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Probability and Statistical Inference in Ancient and Medieval Jewish Literature /
This book throws new light on the origins of probability and statistics. Heretofore these were thought to be entirely the creation of recent centuries, but it is demonstrated here that probability has a much longer history, reaching back to biblical times.
| Autor principal: | |
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| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
[Buffalo] :
University of Toronto Press,
[1973]
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| Colección: | Book collections on Project MUSE.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; PREFACE; Guide to Transliterations; Introduction: Rabbinic Literature; 1 DECISIONS AND LOGIC; 1.0 Deduction and Induction; 1.1 Probability for Decision-Making; 1.2 Rabbinic Hermeneutics; 1.3 From the Particular to the General; 1.4 A Rule for Analogical Inference; 1.5 Undecidable Propositions; 2 RANDOM MECHANISMS; 2.0 Chance and Divination; 2.1 Recourse to Chance in the Bible; 2.2 Chance Mechanisms in the Talmud; 2.3 Lots for the Scapegoat; 2.4 Division of the Holy Land; 2.5 Redemption of the First Born; 2.6 Sharing the Flesh of the Sacrificial Animals
- 2.7 Assignment of Priestly Duties: The Law of Large Numbers3 FOLLOW THE MAJORITY: A FREQUENCY INTERPRETATION; 3.0 Acceptance Rules; 3.1 Follow the Majority; 3.2 Counted and Uncounted Majorities; 3.3 Talmudic Acceptance Rules; 3.4 Approximate Frequencies; 3.5 Standard Majorities; 3.6 Half and Half; 3.7 Relevant Reference Classes; 3.8 A Frequency Interpretation; 4 ADDITION AND MULTIPLICATION OF PROBABILITIES; 4.0 Arithmetic for Acceptance Rules; 4.1 Addition; 4.2 Multiplication: Conditional Probabilities; 4.3 Multiplication: Independent Probabilities; 4.4 Axioms of Probability Theory
- 4.5 Inverse Probabilities and Bayes's Theorem4.6 Summary; 5 LOGICAL ALTERNATIVES; 5.0 The Classical Definition of Probability; 5.1 Enumerating the Alternatives; 5.2 Combinations vs Permutations; 5.3 Ultimate Alternatives; 5.4 Are Logical Alternatives Equiprobable?; 5.5 A Propensity Interpretation of Probability; 5.6 What is 'Random'?; 5.7 Unknowability and Indeterminacy; 6 SAMPLING; 6.0 Statistical Inference; 6.1 Distribution in a Sample; 6.2 Variability in Samples; 6.3 From Sample to Population; 6.4 Mortality Rates; 6.5 Predictive Inference; 6.6 Statistical Laws of Nature; 7 PARADOXES
- 7.0 Logical Difficulties7.1 A Paradox of Indifference; 7.2 An Acceptance Paradox; 7.3 Bertrand's Paradox; 7.4 The Lottery Paradox; 7.5 Whence Paradox?; 7.6 Shrinking Probabilities; 8 EVIDENCE AND ENTAILMENT; 8.0 Two Types of Probability; 8.1 A Comparative Concept of Evidence; 8.2 Legal Presumptions and the Problem of Induction; 8.3 A Hierarchy of Presumptions; 8.4 Evidence in other Legal Systems; 9 INDUCTION AND HYPOTHESIS; 9.0 Competing Hypotheses; 9.1 An Economy Principle; 9.2 Are the Stars Randomly Distributed?; 9.3 Falsifying Hypotheses; 9.4 A Rabbinic Principle of Maximum Likelihood
- 9.5 The Modern Principle of Maximum Likelihood9.6 A Likelihood Ratio; 10 SUBJECTIVE PROBABILITIES; 10.0 Subjectivistic Probability; 10.1 Hunches and Intuition; 10.2 Subjective Objectivity; 10.3 Degrees of Belief; 11 COMBINATIONS AND PERMUTATIONS; 11.0 The Pure Mathematics of Probability; 11.1 Letters and Words; 11.2 Conjunctions of Planets; 11.3 A Major Branch of Mathematics; 11.4 An Application to Probability; 11.5 Combinations in Gaming; 12 THE HISTORICAL PERSPECTIVE; 12.0 Demonstration and Dialectics; 12.1 Etymology and Meaning; 12.2 Equiprobability; 12.3 Greek Combinatorial Analysis