Introduction to symbolic logic and its applications /
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| Author / Creator: | Carnap, Rudolf, 1891-1970 |
|---|---|
| Imprint: | New York : Dover Publications, [1958] |
| Description: | 241 p. : ill. ; 21 cm. |
| Language: | English Undetermined |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/1439000 |
Table of Contents:
- Part 1. System of symbolic logic
- Chapter A. The simple language A
- 1. The problem of symbolic logic
- a. The purpose of symbolic language
- b. The development of symbolic logic
- 2. Individual constants and predicates
- a. Individual constants and predicates
- b. Sentential constants
- c. Illustrative predicates
- 3. Sentential connectives
- a. Descriptive and logical signs
- b. Connective signs
- c. Omission of parentheses
- d. Exercises
- 4. Truth-tables
- a. Truth-tables
- b. Truth-conditions and meaning
- 5. L-concepts
- a. Tautologies
- b. Range and L-truth
- 6. L-implication and L-equivalence
- a. L-implication and L-equivalence
- b. Content
- c. Classes of sentences
- d. Examples and exercises
- 7. Sentential variables
- a. Variables and sentential formulas
- b. Sentential variables
- 8. Sentential formulas that are tautologies
- a. Conditional formulas that are tautologies
- b. Interchangeability
- c. Biconditional formulas that are tautologies
- d. Derivations
- 9. Universal and existential sentences
- a. Individual variables and quantifiers
- b. Multiple quantification
- c. Universal conditionals
- d. Translation from the word-langage
- 10. Predicate variables
- a. Predicate variables
- b. Intensions and extensions
- 11. Value-assignments
- 12. Substitutions
- a. Substitutions for sentential variables
- b. Substitutions for individual variables
- c. Substitutions for predicate variables
- d. Theorems on substitutions
- e. Example and exercises
- 13. Theorems on quantifiers
- 14. L-true formulas with quantifiers
- a. L-true conditionals
- b. L-true biconditionals
- c. Exercises
- 15. Definitions
- a. Interchangeability
- b. Definitions
- c. Examples
- 16. Predicates of higher levels
- a. Predicates and predicate variables of different levels
- b. Raising levels
- c. Examples and exercises
- 17. Identity. Cardinal numbers
- a. Identity
- b. Examples and exercises
- c. Cardinal numbers
- 18. Functors
- a. Functors. Domains of a relation
- b. Conditions permitting the introduction of functors
- 19. Ismorphism
- Chapter B. The language B
- 20. Semantical and syntactical systems
- 21. Rules of formation for language B
- a. The language B
- b. The system of types
- c. Russell's antinomy
- 21. Rules of formation for language B-continued
- d. Sentential formulas and sentences in B
- e. Definitions in B
- 22. Rules of transformation for language B
- a. Primitive sentence schemata
- b. Explanatory notes on the separate primitive sentences
- c. Rules of inference
- 23. Proofs and derivations in language B
- a. Proofs
- b. Derivations
- 24. Theorems on provability and derivability in language B
- a. General theorems for B
- b. Interchangeability
- 25. The semantical system for language B
- a. Value-assignments and evaluations
- b. Rules of designation
- c. Truth
- 26. Relations between syntactical and semantical systems
- a. Interpretation of a language
- b. On the possibility of a formalization of syntax and semantics
- Chapter C. The extended language C
- 27. The language C
- 28. Compound predicate expressions
- a. Predicate expressions
- b. Universality
- c. Class terminology
- d. Exercises
- 29. Identity. Extensionality
- a. Identity
- b. Regarding the types of logical constants
- c. Extensionality
- 30. Relative product. Powers of relations
- a. Relative product
- b. Powers of relations
- c. Supplementary remarks
- 31. Various kinds of relations
- a. Representations of relations
- b. "Symmetry, transitivity, reflexivity"
- c. Theorems about relations
- d. Linear order: series and simple order
- e. One-oneness
- 32. "Additional logical predicates, functors and connectives"
- a. The null class and the universal class
- b. Union class and intersection class
- c. Connections between relations and classes
- d. Theorems
- e. Enumeration classes
- 33. The ?-operator
- a. The ?-operator
- b. Rule for the ?-operator
- c. Definitions with the help of ?-expressions
- d. The R's of b
- 34. "Equivalence classes, structures, cardinal numbers"
- a. Equivalence relations and equivalence classes
- b. Structures
- c. Cardinal numbers
- d. Structural properties
- 35. Individual descriptions
- a. Descriptions
- b. Relational descriptions
- 36. Heredity and ancestral relations
- a. Heredity
- b. Ancestral relations
- c. R-families
- 37. Finite and infinite
- a. Progressions
- b. Sum and predecessor relation
- c. Inductive cardinal numbers
- d. Reflexive classes
- e. Assumption of infinity
- 38. Continuity
- a. "Well-ordered relations, dense relations, rational orders"
- b. Dedekind continuity and Cantor continuity
- Part 2. Application of symbolic logic
- Chapter D. Forms and methods of the construction of languages
- 39. Thing languages
- a. Things and their slices
- b. Three forms of the thing language; language form I
- c. Language form II
- d. Language form III
- 40. Coordinate languages
- a. Coordinate language with natural numbers
- b. Recursive definitions
- c. Coordinate language with integers
- d. Real numbers
- 41. Quantitative concepts
- a. Quantitative concepts in thing languages
- b. Formulation of laws
- c. Quantitative concepts in coordinate languages
- 42. The axiomatic method
- a. Axioms and theorems
- b. Formalization and symbolization; interpretations and models
- c. "Consitency, completeness, monomorphism"
- d. The explicity concept
- e. Concerning the axiom systems (ASs) in Part Two of this book
- Chapter E. Axiom systems (ASs) for set theory and arithmetic
- 43. AS for set theory
- a. The Zermelo-Fraenkel AS
- b. The axiom of restriction
- 53. AS involving biological concepts
- a. Division and fusion
- b. "Hierarchies, cells, organisms"
- 54. AS for kinship relations
- a. Biological concepts of kinship
- b. Legal concepts of kinship
- Appendix
- 55. Problems in the application of symbolic logic
- a. Set theory and arithmetic
- b. Geometry
- c. Physics
- d. Biology
- 56. Bibliography
- 57. General guide to the literature
- Index
- Symbols of the symbolic language of the metalanguage
