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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
Reduced logic      v. "Logic"
Reducibility (axiom of)      226 361 499 507 509 532
Redundant      83
Reflexive relation      93
Regressus in infinitum      11 32 617
Regular space      161
Regular space, valuation      xxviii 264 525 530ff. 655
Reichenbach, H.      363
Relation      66 91ff. 227f. 668
Relation (calculus of relations)      665 cf.
Relation (reflexive, symmetric, transitive)      v. "Abstraction"
Relatives      16 63 cf.
Relativisation      162 550 602 666f. 679
Relativity of logic      229ff.
Relativity of logic (set-theoretic)      401 516
Replacement (axiom of)      385 387f. 391 398
Representable (numeralwise)      345
Representation      168 173 378
Restriction (axiom of)      387f. 390f. 398ff.
Reymond, A.      436
Richard, J.      471 473f. 482 487f. 492 501 503 513 521 571
Riemann, B.      155 618
Ring      135
Ring (Boolean)      173
Robinson, A.      xxvii 138 293 328 539 556
Robinson, J.      600
Robinson, R.M.      297 308 395 398 604
Rose, G.E.      436
Rosenbloom, P.C.      202
Rosser, J. Barkley      202 230 339 392 394 473 507 509f. 584 593 595ff.
Rougier, L.      4 231
Rousseau, J.-J.      39
Rucker, P.      38
Ruediger, A.      54
Ruestow, A.      24
Russell, B.      passim
Ryle, G.      633
Ryll-Nardzewski, C.      708
RZ (Russell — Zermelo)      467ff. 638
S2, S4 (Lewis)      549f. 586f.
Saccheri, G.      153 638
Sartre, J.-P.      617
Scepticism      621
Schmekel, A.      52
Schmidt, A.      666
Schmidt, E.      376
Schoenfinkel, M.      363 510 584
Scholz, H.      4 18 193 202 317 363 627
Schopenhauer, A.      612
Schreier, O.      111
Schroeder, E.      63f. 66 69 73 172 353 368ff. 383 410 498 584 658 661
Schroeter, K.      295 653
Schuette, K.      xxii 193 201 663
Schweikart, F.K.      154
Science (deductive)      31 81ff.
Secondary rule of derivation or inference      414 652
Secured      445
Segment      142 372
Segment (calculus of segments)      143ff.
Seidel, Ph.L.      58
Self-evidence      v. "Evidence"
Semantic tableaux      v. "Tableaux"
Semantical rules      179f. 447 527 621 631 633
Semantics      76 179 200 317ff. 442 444ff. 624f.
Semantics (Chwistek's rational)      622f.
Semantics (Korzybski's)      76 632
Semantics of intuitionistic logic      xxvi 444ff.
Semi-categoric      327
Semi-model      447 461 526
Semiotics      627ff. cf.
Sense      23 355
Sentence      xix 181 217
Sentential connective      178 202 654
Sentential connective, logic      v. "Logic"
Sentential connective, thesis      v. "Thesis by sentential logic"
Sentential connective, variable      202
Separable      157 168 173 524
Separation (axiom of)      382 384 387f.
Separation (theory of)      13f.
SEQUENCE      xvii 373
Sequent      xxiii 275 448
Sequent (calculus of sequents)      449
Set (notion of an arbitrary)      171f. 330
Set, set theory      70 73 75 365ff. 410 465 cf.
Set, theory (intuitionistic)      424ff.
Sextus Empiricus      9 16
Shen Yuting      482
Shirai, T.      230
Shyreswood, William of      54
Sierpinski, W.      381 408 552 567 575
Significant formula      279 286f.
Signifies      521 627ff. cf.
Sikorski, R.      436 675
Similarity      45 370
Simplicius      9
Sinn      v. "Sense"
Skarzewski, W.      363 509
Skolem, Th.      22 65 75 124 128 135 172 193 230f. 253 267 315 321 383f. 401 436 473 482 488ff. 492 494 496 513ff. 584 642f. 645 662 670
Smirnoff, J.      161
Sneider, E.V.      557
Sociomorphic cosmology      xxii 4ff. 632
Socrates      32
Souslin, M.      575f. 593
Space (absolute)      11
Spatial intuition      57 192
Species      425ff. 618
Specker, E.      509
Speusippus      17
Spinoza, B.      23 39 464
Splitting of semantic tableaux      188 197f. 450
Spread, spread law      425ff. 443 cf.
Stable mathematics (van Dantzig)      70 436ff. 674
Standard enumeration of individual variables      xx 210 256
Standard model      v. "Model"
Standard-system of ordinals      395ff. 400
Stanley, R.L.      482
Steck, M.      344 490
Steinitz, E.      110 328
Stenzel, J.      196
Stilpo      32 54
Stoerring, G.      192 632
Stoics      23f. 52 57 355 632
Stone, M.H.      65 164 168 170 173 435 522 535
Stratification      508ff.
Strato of Lampsacus      5 6
Strength of a formula      289ff.
Strength of a formula (sequence of increasing)      544 546
Structural invariant      551
Structure of mathematical thought      636
Sub-tableau      188
Subalgebra      332
Subformula principle      193 273
Subformula principle, theorem      193 253 267 280 282 285 463 667
Subordinate subtableau      197
Subset      xviii 366
Substance, substantial unity      464ff. cf. "Substantialisation"
Substantialisation of notions      362 cf.
