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Beth E.W. — The foundations of mathematics: A study in the philosophy of science
Beth E.W. — The foundations of mathematics: A study in the philosophy of science



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Название: The foundations of mathematics: A study in the philosophy of science

Автор: Beth E.W.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-d edition

Год издания: 1966

Количество страниц: 754

Добавлена в каталог: 25.11.2012

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Предметный указатель
"Formally" and "materially" motivated elements (Bernays)      626
"Nichtgabelbar"      348f.
"Peano's arithmetic"      311 342 605
"Physique de l'objet quelconque" (Gonseth)      626 645
$F_{0}$      451 675
$M_{1}$      238ff. 669
$M_{2}$      241
$M_{3}$      241
$N_{2}$      242 668
$N_{3}$      242ff. 248 312ff. 668
$\omega$-complete, $\omega$-consistent      xxiii xxviii 314 595
$\sigma$-algebra (Boolean)      171 253
$\varepsilon$-axioms, $\varepsilon$-symbol, $\varepsilon$-theorems (Hilbert's)      14 223 227 253 535
$\varepsilon_{0}$ (ordinal number)      375
A      336ff. 510ff.
A, B (Bochvar)      506f.
Absolute entity      9 13
Absolute entity (principle of the)      9
Absolute entity, properties of relations      xxvii 412 571ff.
Absolutes      16
Abstract calculus      63
Abstract calculus, entity      464
Abstract calculus, field of sets      164
Abstract calculus, space (Frechet)      155
Abstraction      18 40 638 640
Abstraction (definition by)      80ff. 138 166 357 367 370 395 655
Absurdity      440ff.
Absurdo (ex)      191
Absurdum (reductio ad)      421
Ackermann, W.      73 202 230 293 300 386 389 510 586 655f. 659
Adaequatio rei et intellectus      76 340f.
Addison, J.W.      571 606
Addition      v. "Sum"
Adequate formalisation of elementary arithmetic      602
Adequate formalisation of elementary arithmetic, matrix      250
Aebi, M.      615
Affirmative mathematics (van Dantzig)      70 436 631
Ajdukiewicz, K.      619ff. 623 643
Alain de Lisle      v. "Alanus de Insulis"
Alarms de Insulis      6
Alexander of Aphrodisias      192
Algebra (algebraisation, algebraic method, algebraic system)      62 64ff. 77 132ff. 163ff. 171 330ff. 435
Algebra (Boolean)      163ff. 326 333 378 430 522 533f. 542ff. 678
Algebra (Brouwerian)      536 549f.
Algebra (closure)      536 549f.
Algebra (cylindric)      536
Algebra (polyadic)      536
Algebra (projective)      536
Algebra (relation)      536
Algebra with operators (Boolean)      536
Ammonius Saccas      54
Analytic judgement      46
Analytic judgement, method      44 193
Analytic judgement, set      557 561ff. 593
Anticipating substitutions      214 236
Antinomies      v. "Paradoxes"
Antipatros      52
Antiphon      5
Application of a formula      217 220
Aquinas      v. "Thomas"
Arche      10
Aristotle      passim
Arithmetic      113ff. 238ff. 297ff.
Arithmetic (formalised)      339 669
Arithmetic (intuitionistic)      436
Arithmetic as part of logic      67 113
Arithmetisation of analysis      128
Arithmetisation of metamathematics      442
Arithmetisation of syntax      296ff. 391
Ars inveniendi      54
Artin, E.      108 110 136
Associated formula      308ff. 587
Assumption      v. "Proof from assumptions"
atom      8 15 365 492
Atom (atomic formula)      177 202 263 272
Aulus Gellius      24
Autological      486
Axiom      81
Axiom-schema      311 329
Axiomatics      31 70 81 139
Axiomatisable      xxvi 543 599ff.
Axiomatisation      184f. 410
Bachelard, G.      623
Baer, R.      111
Baldus, R.      143
Banach, S.      381
Barcan, R.C.      230
Barzin, M.      433 490
Becker, O.      196
Bedeutung      v. "Denotation"
Behmann, H.      504ff. 556 584ff. 664
Belinfante, M.      433
Beltrami, E.      88
ben Gerson, Levi      54
Bennett, A.A.      172
Bentham, J.      54 196
