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Russel B. — Principles of Mathematics
Russel B. — Principles of Mathematics



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Название: Principles of Mathematics

Автор: Russel B.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 534

Добавлена в каталог: 17.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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