# Book:Alfred North Whitehead/Principia Mathematica/Volume 1

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## Alfred North Whitehead and Bertrand Russell:

## Alfred North Whitehead and Bertrand Russell: *Principia Mathematica, Volume $\text { 1 }$*

Published $1910$, **Merchant Books**

- ISBN 978-1-60381-182-3.

### Subject Matter

### Contents

- PREFACE (A.N.W, B.R. Cambridge,
*November*, 1910)

- INTRODUCTION
- Chapter I. Preliminary Explanations of Ideas and Notations
- Chapter II. The Theory of Logical Types
- Chapter III. Incomplete Symbols

- PART I. MATHEMATICAL LOGIC
- Summary of Part I

- Section A. The Theory of Deduction

- $*$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

- Section B. Theory of Apparent Variables

- $*$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

- Section C. Classes and Relations

- $*$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

- Section D. Logic 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

- Section E. Products and Sums of Classes

- $*$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

- Section A. Unit Classes and Couples

- $*$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 $2_r$

- Section B. Sub-Classes, Sub-Relations, and Relative Types

- $*$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

- Section C. One-Many, Many-One, and One-One Relations

- $*$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

- Section D. Selections

- $*$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

- Section E. Inductive Relations

- $*$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