UID:
almahu_9947367841302882
Format:
1 online resource (441 p.)
Edition:
2nd ed., rev. and enl.
ISBN:
1-281-71647-2
,
9786611716479
,
9780080880023
,
1-4356-8698-5
,
0-08-088005-3
Series Statement:
Studies in logic and the foundations of mathematics ; v. 85
Content:
Since the publication of the first edition in 1976, there has been a notable increase of interest in the development of logic. This is evidenced by the several conferences on the history of logic, by a journal devoted to the subject, and by an accumulation of new results. This increased activity and the new results - the chief one being that Boole's work in probability is best viewed as a probability logic - were influential circumstances conducive to a new edition.Chapter 1, presenting Boole's ideas on a mathematical treatment of logic, from their emergence in his early 1847 work on t
Note:
Description based upon print version of record.
,
Front Cover; Boole's Logic and Probability; Copyright Page; Contents; Preface to the First Edition; Preface to the Second Edition; Introduction; Chapter 0. Requisites From Algebra, Logic and Probability; 0.1. Preliminaries; 0.2. Algebraic structures; 0.3. First order theories, models, extensions; 0.4. Semirings, Commutative rings with unit; 0.5. Boolean algebras and Boolean rings. Propositional logic; 0.6. Rings of quotients. Boolean quotients; 0.7. Fourier elimination. Solvability of linear systems; 0.8. Linear programming; 0.9. Probability theory; 0.10. Miscellaneous; PART I . LOGIC
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Chapter 1. Boole's Logic of Class Terms1.0. Symbolical Algebra; 1.1. Boole's first essay; 1.2. The basic principle; I.3. Symbols of Logic and ""operations of the mind"". The fundamental law; 1.4. Boole's algebra of +, -, X, 0, 1; 1.5. Primary propositions and class terms; 1.6. Principles of symbolical reasoning. Development; 1.7. Interpretation; 1.8. Elimination. Reduction; 1.9. Abbreviation. Perfection of method; 1.10. Treatment of ""some"". Aristotelian logic; 1.11. De Morgan. Jevons, Peirce, Macfarlane, Venn; 1.12. Propositions numerically definite; 1.13. Notes to Chapter 1
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Chapter 2. Formalization of Boole's Logic2.1. The calculus of multisets. Axioms for multiset algebra; 2.2. Boole's Algebra (SM algebras); 2.3. Idempotents. Boolean multiset terms; 2.4. Boole's notion of ""uninterpretable""; 2.5. The indefinite class symbol ?; 2.6. The solution of Boolean multiset equations for an unknown; 2.7. Boolean equations and division; 2.8. Additional remarks on 0/0 and 1/0'; 2.9. The partial algebra of Boolean quotients; 2.10. Notes to Chapter 2; Chapter 3. Boole's Propositional Logic; 3.0. The two theories; 3.1. The calculus of elective symbols (operators)
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3.2. The logic of hypotheticals3.3. Secondary propositions and ""time""; 3.4. Boole's illustrative examples; 3.5. Justification of the logic of secondary propositions; 3.6. A two- to four-valued connective; 3.7. Notes to Chapter 3; PART II. PROBABILITY; Chapter 4. Probability From Boole's Viewpoint; 4.1. Critique of the standard theory; 4.2. An additional principle; 4.3. A general method; 4.4. The problem of ""absolute"" probabilities I; 4.5. Boole's method without the mutual independence; 4.6. Elementary illustrations of Boole's method
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4.7. Conditions of possible experience. Bounds on the probability of events4.8. Wilbraham's and Peirce's criticisms; 4.9. Notes to Chapter 4; Chapter 5. Boole'S Probability Made Rigorous; 5.1. Simple and Boole probability algebras, calculi, models; 5.2. Conditioned-events probability realm; 5.3. Reprise of Boole's General Problem in Probability; 5.4. Justification for Boole's solution of the General Problem; 5.5. Conditions of possible experience -a consistency (solvability) problem; 5.6. The problem of absolute probabilities II; 5.7. Boole's General Problem linearly programmed
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5.8. Notes to Chapter 5
Additional Edition:
ISBN 0-444-87952-8
Language:
English
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