|
|
| Line 13: |
Line 13: |
|
| |
|
| I. INTRODUCTION | | I. INTRODUCTION |
| | | *[[Elements of Symbolic Logic/* § 1. Logic and language| § 1. Logic and language]] |
| § 1. Logic and language | | * § 2. Language |
| § 2. Language | | * § 3. Different levels of language |
| § 3. Different levels of language | | * § 4. Instrumental usage of language |
| § 4. Instrumental usage of language | | * § 5. Definitions |
| § 5. Definitions | |
|
| |
|
| II. THE CALCULUS OF PROPOSITIONS | | II. THE CALCULUS OF PROPOSITIONS |
|
| |
|
| § 6. Propositional operations | | * § 6. Propositional operations |
| § 7. Truth tables | | * § 7. Truth tables |
| § 8. Survey of possible operations. Tautologies | | * § 8. Survey of possible operations. Tautologies |
| § 9. Interpretation of tautological operations as connective operations | | * § 9. Interpretation of tautological operations as connective operations |
| § 10. Reduction of operations to other operations | | * § 10. Reduction of operations to other operations |
| § 11. Derivations | | * § 11. Derivations |
| § 12. The rule of substitution | | * § 12. The rule of substitution |
| § 13. The rule of replacement | | * § 13. The rule of replacement |
| § 14. The rule of inference | | * § 14. The rule of inference |
| § 15. Secondary rules of inference | | * § 15. Secondary rules of inference |
| § 16. Remarks on the method of derivation | | * § 16. Remarks on the method of derivation |
|
| |
|
| III. THE SIMPLE CALCULUS OF FUNCTIONS | | III. THE SIMPLE CALCULUS OF FUNCTIONS |
|
| |
|
| § 17. Propositional functions | | * § 17. Propositional functions |
| § 18. Binding of variables | | * § 18. Binding of variables |
| § 19. Negation of operators | | * § 19. Negation of operators |
| § 20. The scope of an operator and the order of operators | | * § 20. The scope of an operator and the order of operators |
| § 21. Synthetic assertions containing free argument variables | | * § 21. Synthetic assertions containing free argument variables |
| § 22. Some concepts referring to functions | | * § 22. Some concepts referring to functions |
| § 23. Truth characters of one-place functions | | * § 23. Truth characters of one-place functions |
| § 24. Definition of tautologies containing functions | | * § 24. Definition of tautologies containing functions |
| § 25. The use of case analysis for the construction of tautologies in propositional functions | | * § 25. The use of case analysis for the construction of tautologies in propositional functions |
| § 26. The rules of substitution and inference in the calculus of functions | | * § 26. The rules of substitution and inference in the calculus of functions |
| § 27. The rule for free variables | | * § 27. The rule for free variables |
| § 28. Derivation of tautologies | | * § 28. Derivation of tautologies |
| § 29. Secondary rules | | * § 29. Secondary rules |
| § 30. Derivations from synthetic premises | | * § 30. Derivations from synthetic premises |
| § 31. The formal and the material conception of language | | * § 31. The formal and the material conception of language |
| § 32. The proof of consistency | | * § 32. The proof of consistency |
| § 33. Two objections against the proof of consistency | | * § 33. Two objections against the proof of consistency |
| § 34. Logical evidence | | * § 34. Logical evidence |
|
| |
|
| V. THE CALCULUS OF CLASSES | | V. THE CALCULUS OF CLASSES |
|
| |
|
| § 35. Classes | | * § 35. Classes |
| § 36. The syllogism | | * § 36. The syllogism |
| § 37. The principle of abstraction | | * § 37. The principle of abstraction |
| § 38. Classes of couples, triplets, and so on | | * § 38. Classes of couples, triplets, and so on |
|
| |
|
| VI. THE HIGHER CALCULUS OF FUNCTIONS | | VI. THE HIGHER CALCULUS OF FUNCTIONS |
|
| |
|
| § 39. Functions of higher types | | * § 39. Functions of higher types |
| § 40. The antinomies and the theory of types | | * § 40. The antinomies and the theory of types |
| § 41. The technique of the higher calculus | | * § 41. The technique of the higher calculus |
| § 42. The treatment of indefinite expressions | | * § 42. The treatment of indefinite expressions |
| § 43. The relation of identity | | * § 43. The relation of identity |
| § 44. The definition of number | | * § 44. The definition of number |
|
| |
|
| VII. ANALYSIS OF CONVERSATIONAL LANGUAGE | | VII. ANALYSIS OF CONVERSATIONAL LANGUAGE |
|
| |
|
| § 45. The deficiencies of traditional grammar | | * § 45. The deficiencies of traditional grammar |
| § 46. Proper names | | * § 46. Proper names |
| § 47. Descriptions | | * § 47. Descriptions |
| § 48. The problem of individuals | | * § 48. The problem of individuals |
