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

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## Rudolf Carnap:

## 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:

### Subject Matter

### 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

- 48. ASs of space-time topology: 1. The

*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