Studies in Inductive Probability and Rational Expectation - Softcover
Book 85 of 304: Synthese Library
Synopsis
1. Introduction.- 1. Concept Explication.- 2. Objectives and Survey.- 2. Cognitive Rationality.- 1. On the Explication of the Concept of Rationality.- 2. Cognitive Rationality and Patterns of Expectation.- 3. Inductive Reasoning and Inductive Probability Theory.- 3. Logico-Mathematical Preliminaries.- 1. Logical Vocabulary.- 2. Set-theoretical Vocabulary.- 3. Some Elements of Probability Theory.- 4. Formally Rational Expectation in a Paradigmatic Context.- 1. Paradigmatic Contexts.- 2. Two Conditions for Rational Expectation.- 3. A Framework for a Paradigmatic Context.- 4. First Analysis of a Rational Expectation Pattern.- 5. A Framework for a Paradigmatic Context (continued).- 6. Third Formal Condition for Rational Expectation.- 7. Decidable Contexts.- 5. Generalized Carnapian Systems.- 1. Introduction.- 2. Constitutive Principles and Definition of GC-systems.- 3. General Analysis of GC-systems.- 1. Some Direct Consequences.- 2. Generalized Special Values.- 3. First Interpretation of GC-systems: the Urn-model (w < ?).- 4. Mathematical Expectations According to GC-systems.- 5. Non-inductive (? = ± ?) and Extreme-inductive (? = 0) GC-systems.- 6. Carnapian Systems (C-systems).- 4. Analysis of Positive Inductive GC-systems (0 < ? < oo).- 1. Possible Reformulations.- 2. Generalized Special Values as Weighted Means.- 3. Second Interpretation of GC-systems: Repeated Experiments Governed by a Density-function (w < ?).- 4. Principle of Structural Indifference (w < ?): C *- systems (? = w).- 5. Analysis of Negative Inductive GC-systems (? < 0).- 1. Possible Reformulations.- 2. Generalized Special Values as Weighted Means (continued).- 3. Hypergeometric Systems.- Appendix to Section 2 (Proof of T2).- 6. Hintikka and Universalized Carnapian Systems.- 1. Introduction.- 2. NH-systems.- 3. Hintikka-systems (H-systems).- 4. Some Fundamental Properties of H-systems.- 5. An Urn-model for H-systems.- 6. The Equivalence of NH- and SH-systems: Universalized Carnapian systems (UC-systems).- 7. Analysis of UC-systems.- 1. General.- 2. Structurally Indifferent UC-systems: UC*-systems (? = 1).- 3. Extreme UC-systems: ? = ?, ? = 0.- 8. Fundamental Discussion Related to Applications.- 9. Finite Parameters for H-systems.- 10. Reformulation of H-systems; k ? ?.- 11. GH-systems and G UC-systems.- 12. Survey of Systems.- Appendix to Section 2 (Proof of T1 ).- 7. Rational Expectation in Multinomial Contexts.- 1. Carnap's Intended Application.- 2. The Multinomial Context.- 3. Formally Rational Patterns for Open Multinomial Contexts.- 4. Material Conditions of Adequacy; UC-systems as Expectation Pattern for Open Multinomial Contexts.- 5. Constitutional Distributions for Open Multinomial Contexts.- 6. The Hypergeometric Context.- 8. Some Problems and Related Topics.- 1. PER-systems.- 2. On Weakening WPERR.- 3. *UC*-systems and k ? ?.- 4. Confirmation Theory.- 5. Falsification.- 6. Rules of Acceptance in UC-systems.- 9. Concluding Remarks.- References.- Index of Names.- Index of Subjects.- Recurring Symbols.- Conditions/Principles/Axioms.- Definition of Systems.
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About the Author
Professor Theo Kuipers is the author of From Instrumentalism to Constructive Realism (Synthese Library 287, 2000). He is the leader of the Groningen Research Group `Cognitive Structures in Knowledge and Knowledge Development', which gained the highest possible scores in two successive assessments of Dutch philosophical research by international committees.
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