# Book:Rudolf Carnap/Introduction to Symbolic Logic and its Applications

## Rudolf Carnap: Introduction to Symbolic Logic and its Applications

Published $\text {1958}$, Dover

ISBN 0-486-66637-9 (translated by William H. Meyer and John Wilkinson)

Translated from:

Einführung in die symbolische Logik

Symbolic Logic

### Contents

Preface to the English Edition (May 1957)
Preface to the German Edition (January 1954)
PART ONE System of symbolic logic
Chapter A. The simple language A
1. The problem of symbolic logic
2. Individual constants and predicates
3. Sentential connectives
4. Truth-tables
5. L-concepts
6. L-implication and L-equivalence
7. Sentential variables
8. Sentential formulas that are tautologies
9. Universal and existential sentences
10. Predicate variables
11. Value-assignments
12. Substititions
13. Theorems on quantifiers
14. L-true formulas with quantifiers
15. Definitions
16. Predicates of higher levels
17. Identity. Cardinal numbers
18. Functors
19. Isomorphism
Chapter B. The language B
20. Semantical and syntactical systems
21. Rules of formation for language B
22. Rules of transformation for language B
23. Proofs and derivations in language B
24. Theorems on provability and derivability in language B
25. The semantical system for language B
26. Relations between syntactical and semantical systems
Chapter C. The Extended language C
27. The language C
28. Compound predicate expressions
29. Identity. Extensionality
30. Relative product. Powers of relations
31. Various kinds of relations
32. Additional logical predicates, functors and connectives
33. The $\lambda$-operator
34. Equivalence classes, structures, cardinal numbers
35. Individual descriptions
36. Heredity and ancestral relations
37. Finite and infinite
38. Continuity

PART TWO Application of symbolic logic
Chapter D. Forms and methods of the construction of languages
39. Thing languages
40. Coordinate languages
41. Quantitative concepts
42. The axiomatic method
Chapter E. Axiom systems (ASs) for set theory and arithmetic
43. AS for set theory
44. Peano's AS for the natural numbers
45. AS for the real numbers
Chapter F. Axiom systems (ASs) for geometry
46. AS for topology (neighborhood axioms)
47. ASs of projective, of affine and of metric geometry
Chapter G. ASs of physics
48. ASs of space-time topology: 1. The C-T system
49. ASs of space-time topology: 2. The Wlin-system
50. ASs of space-time topology: 3. The S-system
51. Determination and causality
Chapter H. ASs of biology
52. AS of things and their parts
53. AS involving biological concepts
54. AS for kinship relations
Appendix
55. Problems in the application of symbolic logic
56. Bibliography
57. General guide to the literature
Index
Symbols of the symbolic language and of the metalanguage