Book:Alfred North Whitehead/Principia Mathematica/Volume 1

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

Published $\text {1910}$, Merchant Books

ISBN 978-1-60381-182-3

Subject Matter


PREFACE (A.N.W, B.R. Cambridge, November, 1910)
Chapter I. Preliminary Explanations of Ideas and Notations
Chapter II. The Theory of Logical Types
Chapter III. Incomplete Symbols

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

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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