| § 49. Fictitious existence | | * § 49. Fictitious existence |
| § 50. Token-reflexive words | | * § 50. Token-reflexive words |
| § 51. The tenses of verbs | | * § 51. The tenses of verbs |
| § 52. Classification of functions | | * § 52. Classification of functions |
| § 53. Functions of higher types | | * § 53. Functions of higher types |
| § 54. Descriptional functions | | * § 54. Descriptional functions |
| § 55. Logical terms in a syntactical capacity | | * § 55. Logical terms in a syntactical capacity |
| § 56. Logical terms in a semantical capacity | | * § 56. Logical terms in a semantical capacity |
| § 57. Logical terms in a pragmatic capacity | | * § 57. Logical terms in a pragmatic capacity |
| § 58. Extraneous terms | | * § 58. Extraneous terms |
| § 59. Classification of the parts of speech | | * § 59. Classification of the parts of speech |
|
| |
|
| VIII. CONNECTIVE OPERATIONS AND MODALITIES | | VIII. CONNECTIVE OPERATIONS AND MODALITIES |
|
| |
|
| § 60. Practical reasons for the introduction of connective operations | | * § 60. Practical reasons for the introduction of connective operations |
| § 61. Formal characterization of connective operations | | * § 61. Formal characterization of connective operations |
| § 62. The logical nature of connective operations | | * § 62. The logical nature of connective operations |
| § 63. Relative nomological statements | | * § 63. Relative nomological statements |
| § 64. The semi-adjunctive implication | | * § 64. The semi-adjunctive implication |
| § 65. Modalities | | * § 65. Modalities |
| § 66. Modal interpretation of connective operations | | * § 66. Modal interpretation of connective operations |
| | |
| Exercises
| |
|
| |
|
| Solutions
| |
|
| |
|
| Index | | *Exercises |
| | *Solutions |
| | *Index |
PREFACE
I. INTRODUCTION
- § 1. Logic and language
- § 2. Language
- § 3. Different levels of language
- § 4. Instrumental usage of language
- § 5. Definitions
II. THE CALCULUS OF PROPOSITIONS
- § 6. Propositional operations
- § 7. Truth tables
- § 8. Survey of possible operations. Tautologies
- § 9. Interpretation of tautological operations as connective operations
- § 10. Reduction of operations to other operations
- § 11. Derivations
- § 12. The rule of substitution
- § 13. The rule of replacement
- § 14. The rule of inference
- § 15. Secondary rules of inference
- § 16. Remarks on the method of derivation
III. THE SIMPLE CALCULUS OF FUNCTIONS
- § 17. Propositional functions
- § 18. Binding of variables
- § 19. Negation of operators
- § 20. The scope of an operator and the order of operators
- § 21. Synthetic assertions containing free argument variables
- § 22. Some concepts referring to functions
- § 23. Truth characters of one-place functions
- § 24. Definition of tautologies containing functions
- § 25. The use of case analysis for the construction of tautologies in propositional functions
- § 26. The rules of substitution and inference in the calculus of functions
- § 27. The rule for free variables
- § 28. Derivation of tautologies
- § 29. Secondary rules
- § 30. Derivations from synthetic premises
- § 31. The formal and the material conception of language
- § 32. The proof of consistency
- § 33. Two objections against the proof of consistency
- § 34. Logical evidence
V. THE CALCULUS OF CLASSES
- § 35. Classes
- § 36. The syllogism
- § 37. The principle of abstraction
- § 38. Classes of couples, triplets, and so on
VI. THE HIGHER CALCULUS OF FUNCTIONS
- § 39. Functions of higher types
- § 40. The antinomies and the theory of types
- § 41. The technique of the higher calculus
- § 42. The treatment of indefinite expressions
- § 43. The relation of identity
- § 44. The definition of number
VII. ANALYSIS OF CONVERSATIONAL LANGUAGE
- § 45. The deficiencies of traditional grammar
- § 46. Proper names
- § 47. Descriptions
- § 48. The problem of individuals
- § 49. Fictitious existence
- § 50. Token-reflexive words
- § 51. The tenses of verbs
- § 52. Classification of functions
- § 53. Functions of higher types
- § 54. Descriptional functions
- § 55. Logical terms in a syntactical capacity
- § 56. Logical terms in a semantical capacity
- § 57. Logical terms in a pragmatic capacity
- § 58. Extraneous terms
- § 59. Classification of the parts of speech
VIII. CONNECTIVE OPERATIONS AND MODALITIES
- § 60. Practical reasons for the introduction of connective operations
- § 61. Formal characterization of connective operations
- § 62. The logical nature of connective operations
- § 63. Relative nomological statements
- § 64. The semi-adjunctive implication
- § 65. Modalities
- § 66. Modal interpretation of connective operations
- Exercises
- Solutions
- Index