Bentley, A.F.      617
Bergson, H.      615 617 622
Berkeley, G.      192 615f.
Bernays, P      xv 49 73f. 127 196 223f. 233 252f. 286ff. 321 344 364 384f. 391f. 394f. 398 436 490 496 642f. 645 657 675
Bernstein — Schroeder (theorem of)      369f. 410
Bernstein, B.A.      164
Bernstein, F.      368ff. 410
Berry, G.G.      482 486f. 492 503 512
Bertrand, J.      101
Beth, E.W.      4 31 48 74f. 124 150f. 186ff. 253 264f. 274ff. 288ff. 330ff. 420 430 443ff. 476 536ff. 602 621 628 635ff. 624ff. 670 680
Betweenness      v. "Order"
Bicompact      v. "Compact"
Bidez, J.      35
BINARY      164 178
Birkhoff, G.      135 172 332f. 680
Black, M.      318 511 621 643
Bocardo (mode of syllogism)      192
Bochenski, I.M.      4 190 192
Bochvar, D.A.      505ff.
Boehner, Ph.      4
Boethius      54
Bolyai, J.      154
Bolzano, B.      14 25 58 224 353 365 493 617 641
Boole's system      61 649
Boole, G.      52 58ff. 154 253 262 326 333 345 353 378 430 649 665
Borel set      557 559ff.
Borel, E.      158 160 521 558ff. 562ff. 568 573f. 606
Bouligand, G.      623
Bound      v. "Variable"
Bouquet, A.C.      35
Brentano, F.      67
Broden, T.      74
Brouwer's fundamental theorem on finitary spreads      427ff. 463 476 676f.
Brouwer, L.E.J.      xv 70 74 196 364 409ff. 476 494 521f. 584 614 616 618f. 630 636 638 641 644f. 671 676
Bruemmer, G.C.L.      xxiv
Brunschvicg, L.      617f.
Bryson      365
Burali-Forti, C.      69 397 482 484f. 495f. 503 508
Calculus      89 cf. of of of
Cantor's set (or Cantor's discontinuum)      526 558f.
Cantor's set (theorem of)      369
Cantor, G.      passim
Cantorism      365ff. 494ff.
cardinal number      366ff. 400ff. 406
Carnap, R.      76 193 226 230f. 257 317 356 362f. 413 437 466 491 504 622 644
Cassirer, E.      618
Categoricity      75 123ff. 326 351 490 514
Categoricity in power      328
Category of a symbol      228
Cauchy, A.-L.      58 91 103 107 111
Cavailles, J.      64 143 489
Cayley, A.      58
Chain      377 539
Chain, condition (ascending)      136
Champeaux, William of      464
Characteristic function      299
Characteristic function, numbers      551
Chaslin, Ph.      632
Choice (axiom of)      74 170 227 376 382ff. 387f. 400ff. 406 410 467 532
Choice (axiom of), sequence      422ff. 461 618
Chrysippus of Soli      6 24 35 52 493
Church's Theorem      253 304 605
Church's thesis      303 603
Church, A.      52 74f. 200 202 226 230 253 297 303f. 307 356 363 375f. 438 443 466 491 498 510 584ff. 598 603 605
Chwistek, L.      363 471f. 504 509 621ff. 643
class      61 465 cf.
Class (arithmetical)      543
Class (empty)      62
Class (proper)      401
Class (transfinite number)      393ff.
Class, existence (axioms for)      388 cf.
Class, theorem (Bernays')      392
Class, variables      385ff.
Closed (algebraically)      110
Closed (arithmetically)      543
Closed, formula      v. "Sentence"
Closed, semantic tableau      188 196
Closed, set      156
Closed, under a relation      92
Closure algebra      v. "Algebra"
Closure algebra (arithmetical)      543
Closure algebra of a formula      xx 181 217
Closure algebra of semantic tableau      188 196
Closure algebra, operator      155ff.
Cohen, H.      48 618
Commutative law      96
Compact      112 158 168 432f. 524 651
Comparability theorem      xxiv 368 376
Compatible      600
Compensation      6
Complementarity      626 645f.
Complementary class      62 64 163 427
Complementation      v. "Complementary class"
Complete system      209
Completeness      75 82ff. 196ff. 230 235 241 251 261 595ff. 678
Completeness (Hilbert's axiom of)      149
Completeness of Boolean algebras      169 678
Completeness of elementary logic      263 330 362 378 399 522ff. 540 659
Completeness of elementary logic with identity      655
Completeness of higher-order logic      526ff.
Completeness of intuitionistic elementary logic      454ff. 463
