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An Objective Theory of Probability (Routledge Revivals).
This reissue of D.A. Gillies highly influential work, first published in 1973, is a philosophical theory of probability which seeks to develop von Mises' views on the subject.
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken :
Taylor and Francis,
2012.
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| Colección: | Routledge revivals.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- An Objective Theory of Probability; Copyright; An Objective Theory of Probability; Copyright; Contents; Preface; Introduction; Von Mises' theory of probability; Keynes' theory of probability; Comparison between von Mises and Keynes; Development of the logical tradition after Keynes; Characterization of the scientific approach; The two-concept view; General outline of the book; PART I: THE SPECIAL SCIENCES IN GENERAL; Chapter 1 Von Mises' Philosophy of Science: Its Machian Origins; Mach's development of mechanics; Operationalism; Some objections to operationalism; Chapter 2 Force and Mass.
- The concepts of force and mass before NewtonHow Newton introduced the concepts of force and mass; The 'moon-test' of the law of gravity; How force and mass came to be measurable; Chapter 3 Conceptual Innovation in the Exact Sciences; Another illustration of conceptual innovation: the concept of temperature; General theory of conceptual innovation; How our theory of conceptual innovation avoids the difficulties in operationalism; A digression on 'testing' and 'accepting' scientific theories; The problem of depth; The generalized principle of correspondence and related questions.
- How the ideas of Part I will be applied to the theory of probabilityPART II: THE AXIOMATIC SUPERSTRUCTURE; Chapter 4 Probability and Frequency; Three views on the relations between probability and frequency; Randomness in von Mises' theory; Comparison between von Mises and Kolmogorov; Two criticisms of Kolmogorov by von Mises; Chapter 5 Repeatability and Independence; Analysis of repeatability; Repeatable conditions with dependent outcomes; Arguments against the axiom of independent repetitions; Main argument for the axiom of independent repetitions.
- Derivation of the law of stability of statistical frequenciesComparison with Newtonian mechanics; Criticism of the views of von Mises and Kolmogorov on the relations between probability and frequency; An answer to some arguments of Doob's; Criticism of the 'laws of large numbers' view; The significance of the laws of large numbers; Chapter 6 Deduction of the Law of Excluded Gambling Systems: The Role of Randomness in Probability Theory; Deduction of the law of excluded gambling systems; Independence and gambling systems; A practical example.
- Definition of random sequences and their generation in practiceRelation to randomness as defined in the frequency theory; Answer to an objection of Braithwaite's; Probability theory and determinism; Discussion of some arguments of Khintchine's; Possible modifications of the axioms of probability in the light of experience; Chapter 7 Probabilities of Single Events: Popper's Propensity Theory; Singular probabilities; Popper's propensity theory; Similarities between Popper's propensity theory and von Mises' frequency theory; A criticism of the propensity theory.
- Another argument for the axiom of independent repetitions.