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| Russel B. — Principles of Mathematics |
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| Предметный указатель |
Grammar 42 497
Grassmann 376
Gravitation 485 487 490 491
greater 122 159 222 306 323 364
Groups, continuous 436
Hamilton 376
Harmonic relation 384
Hegel 105 137 1287 346 355
Helmholtz 241
Hertz 494—496
Heymans 489
hilbert 384n. 405n. 415n.
Idea and object 450
Identity 20 96 219 502
Identity and denoting 63
Identity of Indiscemibles 451
Identity, distinguished from equality 21
Imaginaries 376
Impenetrability 467 480
Implication, formal 5 11 14 36—41 89 106 518
Implication, formal and any, etc. 91
Implication, formal, asserts a class of material implications 38
Implication, material 14 26 33—36 106 203n.
Implication, material, Frege's theory of 518
Importation 16
Inclusion, of classes 19 36 40 78
Incommensurables 287 438 439
Incompatibility, synthetic 233
Indefinables v 112
Indication 502
Individual, relation to class 18 19 26 77 103 512 522
Individual, relation to class, distinct from class whose only member it is? vi 23 68 106 130 513 514 517
Induction 11n. 441
Induction, mathematical 123 192 240 245 246 248 260 307 314 315 357 371 520
Inertia, law of 482
Inextensive 342
Inference, asyllogistic 10
Inference, asyllogistic and deduction 11n.
Inference, asyllogistic, logical and psychological 33
Inference, asyllogistic, two premisses unnecessary 35
Infinite 121 259 260 315 368
Infinite as limit of segments 273
Infinite, antinomies of 188 190 355
Infinite, improper 331—337
Infinite, mathematical theory of 304 355
Infinite, not specially quantitative 194
Infinite, orders of 335
Infinite, philosophy of 355—368
Infinitesimal 188 260 276 325 330 331—331
Infinitesimal and change 347
Infinitesimal and continuity 344
Infinitesimal, defined 331
Infinitesimal, instances of 332
Infinitesimal, philosophy of 338—345
Integers, infinite classes of 299 310n.
Integral, definite 329
Intensity 164
Interaction 446 453
Intuition 260 339 456
Involution 385 426
IS 49 64n. 100 106
Isolated points 290
Jevons 376
Johnson, viii 435n.
JORDAN 329n.
Kant 4 143 158 168 177 184 223n. 227 259 326 339 342 355 373 442 446 450 454 456—461 489
Kerry 505 520—522
Killing 400n. 404n. 405n. 415n. 434n.
Kinetic axes 490
Kirchoff 474
Klein 385 389 390421 422n. 424n. 426n. 434n. 436
kronecker 241
Lav 268
Leibniz 5 10 132 143 144 145 222 227 228 252 287 306 325 329n. 338 342 347 355 410 440n. 445 450 451 456 461 489 492
Lie 436
Likeness 242 261 262 317 321
Limitation, principle of 314
Limiting-point 290 323
Limits 276ff. 320 361
Limits and continuity 353
Limits and infinity 188 189 260
Limits and magnitude 341
Limits and the infinitesimal calculus 325 339
limits of functions 327 328
Limits, conditions for existence of 291ff. 389
Line see "Straight"
Line-Geometry 432
Linearity, axiom of 181 252 254 408
Lobatchewsky 373
Logic, symbolic 10—32
Logic, symbolic and mathematics v 5 8 106 397 429 457
Logic, symbolic, three parts of 11
Lotze 221 446ff.
Macaulay 491
Mach 474 489 492
Magnitude 159 164ff. 194
Magnitude and divisibility 173
Magnitude and existence 174 177 342
Magnitude, absolute theory of 164
Magnitude, axioms of 163 165 168
Magnitude, discrete and continuous 193 346
Magnitude, extensive 182
Magnitude, infinitesimal 332
Magnitude, intensive 182 326 342
Magnitude, kinds of 164 334
Magnitude, limiting 341
Magnitude, positive and negative 229—231
Magnitude, relative theory of 162
Manifold 67
Mass 481n. 483 488 495
Mass, centre of 490
Mathematics, pure vii 3 106 112 397 429 456 497
Mathematics, pure, applied 5 8 112 429
Mathematics, pure, arithmetization of 259
Matter 465—468
Matter as substance 466
Matter, logical definition of 468
Matter, relation to space and time 467
Maxwell 489
McColl 12 13 22
Meaning 47 502
Measure, Zeno's argument of 352
Measurement 157 176—183 195
Meinong 55n. 162n. 168 171n. 173 184 187 252 253 289 419 502n. 503
Mill 373 522
Moebius net 385 388
Monadism 476
Monism 44 447
Moore viii 24 44n. 51n. 446n. 448n. 454n.
Motion 265 344 405 469—473
Motion in geometry 406 418
Motion, absolute and relative 489—493
Motion, Hertz's law of 495
Motion, Laws of 482—488
Motion, logical definition of 473
Motion, state of 351 473
Motions, kinematical 480
Motions, kinematical, kinetic 480
Motions, kinematical, natural 495
Motions, kinematical, possible 495
Motions, kinematical, thinkable 494
Multiplication, arithmetical 119 307 308
Multiplication, arithmetical, ordinal 318
Necessity 454
Negation, of propositions 18 31
Negation, of propositions of classes 23 31 524
Negation, of propositions of relations 25
Neumann 490
Newton 325 338 469 481 482—492
NOEL 348 352
| NTH 243 250 312
Null-class vi 22 23 32 38 68 73 106 517 525
Number, algebraical generalization of 267
Number, cardinal, logical theory of 111ff. 241 519 520—522
Number, cardinal, logical theory of and classes 112 305 306 519
Number, cardinal, logical theory of as a logical type 525
Number, cardinal, logical theory of of cardinal numbers 362
Number, cardinal, logical theory of of classes 362
Number, cardinal, logical theory of of finite integers 122 309 364
Number, cardinal, logical theory of of propositions 362 526 527
Number, cardinal, logical theory of of the continuum 310 364
Number, cardinal, logical theory of, addition of 118 307
Number, cardinal, logical theory of, Cantor's definition of 304
Number, cardinal, logical theory of, Dedekind's definition of 247 249
Number, cardinal, logical theory of, definable? 111 112 130
Number, cardinal, logical theory of, defined 115 305
Number, cardinal, logical theory of, defined by abstraction 114
Number, cardinal, logical theory of, finite 124 260 357
Number, cardinal, logical theory of, is there a greatest? 101 362ff.