Completeness of many-sorted logic      666
Completeness of sentential logic      211 524 659
Completeness, theorems and representation theorems      522 533ff.
Comprehension axiom      229 231 366 369 392 407 465ff. 668
Compression      392 401 465ff.
Computable (effectively)      131 461 cf. "Recursive"
Computation (formal)      297ff. 680f
Conceptualism      471
Conclusion      198
Conditional existence      363f. 514f. 642
Confusion of free and bound variables      216
Congruence (in geometry)      140
Congruence (in geometry), relation, congruent      65 166 173
Conjugate column (in semantic tableau)      196
Conjunction      178
Conjunctive      446
Connected (conjunctively, disjunctively)      450
Connectives      v. "Sentential connectives"
Consequence (logical)      76 183f. 319
Consequentiae      55
Consistency, consistent      22 71 73f. 82ff. 148 248 251 261
Consistency, proof      231 233 235 241 243 375 391f. 398 402 411f. 596 607 616 641
Consistency, theorem (Bernays')      286
Constituant      267
Constructible, constructibility axiom (Goedel's)      403 406 408 473ff. 571
Construction      8 500
Constructive element in mathematical thought      636
Constructivistic views      xxv 469 640ff.
Continuous mapping      162
Continuum, continuity      8 15 141f. 365 368 381 420ff. 492
Continuum, hypothesis, continuum problem      381 402ff. 406 488
Conventionalism      70
Convergence      103 107 156f.
Convergent system      547
Conversio simplex      192
Copi, I.M.      74
Correspondence      211 cf.
Countable      xxvii cf.
Counter-model      448
Counter-model (approximate)      457
Counterexample      11 184ff. 275
Counting      365 379 668
Cournot, A.-A.      33
Couturat, L.      64 69 361 489 499
Craig's lemma      290 292
Craig, W.      292 344
Creative subject (Brouwer)      440 645
Crombie, A.C.      38
Curry, H.B.      193 363 482 510
Cusanus, Nicolaus      640
Cut      101 329
Darapti (mode of syllogism)      192
Dashiell, J.F.      xxvm 634
Davis, M.      608
de Bengy-Puyvallee, R.      439
de Bouvere, K.L.      xxiv
de Bruyn, N.G.      263 678
de Chateaubriand, F.-R.      39
de Iongh, J.J.      196
de Loor, B.      433
Decidable (effectively)      v. "Decision problem decision
Decision problem      75 131 149 200 212 239ff. 242 248 253f. 414 420 435 583ff.
Decision problem, procedure      322 330 333f. 555f. 583ff. 664f.
Dedekind, R.      passim
Deduction      v. "Derivation" "Inference" "Natural "Proof"
Deduction (law of)      86
Deduction, theorem      148 207ff. 219f. 227 653
Deductive      v. "Science" "System"
Deductive, method      636
Deductive, system Q (notation of)      306
Deductivity postulate      32 47
Definable      v. "Definition"
Definable (explicitly)      290
Definable (implicitly)      290
Definable (provably)      290 343
Defined notion or term      81 150ff.
Definite condition (Zermelo)      382ff. 392
Definition      44 76 81 288 403 500 503 512 568ff. 588 cf. "Recursion"
Definition (implicit)      57 344f. 489f. 492
Degree of a set      399
Dekker, J.C.E.      430
Democritus      5 33 365
DeMorgan, A.      52 58f. 61 63 92
Denotation      23 76 260 354f. cf.
Dense      v. "Order"
Dense, set      157
Depth of approximate counter-model      457
Dequoy, N.      439
Derivable      xvii 319
Derivation (formal, logical)      186 190 198 204f.
Descartes, R.      36 38 40f. 52 55f. 192 297 633 640 645
Designated element of a matrix      249
Destouches-Fevrier, P.      439 441 626
Detachment (rule of)      v. "Modus ponens"
Dewey, J.      617
Diagonal principle (Cantor's)      339 369 487 492 564f. 580 591 602
Dialectical epistemology      623ff.
Difference of classes      61
Dijkman, J.G.      433
Dijksterhuis, E.J.      38
Diodorus Cronus      9 20 32
Disjoint      xviii 382
Disjunction      793
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