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| Chapter 1 Historical background of mathematical logic 1 Introduction 2 Mathematics before Aristotle 3 Argumentation before Aristotle 4 Aristotle's logic A. Preliminaries B. Immediate inferences C. Syllogistic theory Greek mathematics and logic after Aristotle A. Mathematics B. Logic Logic from the Stoics to the nineteenth century Summary Chapter 2 Period of transition 8 Introduction 9 Non-Euclidean geometry 10 Mathematics and argumentation A. Numbers B. Analytic geometry 11 Set theory 12 Paradoxes 13 Summary Chapter 3 Mathematical logic 14 Introduction 15 Formal axiomatic method 16 Primary logic: The propositional calculus 17 General logic: The predicate calculus 18 Set-theoretic logic: Higher-order predicate calculi Chapter 4 The metatheory of mathematical logic 19 Introduction 20 The metatheory of the propositional calculus 21 The metatheory of the predicate calculus 22 The theory of recursive functions 23 The metatheory of arithmetic A. Preliminaries B. The incompleteness of arithmetic C. Consistency and categoricalness 24 The metatheory of set theory Chapter 5 Philosophical fmmplicatiolw of matematicai logic 25 Introduction 26 Church's thesis 27 The nature of indeterminate statements 28 The problem of unsolved problems 29 The question of consistency 30 Logic and philosophy Epilog Aplendix A Appendix B Answers to Problems Bibliography Symbol Index General Index |
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