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| Russel B. — Principles of Mathematics |
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| Предметный указатель |
Absolute 226 448
Abstraction, Principle of ix 166 219 242 285 305 314 497 519
Acceleration 474 483
Acceleration, absolute 490 491
Achillea and the tortoise 350 358
Action and reaction 483
Activity 450
Addition of individuals 71 133—135
Addition of quantities 179 180
Addition of relations 321
Addition of vectors 477
Addition, arithmetical 118 307
Addition, logical 17 21 116
Addition, ordinal 318
Addition, relational 182 254
Addition, relative 26 387n.
Adjectives 20n. 42
aggregates 67 139 442
Aggregates and classes as one 141
Aggregates, infinite 143
Algebra, universal 376
Aliorelative 203n. 320n.
ALL 72 105 113 305
Analysis, conceptual and real 466
Analysis, how far falsification 141 466
AND 67 69 71 130
angles 205 414
Angles, axioms of 415 416
Anharmonic ratio 390 391 420
Antinomies, of infinity 188 190—193
Antinomies, of infinity, Kant's 259 458—461
ANY 45 46 57 105 263 305 351
Any and kindred words 55 56 59 89 91
Archimedes, axiom of 181 252 254 288 332 333 837 408
Area 333 417
Arithmetic and progressions 240
Arithmetic, has no indemonstrables 127
Arithmetic, relation- 321
Arrow, Zeno's argument of 350
assertion 34—35 48 100 502ff.
assertions 39 44 82 83 98 106 505
Associative law 307
assumptions 503
Axioms, In geometry 373 441
Being 43 49 71 446 449
Bernouilli 329n.
Bernstein 306n. 367n.
Bettazzi 181n. 185
BETWEEN 200 201 205 207 214
Between and difference of sense 211
Between in descriptive Geometry 393
Between in projective Geometry 391 393 426
Between, indefinable? 213
Between, is a relation between its terms? 210
Between, three theories of 208
Bight and left 223 231 417
Bolyai 373
Bolzano 70 201n. 307 357n.
Boole 10 24 376
Borel 306n. 367n.
Bradley 41 43n. 47 90 99 161ff. 221 224 448 471
Burali-Forti 112n. 323 364n.
Calculus of classes 18—23
Calculus of relations 23—26
Calculus, infinitesimal 259 276 304 325—330 338ff.
Calculus, logical 142
Calculus, prepositional 13—18
Calculus, principles of a 376
Cantor, Georg viii 101 111 112 119 120 121n. 144 157 161 177 199 239 259ff. 267 270ff. 282 331 334 347 350 353 371 375 381 390 437ff. 444 527
Cantor, Georg, against greatest number 363ff.
Cantor, Georg, on continuity 287ff.
Cantor, Georg, on infinitesimal segments 335
Cantor, Georg, on irrationals 283
Cantor, Georg, on orders of infinity 336
Cantor, Georg, on transfinite cardinals 304—311
Cantor, Georg, on transfinite ordinals 312—324
Carroll, Lewis 18n. 35
Cassirer 287n.
Cauchy 329n.
Causal laws 481 486
Causality 474—479 481
Causality in rational dynamics 479
Causation, of particulars by particulars vii 475 477 481 487
Cause, equal to effect? 496
Cayley 422n.
Chain 245 246
Chain of an element 245 246
Change 347 469ff.
Chasles 420
Circle, postulate of 438 440
class v ix 18ff. 40 66—81 349 356 497 510ff.
Class and well-ordered series 322
Class as many 68 76 104 106 132
Class as one 76 103 104 106 132 513 523
Class of one term see "Individual"
Class of terms not having a given relation to themselves 102
Class, always definable by a predicate? 98 526
Class, concept of 67
Class, defined by relation 97 98
Class, denumerable 309
Class, extensional view of 20 67 69 131ff. 513 526
Class, infinite 72 106 260 306 356 357
Class, intensional genesis of 67 515
Class, multiplicative 308
Class, when a member of itself 102
Class-concept 19 20 54 56 58 67 101 113
Class-concept, distinct from class 68 116 131 514
Clifford 434
Cohen 276n. 326 338—345
collections 69 133 140 513 514
Colours 466 467
Commutative law 118 240 307 312
composition 17 31
concepts 44 211 508
Concepts as such and as terms 45
Concepts, can they be subjects? 46 507 510
Concepts, propositional 503 526
Concepts, variation of 86
Congruent figures 417
Conjunction, numerical 57 67 72 113 131ff.
Conjunction, numerical, propositional 57
Conjunction, numerical, variable 57
Connection 202 239
consecutive 201
Constants, logical 3 7 8 11 106 429
Constants, logical and parameters 6
Constituent of a proposition 356 510
Constituent of a whole 143 144
Continuity 188 193 259 286ff. 368
Continuity in projective Geometry 387 390 437
Continuity of Euclidean space 438ff.
Continuity, antinomies of 347ff.
Continuity, Dedekind's axiom of 279 294
Continuity, ordinal 296—303
Continuity, philosophy of 346—354
Continuum in mathematical sense 297 299n. 310
Continuum in philosophical sense 146 440
Continuum, composed of elements 3447 347 353 440ff.
