy and Religion, The College of Arts and Sciences, and the Division of Research of Virginia Polytechnic Institute and State University. The papers that follow deal with problems OIf Galileo's philosophy of science, specific and general problems connected with his methodology, and with historical and conceptual questions concerning the relationship of his work to that of contemporaries and both earlier and later scientists. New perspectives take many forms. In this book the 'newness' has, for the most part, two forms. First, in the papers by Wisan, Shea, Le Grand and Wallace (the concerns will also appear in some of the other contributions), greatly enriched historical discoveries of how Galileo's science and its method ology developed are provided. It should be stressed that these papers are attempts to recapture a deep sense of the kind of science Galileo was creating. Other papers in the volume, for example, those by McMullin, Machamer, Butts and Pitt, underscore the importance of this historical venture by discussing various aspects of the philosophical background of Galileo's thought. The historical and philosophical evaluations and analyses compliment one another.