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

Title Principia Mathematica, I
Author Bertrand Russell, Alfred North Whitehead
Editor Cambridge, University Press
Year 1910
Location Cambridge
Source djvu
Progress To be proofread
Transclusion Index not transcluded or unreviewed
Volumes III
Pages (key to Page Status)
ToC ToC ToC ii iii iv v vi vii viii ix x 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666
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