Book:Alfred North Whitehead/Principia Mathematica/Volume 1

Subject Matter

 * Mathematical Logic

Contents

 * PREFACE


 * INTRODUCTION


 * PART I. MATHEMATICAL LOGIC
 * Summary of Part I




 * $*$1. Primitive Ideas and Propositions
 * $*$2. Immediate Consequences of the Primitive Propositions
 * $*$3. The Logical Product of two Propositions
 * $*$4. Equivalence and Formal Rules
 * $*$5. Miscellaneous Propositions




 * $*$9. Extension of the Theory of Deduction from Lower to Higher Types of Propositions
 * $*$10. Theory of Propositions containing one Apparent Variable
 * $*$11. Theory of two Apparent Variables
 * $*$12. The Hierarchy of Types and the Axiom of Reducibility
 * $*$13. Identity
 * $*$14. Descriptions




 * $*$20. General Theory of Classes
 * $*$21. General Theory of Relations
 * $*$22. Calculus of Classes
 * $*$23. Calculus of Relations
 * $*$24. The Universal Class, the Null-Class, and the Existence of Classes
 * $*$25. The Universal Relation, the Null Relation, and the Existence of Relations




 * $*$30. Descriptive Functions
 * $*$31. Converses of Relations
 * $*$32. Referents and Relata of a given Term with respect to a given Relation
 * $*$33. Domains, Converse Domains, and Fields of Relations
 * $*$34. The Relative Product of two Relations
 * $*$35. Relations with Limited Domains and Converse Domains
 * $*$36. Relations with Limited Fields
 * $*$37. Plural Descriptive Functions
 * $*$38. Relations and Classes derived from a Double Descriptive Function


 * Note to Section D




 * $*$40. Products and Sums of Classes of Classes
 * $*$41. The Product and Sum of a Class of Relations
 * $*$42. Miscellaneous Propositions
 * $*$43. The Relations of a Relative Product to its Factors


 * PART II. PROLEGOMENA TO CARDINAL ARITHMETIC
 * Summary of Part II




 * $*$50. Identity and Diversity as Relations
 * $*$51. Unit Classe
 * $*$52. The Cardinal Number $1$
 * $*$53. Miscellaneous Propositions involving Unit Classes
 * $*$54. Cardinal Couples
 * $*$55. Ordinal Couples
 * $*$56. The Ordinal Number $2_r$




 * $*$60. The Sub-Classes of a Given Class
 * $*$61. The Sub-Relations of a Given Relation
 * $*$62. The Relationship of Membership of a Class
 * $*$63. Relative Types of Classes
 * $*$64. Relative Types of Relations
 * $*$65. On the Typical Definition of Ambiguous Symbols




 * $*$70. Relations whose Classes of Referents and of Relata belong to given Classes
 * $*$71. One-Many, Many-One, and One-One Relations
 * $*$72. Miscellaneous Propositions concerning One-Many, Many-One, and One-One Relations
 * $*$73. Similarity of Classes
 * $*$74. On One-Many and Many-One Relations with Limited Fields




 * $*$80. Elementary Properties of Selections
 * $*$81. Selections from Many-One Relations
 * $*$82. Selections from Relative Products
 * $*$83. Selections from Classes of Classes
 * $*$84. Classes of Mutually Exclusive Classes
 * $*$85. Miscellaneous Propositions
 * $*$86. Conditions for the Existence of Selections




 * $*$90. On the Ancestral Relation
 * $*$91. On Powers of a Relation
 * $*$92. Powers of One-Many and Many-One Relations
 * $*$93. Inductive Analysis of the Field of a Relation
 * $*$94. On Powers of Relative Products
 * $*$95. On the Equi-factor Relation
 * $*$96. On the Posterity of a Term
 * $*$97. Analysis of the Field of a Relation into Families