Table of Contents

1. Chapter I. Definition of Pure Mathematics

   1. § 1. Definition of pure mathematics
   2. § 2. The principles of mathematics are no longer controversial
   3. § 3. Pure mathematics uses only a few notions, and these are logical constants
   4. § 4. All pure mathematics follows formally from twenty premisses
   5. § 5. Asserts formal implications
   6. § 6. And employs variables
   7. § 7. Which may have any value without exception
   8. § 8. Mathematics deals with types of relations
   9. § 9. Applied mathematics is defined by the occurrence of constants which are not logical.
   10. § 10. Relation of mathematics to logic.

2. Chapter II. Symbolic Logic

   1. § 11. Definition and scope of symbolic logic
   2. § 12. The indefinables of symbolic logic
   3. § 13. Symbolic logic consists of three parts

   4. The Propositional Calculus

      1. § 14. Definition
      2. § 15. Distinction between implication and formal implication.
      3. § 16. Implication indefinable
      4. § 17. Two indefinables and ten primitive propositions in this calculus
      5. § 18. The ten primitive propositions
      6. § 19. Disjunction and negation defined

   5. The Calculus of Classes

      1. § 20. Three new indefinables
      2. § 21. The relation of an individual to its class
      3. § 22. Propositional functions
      4. § 23. The notion of such that
      5. § 24. Two new primitive propositions
      6. § 25. Relation to propositional calculus
      7. § 26. Identity

   6. The Calculus of Relations

      1. § 27. The logic of relations essential to mathematics
      2. § 28. New primitive propositions
      3. § 29. Relative products
      4. § 30. Relations with assigned domains

   7. Peano's Symbolic Logic

      1. § 31. Mathematical and philosophical definitions
      2. § 32. Peano’s indefinables
      3. § 33. Elementary definitions
      4. § 34. Peano’s primitive propositions
      5. § 35. Negation and disjunction
      6. § 36. Existence and the null-class

3. Chapter III. Implication and Formal Implication

   1. § 37. Meaning of implication
   2. § 38. Asserted and unasserted propositions
   3. § 39. Inference does not require two premisses
   4. § 40. Formal implication is to be interpreted extensionally
   5. § 41. The variable in formal implication has an unrestricted field
   6. § 42. A formal implication is a single propositional function, not a relation of two
   7. § 43. Assertions
   8. § 44. Conditions that a term in an implication may be varied
   9. § 45. Formal implication involved in rules of inference

4. Chapter IV. Proper Names, Adjectives and Verbs

   1. § 46. Proper names, adjectives and verbs distinguished
   2. § 47. Terms
   3. § 48. Things and concepts
   4. § 49. Concepts as such and as terms
   5. § 50. Conceptual diversity
   6. § 51. Meaning and the subject-predicate logic
   7. § 52. Verbs and truth
   8. § 53. All verbs, except perhaps is, express relations
   9. § 54. Relations per se and relating relations
   10. § 55. Relations are not particularized by their terms

5. Chapter V. Denoting

   1. § 56. Definition of denoting
   2. § 57. Connection with subject-predicate propositions
   3. § 58. Denoting concepts obtained from predicates
   4. § 59. Extensional account of all, every, any, a and some
   5. § 60. Intensional account of the same
   6. § 61. Illustrations
   7. § 62. The difference between all, every, etc. lies in the objects denoted, not in the way of denoting them.
   8. § 63. The notion of the and definition
   9. § 64. The notion of the and identity
   10. § 65. Summary

6. Chapter VI. Classes

   1. § 66. Combination of intensional and extensional standpoints required
   2. § 67. Meaning of class
   3. § 68. Intensional and extensional genesis of classes
   4. § 69. Distinctions overlooked by Peano
   5. § 70. The class as one and as many
   6. § 71. The notion of and
   7. § 72. All men is not analyzable into all and men
   8. § 73. There are null class-concepts, but there is no null class
   9. § 74. The class as one, except when it has one term, is distinct from the class as many
   10. § 75. Every, any, a and some each denote one object, but an ambiguous one
   11. § 76. The relation of a term to its class
   12. § 77. The relation of inclusion between classes
   13. § 78. The contradiction
   14. § 79. Summary

7. Chapter VII. Propositional Functions.

   1. § 80. Indefinability of such that
   2. § 81. Where a fixed relation to a fixed term is asserted, a propositional function can be analysed into a variable subject and a constant assertion
   3. § 82. But this analysis is impossible in other cases
   4. § 83. Variation of the concept in a proposition
   5. § 84. Relation of propositional functions to classes
   6. § 85. A propositional function is in general not analysable into a constant and a variable element

8. Chapter VIII. The Variable.

   1. § 86. Nature of the variable
   2. § 87. Relation of the variable to any
   3. § 88. Formal and restricted variables
   4. § 89. Formal implication presupposes any
   5. § 90. Duality of any and some
   6. § 91. The class-concept propositional function is indefinable
   7. § 92. Other classes can be defined by means of such that
   8. § 93. Analysis of the variable

9. Chapter IX. Relations

   1. § 94. Characteristics of relations
   2. § 95. Relations of terms to themselves
   3. § 96. The domain and the converse domain of a relation
   4. § 97. Logical sum, logical product and relative product of relations
   5. § 98. A relation is not a class of couples
   6. § 99. Relations of a relation to its terms

10. Chapter X. The Contradiction

    1. § 100. Consequences of the contradiction
    2. § 101. Various statements of the contradiction
    3. § 102. An analogous generalized argument
    4. § 103. Various statements of the contradiction
    5. § 104. The contradiction arises from treating as one a class which is only many
    6. § 105. Other primâ facie possible solutions appear inadequate
    7. § 106. Summary of Part I