# Index:Russell, Whitehead - Principia Mathematica, vol. I, 1910.djvu

Title Principia Mathematica, I Bertrand Russell, Alfred North Whitehead Cambridge, University Press 1910 Cambridge djvu To be proofread Index not transcluded or unreviewed I - II

Pages   (key to Page Status)

CONTENTS OF VOLUME I

PAGE

PREFACE....................................................................................................................................................................................................................................................v

INTRODUCTION....................................................................................................................................................................................................................................................1

Chapter I. Preliminary Explanations of Ideas and Notations.................................................................................................................................................................................................................................................... 4

Chapter II. The Theory of Logical Types.................................................................................................................................................................................................................................................... 39

Chapter III. Incomplete Symbols.................................................................................................................................................................................................................................................... 69

PART I. MATHEMATICAL LOGIC.

Summary of Part I.................................................................................................................................................................................................................................................... 91

Section A. The Theory of Deduction.................................................................................................................................................................................................................................................... 94

*1. Primitive Ideas and Propositions.................................................................................................................................................................................................................................................... 95

*2. Immediate Consequences of the Primitive Propositions.................................................................................................................................................................................................................................................... 102

*3. The Logical Product of two Propositions.................................................................................................................................................................................................................................................... 114

*4. Equivalence and Formal Rules.................................................................................................................................................................................................................................................... 120

*5. Miscellaneous Propositions.................................................................................................................................................................................................................................................... 128

Section B. Theory of Apparent Variables.................................................................................................................................................................................................................................................... 132

*9. Extension of the Theory of Deduction from Lower to Higher Types of Propositions.................................................................................................................................................................................................................................................... 132

*10. Theory of Propositions containing one Apparent Variable.................................................................................................................................................................................................................................................... 143

*11. Theory of two Apparent Variables.................................................................................................................................................................................................................................................... 157

*12. The Hierarchy of Types and the Axiom of Reducibility.................................................................................................................................................................................................................................................... 168

*13. Identity.................................................................................................................................................................................................................................................... 176

*14. Descriptions.................................................................................................................................................................................................................................................... 181

Section C. Classes and Relations.................................................................................................................................................................................................................................................... 196

*20. General Theory of Classes.................................................................................................................................................................................................................................................... 196

*21. General Theory of Relations.................................................................................................................................................................................................................................................... 211

*22. Calculus of Classes.................................................................................................................................................................................................................................................... 217

*23. Calculus of Relations.................................................................................................................................................................................................................................................... 226

*24. The Universal Class, the Null-Class, and the Existence of Classes.................................................................................................................................................................................................................................................... 229

*25. The Universal Relation, the Null Relation, and the Existence of Relations.................................................................................................................................................................................................................................................... 241

Section D. Logic of Relations.................................................................................................................................................................................................................................................... 244

*30. Descriptive Functions.................................................................................................................................................................................................................................................... 245

*31. Converses of Relations.................................................................................................................................................................................................................................................... 251

*32. Referents and Relata of a given Term with respect to a given Relation.................................................................................................................................................................................................................................................... 255

*33. Domains, Converse Domains, and Fields of Relations.................................................................................................................................................................................................................................................... 260

*34. The Relative Product of two Relations.................................................................................................................................................................................................................................................... 269

*35. Relations with Limited Domains and Converse Domains.................................................................................................................................................................................................................................................... 278

*36. Relations with Limited Fields.................................................................................................................................................................................................................................................... 291

*37. Plural Descriptive Functions.................................................................................................................................................................................................................................................... 293

*38. Relations and Classes derived from a Double Descriptive Function.................................................................................................................................................................................................................................................... 311

Note to Section D.................................................................................................................................................................................................................................................... 314

Section E. Products and Sums of Classes.................................................................................................................................................................................................................................................... 317

*40. Products and Sums of Classes.................................................................................................................................................................................................................................................... 319

*41. The Product and Sum of a Class of Relations.................................................................................................................................................................................................................................................... 331

*42. Miscellaneous Propositions.................................................................................................................................................................................................................................................... 336

*43. The Relations of a Relative Product to its Factors.................................................................................................................................................................................................................................................... 319

PART II. PROLEGOMENA TO CARDINAL ARITHMETIC.

Summary of Part II.................................................................................................................................................................................................................................................... 345

Section A. Unit Classes and Couples.................................................................................................................................................................................................................................................... 347

*50. Identity and Diversity as Relations.................................................................................................................................................................................................................................................... 349

*51. Unit Classes.................................................................................................................................................................................................................................................... 356

*52. The Cardinal Number 1.................................................................................................................................................................................................................................................... 363

*53. Miscellaneous Propositions involving Unit Classes.................................................................................................................................................................................................................................................... 368

*54. Cardinal Couples.................................................................................................................................................................................................................................................... 376

*55. Ordinal Couples.................................................................................................................................................................................................................................................... 383

*56. The Ordinal Number 2.................................................................................................................................................................................................................................................... 395

Section B. Sub-Classes, Sub-Relations, and Relative Types.................................................................................................................................................................................................................................................... 404

*60. The Sub-Classes of a given Class.................................................................................................................................................................................................................................................... 406

*61. The Sub-Relations of a given Realtion.................................................................................................................................................................................................................................................... 412

*62. The Relation of Membership of a Class.................................................................................................................................................................................................................................................... 414

*63. Relative Types of Classes.................................................................................................................................................................................................................................................... 419

*64. Relative Types of Relations.................................................................................................................................................................................................................................................... 429

*65. On the Typical Definition of Ambiguous Symbols.................................................................................................................................................................................................................................................... 434

Section C. One-Many, Many-One, and One-One Relations.................................................................................................................................................................................................................................................... 437

*70. Relations whose Classes of Referents and of Relata belong to given Classes.................................................................................................................................................................................................................................................... 439

*71. One-Many, Many-One, and One-One Relations.................................................................................................................................................................................................................................................... 446

*72. Miscellaneous Propositions concerning One-Many, Many-One, and One-One Relations.................................................................................................................................................................................................................................................... 462

*73. Similarity of Classes.................................................................................................................................................................................................................................................... 476

*74. On One-Many and Many-One Relations with Limited Fields.................................................................................................................................................................................................................................................... 490

Section D. Selections.................................................................................................................................................................................................................................................... 500

*80. Elementary Properties of Selections.................................................................................................................................................................................................................................................... 505

*81. Selections from Many-One Relations.................................................................................................................................................................................................................................................... 519

*82. Selections from Relative Products.................................................................................................................................................................................................................................................... 524

*83. Selections from Classes of Classes.................................................................................................................................................................................................................................................... 531

*84. Classes of Mutually Exclusive Classes.................................................................................................................................................................................................................................................... 540

*85. Miscellaneous Propositions.................................................................................................................................................................................................................................................... 549

*88. Conditions for the Existence of Selections.................................................................................................................................................................................................................................................... 561

Section E. Inductive Relations.................................................................................................................................................................................................................................................... 569

*90. On the Ancestral Relation.................................................................................................................................................................................................................................................... 576

*91. On Powers of a Relation.................................................................................................................................................................................................................................................... 585

*92. Powers of One-Many and Many-One Relations.................................................................................................................................................................................................................................................... 601

*93. Inductive Analysis of the Field of a Relation.................................................................................................................................................................................................................................................... 607

*94. On Powers of Relative Products.................................................................................................................................................................................................................................................... 617

*95. On the Equi-factor Relation.................................................................................................................................................................................................................................................... 626

*96. On the Posterity of a Term.................................................................................................................................................................................................................................................... 637

*97. Analysis of the Field of a Relation into Families.................................................................................................................................................................................................................................................... 654