Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science
Volume III Foundations and Philosophy of Statistical Theories in the Physical Sciences

Editors: William L. Harper, Clifford Alan Hooker



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 Bayesian 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.

Table of contents

Front Matter
Pages I-XII

The Statistics of Non-Boolean Event Structures
Pages 1-16

Possibility and Probability
Pages 17-33

Some Remarks on Hamiltonian Systems and Quantum Mechanics
Pages 35-53

The Possibility Structure of Physical Systems
Pages 55-80

Quantum Mechanical Physical Quantities as Random Variables
Pages 81-103

On the Interference of Probabilities
Pages 105-109

Classical and Quantum Probability and Set Theory
Pages 111-119

A Generalized Measure and Probability Theory for the Physical Sciences
Pages 121-141

Quantum Logic, Convexity, and a Necker-Cube Experiment
Pages 143-153

On the Applicability of the Probability Concept to Quantum Theory
Pages 155-167

A Mathematical Setting for Inductive Reasoning
Pages 169-205

Classical Statistical Mechanics Versus Quantal Statistical Thermodynamics: A Study in Contrasts
Pages 207-219

A Semantic Analysis of Niels Bohr’s Philosophy of Quantum Theory
Pages 221-241

Back Matter
Pages 243-243



Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science

Volume I Foundations and Philosophy of Epistemic Applications of Probability Theory
https://bbs.pinggu.org/thread-4979485-1-1.html

Volume II Foundations and Philosophy of Statistical Inference
https://bbs.pinggu.org/thread-4979489-1-1.html


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