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

Subject Matter

 * 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