Substitution      203 213
Substitution (anticipating)      v. "Anticipating"
Substitution (rule of)      208 652 654 656
Substitution (simultaneous)      652
Successor, successor function      116 357 680
Suetuna, Z.      xxvi
Sum (logical)      xviii 61 164
Sum (of numbers)      238
Sum (ordinal)      v. "Ordinal"
Suranyi, J.      586
Syllogism, syllogistics      19 53 58 63 67 188ff. 192 293 464 cf. "Darapti" "Festino"
Syllogismus expositorius      v. "Proof"
Symbol      cf. "Denotation" "Meaning" "Sense"
Symbol (category of a)      v. "Category"
Symbol (complete, incomplete)      354
Symbolic logic      202ff. 410 cf.
Symmetric relation      93
Syntax, syntactic      71 186 257 260 267 293ff. 621f. 630 633 cf. "Formal"
Synthetic judgement, synthetic judgement a priori      36 46 69
Synthetic method      44
System (axiomatisable)      v. "Axiomatisable"
System (calculus of systems)      76 542ff. 678
System (in connection with matrix method)      250
System, deductive system      xvii xxvi 208ff. 542
Szmielew, W.      xxvi 555 586 605
Szpilrajn, E.      381
t      514ff.
Tableau (semantic)      xxii 186ff. 269ff. 275ff. 321 449ff.
Tannery, P.      365
Tarski's theorem on complete extensions      210 262 523
Tarski's theorem on notion of truth      335ff. 510ff.
Tarski, A.      passim
Tarski, J.      164
Taurinus, Fr.A.      154
Tautology      128 362 cf.
Teensma, E.      677
Teichmueller, O.      377
Teilformelnsatz (Gentzen's)      v. "Subformula"
Term      65 222 238 241 385
Theaetetus      37
Theophrastus      18 190
Theorem      81 239 cf. "Thesis"
Theory      cf. "System"
Theory of types      v. "Types"
Thesis      203ff. 215 218 319
Thesis (intuitionistic)      463
Thesis by sentential logic      218 220
Thomas Aquinas      54
Thompson, F.B.      536
Thomson, J.F.      318
Thought      634
Tolerance principle      413 cf.
Topological mapping      162f.
Topological mapping, space (Kuratowski)      163
topology      161ff. 435 521ff. 651f. 680
Topology, (intuitionistic)      430
Transfinite number      374 cf.
Transformation (Poincare)      85 88 147ff. 154f.
Transitive relation      93
TREE      194ff. 252 444ff. 676 680 cf.
Tree (Ramean)      190
Triangle (Locke's)      56 192f.
Truth      24 76 85 335 503 511 cf. "Semantics"
Truth and falsehood      355
Truth, criterion      342 512
Truth, definition      76 625 cf.
Truth, postulate      32
Truth, table      73 654
Truth, value      67 188 198f. 241 246
Tukey, J.W.      377f.
Turquette, A.R.      230
Two-ity phenomenon (Brouwer)      618
Tychonoff (theorem of)      378 433 651f.
Tychonoff, A.      167 378 433 651f.
Type (arithmetical or elementary)      322 543
Type (Eudoxian)      334
Type (order)      370
Type (structural)      550
Type of an entity      226
Types (Chwistek's constructive)      509
Types (theory of logical)      69 73ff. 226ff. 253 345 361f. 496ff.
Ulam, S.      536
unary      165 178
Unity      7
Universal      15 21 362 464ff.
Universal, function      560 579 589
Universal, mathematics      37 55
Universe      183 224 514
Universe of discourse      59 61
Upper bound      377 cf.
Urysohn, P.      161
Use and mention of symbols      258ff. 317 353 472
Valid      239 319 448
Validity      181 187ff. 336ff.
Valuation      xxviii 210 241ff. 318 523 cf. "Regular"
van Dantzig, D.      111f. 436f. 439ff. 621 628 629 631
Van der Waerden, B.L.      135f. 141 149 172
van Eeden, Fred      630
Variable      53 55 179
Variable (bound or free occurrence of a)      181 216 260 296
Variable (value of a)      179
Vaught, R.L.      328
Vergilius      35
Veritates (primae)      36
Veronese, G.      139
Vicious circle      32 82
Vicious circle, principle (Russell's)      497 cf.
Vico, G.      640
Vienna Circle      48 73 362 615 625 628f.
von Hartmann, Ed.      615
von Mises, B.      363
von Neumann, J.      230 383ff. 391 395 397f. 467 489 496 604
von Rootselaar, B.      xxvi 433
von Staudt, K.C.C.      58
von Wright, G.H.      586 664
Vredenduin, P.G.J.      439
Vuysje, D.I.      630
Wajsberg, M.      653
Wallace, A.D.      540
Wang, Hao      392 394 473 482 497 508f. 666
Welby, Victoria      630
Well-ordered set      370
Well-ordering      370ff.
Well-ordering (non-elementary character of)      335 568
Well-ordering, theorem (Zermelo's)      170 368 376 394 410
Weyl, H.      196 482
Whitehead, A.N.      63 69 293 356 497 627
Wiener, N.      227f. 497
Wittgenstein, L.      xxii 73 362
Wolff, Chr.      40 45
Woodger, H.J.      318 363 471
Xenocrates      17
Z      307
Zeller, Ed.      32
Zeno of Elea      6ff. 14 35 365 492f.
Zermelo's axioms      381ff. 521
Zermelo, E.      70 75 230 376 381ff. 391 394ff. 401 410 467 488 492 494ff. 503 521 569 670
Ziehen, Th.      632
Zigzag theory (Russell's)      497
Zilsel, E.      634
Zorn's lemma      170 377
Zorn, M.      170 377
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