Profile of Mathematical Logic数理逻辑轮廓

Readers need only an acquaintance with high school–level math to appreciate this text, which explores the historical reasons for the formation of Aristotelian logic, the rise of mathematical logic, the nature of the formal axiomatic method and its use, and the main results of metatheory and their import. 1971 edition. 22 figures. 19 tables. Appendixes. Bibliography. Indexes.

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