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This is an important collection of essays dealing with the foundations of probability that will be of value to philosophers of science, mathematicians, statisticians, psychologists and educationalists. The collection falls into three parts. Part I comprises five essays on the axiomatic foundations of probability. Part II contains seven articles on probabilistic causality and quantum mechanics, with an emphasis on the existence of hidden variables. The third part consists of a single extended essay applying probabilistic theories of learning to practical questions of education: it incorporates extensive data analysis. Patrick Suppes is one of the world's foremost philosophers in the area of probability, and has made many contributions to both the theoretical and practical side of education. The statistician Mario Zanotti is a long-time collaborator.
Table of contents:
Part I. Foundations of Probability: 1. Necessary and sufficient conditions for existence of a unique measure strictly agreeing with a qualititative probability ordering; 2. Necessary and sufficient qualitative axioms for conditional probability; 3. On using random relations to generate upper and lower probabilities; 4. Conditions on upper and lower probabilities to imply probabilities; 5. Qualitative axioms for random-variable representation of extensive quantifiers; Part II. Causality and Quantum Mechanics: 6. Stochastic incompleteness of quantum mechanics; 7. On the determinism of hidden variable theories with strict correlation and conditional statistical independence of observables; 8. A new proof of the impossibility of hidden variables using the principles of exchangeability and identity of conditional distribution; 9. When are probabilistic explanations possible?; 10. Causality and symmetry; 11. New Bell-type inequalities for N>4 necessary for existence of a hidden variable; 12. Existence of hidden variables having only upper probabilities; Part III. Applications in Education: 13. Mastery learning of elementary mathematics: theory and data.
Patrick Suppes, one of the world's foremost philosophers in the area of probability, has produced a masterly study, which will interest philosophers and mathematicians alike. The Foundations of Probability with Applications is divided into three parts addressing axiomatic foundations of probability, probabilistic causality and quantum mechanics, and probabilistic theories of learning.
This is an important collection of essays by a leading philosopher, dealing with the foundations of probability.
Table of contents:
Part I. Foundations of Probability: 1. Necessary and sufficient conditions for existence of a unique measure strictly agreeing with a qualititative probability ordering; 2. Necessary and sufficient qualitative axioms for conditional probability; 3. On using random relations to generate upper and lower probabilities; 4. Conditions on upper and lower probabilities to imply probabilities; 5. Qualitative axioms for random-variable representation of extensive quantifiers; Part II. Causality and Quantum Mechanics: 6. Stochastic incompleteness of quantum mechanics; 7. On the determinism of hidden variable theories with strict correlation and conditional statistical independence of observables; 8. A new proof of the impossibility of hidden variables using the principles of exchangeability and identity of conditional distribution; 9. When are probabilistic explanations possible?; 10. Causality and symmetry; 11. New Bell-type inequalities for N>4 necessary for existence of a hidden variable; 12. Existence of hidden variables having only upper probabilities; Part III. Applications in Education: 13. Mastery learning of elementary mathematics: theory and data.
Patrick Suppes, one of the world's foremost philosophers in the area of probability, has produced a masterly study, which will interest philosophers and mathematicians alike. The Foundations of Probability with Applications is divided into three parts addressing axiomatic foundations of probability, probabilistic causality and quantum mechanics, and probabilistic theories of learning.
This is an important collection of essays by a leading philosopher, dealing with the foundations of probability.