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