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## Details

Document Type: | Book |
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All Authors / Contributors: |
Arthur W Burks |

ISBN: | 0226080870 9780226080871 0226080889 9780226080888 |

OCLC Number: | 1031137 |

Description: | xvi, 694 pages illustrations 24 cm |

Contents: | I. Concepts and problems : 1. Questions and answers -- 2. Mathematics and empirical science : Logical and empirical statements ; The logical and empirical status of geometry ; The logical modalities -- 3. Specifying the meaning of a technical term -- 4. Inquiry and argument ; Kinds of logic ; The logic of empirical inquiry -- 5. Deductive and inductive arguments : Deductive arguments ; Inductive arguments and probability -- 6. Problems and methods : The four main problems of this book ; Theories and models in empirical science ; The methods of this book II. The calculus of inductive probability : 1. Introduction -- 2. The calculus of inductive probability : Axioms ; Truth-functional and modal logic -- 3. Some theorems of the calculus of inductive probability : Probability and the logical modalities ; Multiplication principles ; Addition principles -- 4. Relative frequency -- 5. Bayes' theorem and induction : Bayes' theorem ; Confirmation by repeated experimentation ; The confirmation theorem ; Applications to induction -- 6. Unconditional probability III. Alternative inductive logics and the justification of induction : 1. Three inductive logics -- 2. Inductive logics for simple models of reality : Simple models of reality ; Carnap's inductive logics -- Induction and statistical uniformity ; Inductive logics and Bayes' method -- 3. Hume's thesis on the justification of induction : Alternative inductive logics and Hume's thesis ; Historical comment ; Speculative character of Hume's thesis -- 4. Frequency theories of probability : The frequency theory of empirical probability ; The frequency theory of inductive probability IV. Probability and action : 1. Introduction -- 2. Peirce's pragmatism : The pragmatic principle of meaning ; Sameness of meaning ; Analysis ; The descriptive component ; The normative component ; Probability and pragmatism -- 3. The traditional theory of utility : Utility and choice ; Quantitative probabilities and valuations ; Infinite utilities ; Two paradoxes of utility ; Insurance and gambling ; Simple ordering of preferences and uncertainties -- 4. The book theorem V. The pragmatic theory of inductive probability :1. Introduction : Preview ; Historical remarks -- 2. The calculus of choice: grammar : The marking game ' Choice and act trees ' Complete sets of trees -- 3. The calculus of choice: simple ordering : Marking and logical equivalence axioms ; Simple ordering of preferences ; Simple ordering of uncertainties -- 4. The calculus of choice: normal forms : Normal form axiom ; Comparative values ; Comparative probabilities -- 5. The calculus of choice: quantitative : Utilities and quantitative probabilities ; Proof of the main theorem ; Savage's axiomatic system -- 6. The pragmatic theory of inductive probability : Introduction ; The normative use of the calculus of choice ' Probability statements and logical truth -- 7. Closely related theories of inductive probability : The a priori theory ; The personalistic theory VI. The logic of casual statements as a formal language -- 1. Introduction -- 2. The structure of the logic of casual statements : Grammar ; Axioms ; Proofs and theorems -- 3. An abstract interpretation : Examples ; Modal models ; Logical truth -- 4. The mechanical character of a formal language : Arithmetization of a formal language ; Godel's incompleteness theorem ; Machines and algorithms ; Machines and formal language -- 5. Some theorems of the logic of casual statements : Derived rules of inference ; Some metatheorems ; Paradoxes of implication VII. The logic of casual statements as a model of natural language : 1. Introduction -- 2. Laws of nature : Laws and theories ; Causal laws -- 3. Subjunctives and dispositions : Causal modalities and subjunctives ; Causal dispositions ; Elliptical causal implication -- 4. Causality : Causes and effects ; Contravening causes and completeness -- 5. Iterated modalities : Change of dispositions ; Comprehensive modal logics VIII. The dispositional theory of empirical probability : 1. Introduction -- 2. A fair coin : Dispositional model of the fair coin hypothesis ; Causal and probabilistic dispositions ; Dispositional models of atomic empirical probability statements -- 3. Dispositional models of empirical probability theories : Empirical probability theories ; The dispositional theory of empirical probability ; The positivistic theory of empirical probability -- 4. Alternative theories of empirical probability : The frequency theory of empirical probability ; Peirce's dispositional-frequency theory of probability ; The personalisitic account of empirical probability IX. Cause and chance in space-time systems : 1. Introduction -- 2. Space-time systems : Induction and repetition ; Indexical symbols and properties ; Cellular automata ; Local and global laws -- 3. Causality in nature : Uniformity of nature ; Determinism ; Near-determinism ; Tychism -- 4. Determinism and chance : Embedded systems and probability ; Entropy and randomness ; Determinism and randomness X. The presupposition theory of induction : 1. Introduction -- 2. The epistemological status of causal necessity : Empirical and a priori concepts ; Causal necessity is a priori ; Causal necessity is irreducibly model -- 3. Causal models of standard inductive logic : Possible causal systems ; Verification of causal systems -- 4. The presupposition theory of induction : The a priori aspect of inductive probability ; Epistemological status of the presuppositions -- 5. Historical antecedents : Keynes' principles of induction ; Kant's theory of causality -- 6. Summary of the presupposition theory XI. Chance, cause, and reason : 1. Fundamental concepts ; 2. Questions and answers ; 3. A unified theory of probability, causality, and induction. |

Responsibility: | [by] Arthur W. Burks. |

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