Foundations of probability with applications. Selected papers, 1974-1995 (Q2785793)

This book contains a collection of essays by the authors, divided into three parts. The first part contains essays concerning the foundations of probability, dating between 1976 and 1992. This group contains two essays on upper and lower probabilities. There is a paper on necessary and sufficient conditions for the existence of a probability satisfying qualitative constraints, and a paper providing necessary and sufficient conditions for conditional probability. The fifth essay of this section addresses the ``random variable representation'' of extensive quantities; it is intended as a contribution to the theory of errors of measurement. The second part of the book contains essays on the foundations of quantum mechanics dating from 1974 to 1991. They primarily concern hidden variable questions. The third part of the book contains a hitherto unpublished essay on the learning of elementary mathematics: it is an application of Bayesian (subjective) probability to the design of computer based learning of mathematics. As the fourth essay in the first part of the volume makes clear, both authors regard themselves as highly indebted to de Finetti. Those whose point of view is similar will find this volume essential reading. But there is material here that will be of considerable interest to many who do not share this view of the foundations of probability, particularly the essays on upper and lower probabilities in the second part.