Algebra of Probable Inference

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Algebra of Probable Inference

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  • 製本 Paperback:紙装版/ペーパーバック版／ページ数 127 p.
  • 言語 ENG
  • 商品コード 9780801869822
  • DDC分類 512

基本説明

Hardcover edition published in 1961 is out of print.

Full Description

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.

Contents

Preface
Part I. Probability
Chapter 1. Axioms of Probable Inference
Chapter 2. The Algebra of Propositions
Chapter 3. The Conjunctive Inference
Chapter 4. The Contradictory Inference
Chapter 5. The Disjuntive Inference
Chapter 6. A Remark on Measurement
Part II. Entropy
Chapter 7. Entropy as Diversity and Uncertainty and the Measure of Information
Chapter 8. Entropy and Propositions
Chapter 9. Systems of Propoisitions
Chapter 10. The Entropy of Systems
Chapter 11. Entropy and Relevance
Chapter 12. A Remark on Chance
Part III. Expectation
Chapter 13. Expectations and Deviations
Chapter 14. The Expectation of Numbers
Chapter 15. The Ensemble of Instances
Chapter 16. The Rule of Succession
Chapter 17. Expectation and Experience
Chapter 18. A Remark on Induction
Notes
Index