Algebra of Probable Inference

Häftad, Engelska, 2002

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Beskrivning

In Algebra of Probable Inference, Richard T. Cox develops and demonstrates that probability theory is the only theory of inductive inference that abides by logical consistency. Cox does so through a functional derivation of probability theory as the unique extension of Boolean Algebra thereby establishing, for the first time, the legitimacy of probability theory as formalized by Laplace in the 18th century. Perhaps the most significant consequence of Cox's work is that probability represents a subjective degree of plausible belief relative to a particular system but is a theory that applies universally and objectively across any system making inferences based on an incomplete state of knowledge. Cox goes well beyond this amazing conceptual advancement, however, and begins to formulate a theory of logical questions through his consideration of systems of assertions -- a theory that he more fully developed some years later. Although Cox's contributions to probability are acknowledged and have recently gained worldwide recognition, the significance of his work regarding logical questions is virtually unknown.The contributions of Richard Cox to logic and inductive reasoning may eventually be seen to be the most significant since Aristotle.

Produktinformation

Utgivningsdatum:2002-02-09
Mått:152 x 229 x 7 mm
Vikt:204 g
Format:Häftad
Språk:Engelska
Antal sidor:127
Förlag:Johns Hopkins University Press
ISBN:9780801869822

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Mer om författaren

Richard T. Cox was a professor of physics at the Johns Hopkins University. He was the author of several books on physics and biology.

Recensioner i media

[This book] is, in my opinion one of the most important ever written on the foundations of probability theory, and the greatest advance in the conceptual, as opposed to the purely mathematical, formulation of the theory since Laplace. -- E. T. Jaynes American Journal of Physics Transformed my view of probability and enriched my career as a physicist. -- Bruce Partridge Physics Today

Innehållsförteckning

PrefacePart I. ProbabilityChapter 1. Axioms of Probable InferenceChapter 2. The Algebra of PropositionsChapter 3. The Conjunctive InferenceChapter 4. The Contradictory InferenceChapter 5. The Disjuntive InferenceChapter 6. A Remark on MeasurementPart II. EntropyChapter 7. Entropy as Diversity and Uncertainty and the Measure of InformationChapter 8. Entropy and PropositionsChapter 9. Systems of PropoisitionsChapter 10. The Entropy of SystemsChapter 11. Entropy and RelevanceChapter 12. A Remark on ChancePart III. ExpectationChapter 13. Expectations and DeviationsChapter 14. The Expectation of NumbersChapter 15. The Ensemble of InstancesChapter 16. The Rule of SuccessionChapter 17. Expectation and ExperienceChapter 18. A Remark on InductionNotesIndex