Page:Russell, Whitehead - Principia Mathematica, vol. I, 1910.djvu/12

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Contents
Page
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