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