Book:Alfred North Whitehead/Principia Mathematica/Volume 1

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

Published $\text {1910}$, Merchant Books

ISBN 978-1-60381-182-3

Subject Matter

• Mathematical Logic

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

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• 1910: Alfred North Whitehead and Bertrand Russell: Principia Mathematica: Volume $\text { 1 }$ ... (previous): Chapter $\text{I}$: Preliminary Explanations of Ideas and Notations