Continuum, primarily arithmetical 444
Contradiction, the vi ix 20 66 79 97 101—107 305 362 513 515 517 523 524 525
Contradiction, the, Frege's solution of 522
Contradiction, the, law of 455
Conturat 66 194n. 267n. 291n. 296n. 310n. 326n. 410n. 441n.
coordinates 439
Coordinates, projective 385 388 390 422 427
Correlation 260
Correlation of classes 261
Correlation of series 261 321
Counting 114 133 309
Couples and transitive asymmetrical relations 215 238
| Couples in projective geometry 386 387
Couples with sense 99 512 524
Couples, are relations classes of? 24 99 524
Couples, separation of 200 205 214 237
Cremona 384n. 420
De Morgan 23 64n. 218n. 219n. 326 376
Dedekind 90 111 157 199 239n. 245—251 294 307 315 357n. 381 387 438
Dedekind on irrationals 278ff.
Deduction 522
Deduction, principles of 4 15 16
Definition 15 27 111 429 497
Definition and the 62
Definition by abstraction 114 219 249
Definition, always nominal 112
Denoting 45 47 53 106 131
Denoting and any, etc. 55 62
Denoting and identity 63
Denoting and infinite classes 72 73 145 350
Denoting and predicates 54
Denoting, are there different kinds of? 56 61
Derivatives, of a series 290ff. 323
Derivatives, of a series of functions 328
Descartes 157
Dichotomy, Zeno's argument of 348
Differential coefficients 173 328
dimensions 372 374
Dimensions, axiom of three 388 399
Dimensions, definable logically 376
Dini 324n. 327 328n. 329n.
Direction 435
Disjunction 15n. 17 31
Disjunction, variable and constant 22 58
Distance 171 179 182n. 195 252—256 288 353
Distance and limits 254
Distance and order 204 409 419
Distance and relative position 252
Distance and straight line 410
Distance and stretch 254 342 352 408ff. 435
Distance in Arithmetic 254
Distance, axioms of 407ff. 413 424
Distance, definition of 253
Distance, descriptive theory of 423—425
Distance, measurement of 180 181 254 408
Distance, not implied by order 252 254
Distance, projective theory of 422 425 427
Distributive law 240 307
Diversity 23
Diversity, conceptual 46
Divisibility and measurement 178
Divisibility, infinite 460
Divisibility, magnitude of 149 151 153 173 230 333 345 411 425 428
Divisibility, not a property of wholes as such 179 412
Domain see "Relation"
Du Bois Beymond 181n. 254 336
Duality, geometrical 375 392
Duality, logical 26
Dynamics as pure mathematics 465
Dynamics as pure mathematics, two principles of 496
Economics, mathematical 233n.
electricity 494 496
Empiricism 373 492
Epistemology 339
Equality 219 339
Equality of classes 21
Equality of relations 24
Equivalence, of propositions 15 527
Ether 485 496
Euclid 157 287 373 404 420 438
Euclid, his errors 405—407
Euler 329n.
Evellin 352
Existence vii 449 458 472
Existence of a class 21 32
Existence-theorems ix 322 431 497
Existence-theorems and Euclid's problems 404
exponentiation 120 308
Exportation 16
Extension and intension 66
Fano 385n.
Field see "Relation"
finite 121 192 371
Finitude, absolute and relative 332
Finitude, axiom of 188 191 460
force 474 482
Formal truth 40 105
Formalism, limits of 16 41
Formula 267
Fractions 149 150 151
Frege, his Arithmetic 519
Frege, his Begriff 505 507
Frege, his sign of judgment 503 519
Frege, his Symbolic Logic 518
Frege, his theory of progressions 520
Frege, his theory of ranges 505 510ff.
Frege, his three elements in judgment 502
Frege, Kerry's criticism of 520
Frege, three points of disagreement with 501
Fregevi viii 19 68n. 78n. 111 124n. 132 142 451n. 501ff.
Frischauf 410
Functions 32 262 263
Functions, complex 266 376
Functions, continuous 326
Functions, Frege's theory of 505ff.
Functions, non-serial 263
Functions, numerical 265
Functions, propositional 13 19 82—88 92 263 356 508ff.
Functions, propositional and classes 19 88 93 98
Functions, propositional and the contradiction 103
Functions, propositional with two variables 94 506
Functions, propositional, cardinal number of 367
Functions, propositional, definable? 83
Functions, propositional, indefinable 88 106
Functions, propositional, more numerous than terms? 103
Functions, propositional, range of significance of 523
Functions, propositional, variable 103 104
Functions, real 324
Fundamental bodies 491
Generalization 7
Generalization, algebraical 267 377
Geometry 199 372
Geometry and actual space 372 374
Geometry and order 419
Geometry, based on distance 410 492
Geometry, descriptive 199 382 393—403
Geometry, descriptive, and. distance 423—425
Geometry, descriptive, axioms of 394ff.
Geometry, descriptive, indefinables of 394 395 397
Geometry, descriptive, relation to projective Geometry 400ff.
Geometry, descriptive, their mutual independence 396
Geometry, distance and stretch theories of 181
Geometry, elliptic 206 382 391 399 413
Geometry, elliptic of position 393
Geometry, elliptic, Euclidean 391 399 442
Geometry, elliptic, hyperbolic 255 382 391 399
Geometry, elliptic, non-Euclidean 158 179 255 373 381 436
Geometry, has no indemonstrables 429
Geometry, metrical 382 392 403 404—418
Geometry, metrical and distance 407
Geometry, metrical and quantity 407
Geometry, metrical and stretch 414
Geometry, metrical, relation to projective and descriptive Geometry 419—428
Geometry, projective 199 206 381—392
Geometry, projective and distance 421 425 427
Geometry, projective and order 385ff. 389 421
Geometry, projective, differences from descriptive Geometry 419
Geometry, projective, history of 420
Geometry, projective, independent of metrical Geometry 419—421
Geometry, projective, requires three dimensions 394 399n.
Geometry, three kinds of 381
Gilman 203n.
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