Number, cardinal, logical theory of, multiplication of 119 307 308
Number, cardinal, logical theory of, transfinite 112 260 304—311
Number, cardinal, logical theory of, well-ordered 323 364
Number, ordinal 240 319
Number, ordinal of finite ordinals 243 313
Number, ordinal, addition of 317
Number, ordinal, Dedekind's definition of 248
Number, ordinal, defined 242 317
Number, ordinal, division of 318
Number, ordinal, finite 243 260
Number, ordinal, multiplication of 318
Number, ordinal, no greatest 323 364
Number, ordinal, not prior to cardinal 241 249—251
Number, ordinal, positive and negative 244
Number, ordinal, second class of 312 315 322
Number, ordinal, subtraction of 317
Number, ordinal, transfinite 240n. 260 312—324
Number, ordinal, two principles of formation of 313
Number, relation- 262 321
Numbers, complex 372 376ff. 379
Numbers, complex, ordinal, series of 323
Numbers, complex, positive and negative 229
Numbers, complex, real 270
Numbers, irrational 157 270ff. 320
Numbers, irrational, arith-metical theories of 277ff.
Numbers, rational 149ff. 259 335
Numbers, rational, cardinal number of 310
Numbers, rational, ordinal type of 296 316 320
Object 55n.
Occupation (of space or time) 465 469 471
of quantities 159
One 241 356 520
One, applicable to individuals or to classes? 130 132 517
One, definable? 112 130 135
Oppositeness 96 205
Order 199ff. 207—217 255
Order and infinity 188 189 191 195
Order in descriptive space 394 395
Order in projective space 385ff. 389
Order, cyclic 199
Order, not psychological 242
Ordinal element 200 353
Padoa 111n. 114n. 125 205
Parallelism, psychophysical 177
Parallelogram law 477
Parallels, Axiom of 404
Part 360
Part, ordinal 361
Part, proper 121 246n.
Part, similarity to whole 121 143 306 316 350 355 358 371
Part, three kinds of 138 143
Pascal 420
Pasch 390n. 391n. 393ff. 407n. 417
Peano vi vii 4 10ff. 23 26—32 36 62 68 76ff. 111 114 115 131 139 142 152 159n. 163n. 199 205n. 219 241n. 248 270 290 300n. 328n. 334 335 341 360 410 437 443 501 514 519
Peano on descriptive geometry 393ff.
Peano on real numbers 274
Peano on theory of vectors 432
Peano, hie indefinables 27 112
Peano, his Arithmetic 124—128 238n.
Peano, his indemon-strablee 29
Pearson 474 489
Peirce 23 26 203n. 232n. 320n. 376 387n.
Pencils of planes 400
Perception, its function in philosophy v 129
permutations 316
Philosophy, of Mathematics 4 226
Philosophy, of Mathematics and Mathematics 338
Philosophy, of Mathematics, distinguished from Mathematics 128
Pieri 199 216n. 382ff. 410 421
Planes, projective 384
Planes, projective, descriptive 398
Planes, projective, ideal 400 402
Planes, projective, kinds of 391
Planes, projective, metrical 410
Plato 73 355 357 438 446
Pleasure, quantity of 162 174
Pleasure, quantity of and pain 233n.
Pleasure, quantity of, magnitude of 164
Pluralism viii
Poincare 347
Point-pairs 426
POINTS 382 394 437 443
Points, ideal 400
Points, imaginary 420
Points, indiscernible? 446 451
Points, logical objections to 445—455
Points, material 445
Points, proper and improper ideal 423
Points, rational and irrational 389
Position, absolute and relative 220 221 444ff.
Power 364n. see cardinal"
predicates 46 56
Predicates, predicable of themselves 96 97 102
Premiss, empirical 441
presentations 446 450
Primes, ordinal 319
Process, endless see "Regress"
Product, logical, of classes 21
Product, logical, of propositions 16 519 527
Product, relative 28 98
Progressions 199 239ff. 247 283 313 314 520
Progressions, existence of 322 497
Projection 390 393
Proper names 42 44 502
Propositions ix 13 15 211 502 525
Propositions, can they be infinitely complex? 145
Propositions, cardinal "number of 367
Propositions, contradiction as to number of 527
Propositions, existential theory of viii 449 493
Propositions, unity of 50 51 107 139 466 507
Propositions, when analyzable into subject and assertion 83ff. 106 505—510
Quadratic forms 104 512 514
Quadrics 403
Quadrilateral construction 333 384
Quadrilateral construction in metrical geometry 417
quantity 159
Quantity and infinity 188
Quantity, does not occur in pure mathematics 158 419
Quantity, not always divisible 160 170
Quantity, range of 170—175
Quantity, relation to number 157 158 160
Quantity, sometimes a relation 161 172
Quaternions 432
ranges 511ff. 524
Ranges, double 512
Ranges, extensional or in-tensional? 511
ratio 149 335
Rays 231 398 414
Rays, order of 415
Reality, Kant's category of 342 344
Reduction 17
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