最 低 价：￥137.90
定 价：￥153.23
作 者：G. T. Kneebone 著 著
出 版 社：Oversea Publishing House
出版时间：2001-4-1
I S B N：9780486417127
| Preface Acknowledgements PART I MATHEMATICAL LOGIC Chapter 1 Traditional Logic 1 Introduction : mathematics and logic 2 The nature of mathematics 3 The nature of logic 4 Terms and propositions 5 Syllogistic inference 6 The reduction of syllogisms 7 Deductive arguments of more complex form Supplementary notes on Chapter 1 1 Aristotle's Organon 2 Transitional logic 3 Venn's diagrams 4 Additional reading 5 The Development of Logic Chapter 2 Symbolic Logic I--The Propositional Calculus 1 Propositional logic 2 Propositional variables and the basic connectives 3 Equiveridicity of formulae 4 Elementary transformations in the propositional calculus 5 Normal forms 6 Axiomatic treatment of the propositional calculus Supplementary notes on Chapter 2 1 The term 'semantic' 2 The logical notation of Lukasiewicz 3 The sixteen truth-functions of two propositional variables 4 Boole's application of algebraic symbolism to logic 5 Logical sum and logical product 6 C. I. Lewis's modal logic of strict implication 7 Many-valued logics 8 Books on symbolic logic Chapter 3 Symbolic Logic H The Restricted Calculus of Predicates 1 Propositional functions 2 Quantification 3 Axiomatic treatment of the calculus of predicates 4 Completeness of the restricted calculus of predicates 5 The deduction theorem Supplementary notes on Chapter 3 1 Some points concerning symbolism 2 A strong sense of 'complete' Chapter 4 Further Development of Symbolic Logic 1 The relation of identity 2 Descriptions and the t-symbol 2.1 Characteristic functions of formulae 3 Formalized mathematical theories 4 Hilbert's e-symbol 4.1 Symbolic resolution of existential axioms 5 Classes and relations 6 The extended calculus of predicates 6.1 Russell's antinomy 6.2 Axiomatization of the extended calculus of predicates 7 The logical calculus of Bourbaki's Elements de Mathematipue 8* Gentzcn's calculus of natural deduction Supplementary notes on Chapter4 1 The vicious-circle paradoxes 2 Tarski's formalization of semantics 3 The e-symbol as a selection operator 4 Additional reading PART II FOUNDATIONS OF MATHEMATICS Chapter 5 The Critical Movement in Mathematics in the Nineteenth Century 1 Symbolic logic in relation to the foundations of mathe- matics 2 Greek mathematics 3 The beginnings of modem mathematics 4 The first phase of the critical movement 5 Peano's Formulaire de Mathematipue 6 The symbolic language of Leibniz …… Chapter 5 The Critical Movement in Mathematics in the Nineteenth Century Chapter 6 The Logistic Identification of Mathematics with Logie Chapter 7 Fromalized Mathematics and Metamathematics Chapter 8 Godel's Theorems on the Inherent Limitations of Formal Chapter 9 Intuitionism Chapter 10 Recursive Arthmetic Chapter 11 The Axiomatie Theory of Sets PART III PHLOSOPHY OF MATHEMATICS Chapter 12 The Epistemological Status of Mathematics Chapter 13 The Application of Mathematics to the Natrual World Chapter 14 Logic and the Activity of Thenking Appendix Developments since 1939 in the Study of Foundations Bibliography The Greek and German Alphabets Index of Symbols General Index |
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