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| Beth E.W. — The foundations of mathematics: A study in the philosophy of science |
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| Предметный указатель |
Disjunction (intuitionistic conception of) 438
Disjunctive 446
Dispersion (significal) 629
Distance 159
Distinct (intuitionism) 437 672
Distinct (numerically) 13 19
Divisibility 5
Divisibility (of numbers, ideals) 133 135 607
Division (no logical) 66 138
Doxography 34
Duality (Schroeder's law of) 173 658 661
Duerr, K. 4
Effective notation 375
Effectivity 234 241 244 274 286 cf. "Recursive"
Eisenstein, F.M.G. 58
Eisler, R. 38
Element 15
Elementary logic v. "Logic"
Elementary logic, syntax 297
Emerson, R.W. 6
Empirical science 47
Empiricism 38 353ff. 362 632
Enriques, F. 4 633
Entity 348 366
Entscheidungsproblem v. "Decision problem"
Epicurus 6
Epimenides 485 491
Equality v. "Identity"
Equality (pure theory of) 544 555 664f.
Equals (rule of replacing equals by equals) 298 680
Equations (generalised) 331ff.
Equinumerous 357
Erdmann, B. 353 633
Erdos, P. 190 365 678
Errera, A. 433
Essentially negative predicates (Brouwer on) 439 619
Essentially negative predicates, undecidable 589ff.
Eubulides of Miletus 20ff. 32 341
Euclides of Megara 32 493
Euclides, the mathematician 37 45 57 139 141 143 150ff. 583
Eudemus 18
Eudoxian family, Eudoxian type 334f.
Eudoxus 14f. 37 90 141 334f. 365 492
Evaluation 298
Evidence (self-evidence) 22
Evidence, postulate 32 47 82 616
Excluded third (principle of) 252 413ff. 434
Existence of mathematical entities 353ff. 363 411f. 639ff. cf.
Existentialism 48 616ff.
Experience 40 47
Exposition v. "Proof"
Expression (logical, polynomial) 65 202 cf. "Sentence"
Extension (of algebraic system or number system) 97 110 137f. 649f.
Extension (of deductive system) 209 550f.
Extension (of function) 118
Extension (spatial) 7
Extension and intension 466f.
Extensionality axiom 260 382 387f. 532
f 200ff. 275ff. 527
Factor (prime) 132
Factorisation 132ff.
Falsehood 24 76 cf.
Feferman, S. 679
Fermat, P. 297
Festino (mode of syllogism) 189
Field (number) 137 146 153 650
Field of sets 164ff.
Filaments (derivation) 236 cf.
Finitary cf. "Finitistic"
Finitary, spreads 196 427ff. 462 653f.
Finite (number, set) 367 373 379f. cf.
Finite, character (property of) 377
Finitistic 73 75 200 233 268 275
Finitistic, proof theory (limitations inherent in) 248 257 616 cf.
Finsler, P. 74
Fitch, F.B. 253 510
Form of a formula 215
Formal 71 186 cf. "Syntax"
Formal, rule 193 cf.
Formalisation 411 433
Formalised language 89
Formalism, formal conception of logic and mathematics 23 57 59 70 88 354 638
Formula 202 cf. "Sentence"
Formula (in the restrictive sense of Section 76) 216
Foundations (research on) 33
Fraenkel, A. 75 230f. 363 383f. 391 467 489 494 496 627 670
Fraisse R. 328
Framework (existence within a) v. "Conditional existence"
Frechet, M. 155ff. 162f. 558
free v. "Variable"
Frege, G. passim
Fremlin, G. 633
Frenkian, A. 38
Freudenthal, H. 430 442 476
FS (Fraenkel — Skolem) 231 386ff. 407ff. 497 508
Fulfilment xxi 76 179f. 250 286 318 323 447 526
Function 67 354 357
Function (descriptive) 260
Function (index) v. "Index function"
Function (sentential) 355
Function, parameters 221
Functionality axioms 222 303
Fundierungsaxiom v. "Restriction"
G3 (Kleene) 282f.
Galilei, Galileo 365 629
Galois, E. 57
Gamma-set 394
Gandy, R.O. xxvi 527
Garvin, L. 633
Gauss, K.F. 33 132
Geach, P.T. 318 482
General recursive 298
Generalisation 178
Gentzen's Hauptsatz xxiii 267 278ff. 285 462
Gentzen's systems 282ff. 434 451 463
Gentzen, G. xxvi 74 76 193 253 267 273 280ff. 285 375 434 451 463 586 675
Geometry (euclidean) 139ff. 650
Geometry (non-euclidean) 57 90 153ff. 638 650
Gergonne, J.D. 57
Gilmore, P.C. 438f.
Giordano Bruno 493
Glivenko, V. 172 433 675
Goedel numbers 296 302 337
Goedel's theorem 74ff. 391 495 584 593 616 641
Goedel, K. passim
Goethe, J.W. 34
Gonseth, F. 318 621 623ff. 645
Goodman, N. 363 437 471
Goodstein, R.L. xxvi 375
Grand logic v. "Logica Magna"
Grassmann, R. 58
Grelling, K. 482 486 492 503
Griss, G.F.C. 70 436ff. 441 519 616 631 674
Group (Abelian) 136
Group, group theory 45 136 172
Grzegorczyk, A. xxvi 586
Guillaume, M. xxii
Guilmin, Ch. 58 91 101
Hahn, H. 231
Hailperin, Th. 509 664
Halmos, P. 536
Hamel, G. 378 379
Hamilton, W. 54 58
Harmony 4
Hartmann, N. 618 645
Hartogs, F. xxiv 376
Hasenjaeger, G. 265 311 607f. 659
Hasse, H. 111 606
Hausdorff, F. 111f. 155ff. 168 172 225 377 523 525 540 568
Hegel, G.W.F. 88 493 633 644
| Heijmans, G. 633
Heine, E. 158
Helmholtz, H. 618
Henkin, L. 124f. 196 253 265 349 363f. 378 412 435 471ff. 482 490 515 516f. 533 536f. 539 653 668
Hensel, K. 110
Heraclitus xxii 4ff. 632
Herbrand field 454
Herbrand's theorem 193 252 274ff. 282
Herbrand, J. 64 74 127 193 208 238 242 252 274 282 454 584 586
Hermann, I. 623
Hermes, H. 202 295 465 540
Hertz, P. 74 626
Herzberg, J. 363 509
Hessenberg, G. 150 669
Heterological 486
Hetper, W. 363 509
Heuristics 239ff. 323
Heyting, A. 196 230 423 433ff. 461 476 616 619 673f.
Hierarchy (Borel, recursive, type) 224 497 508 526 588 608
Hilbert, D. 14 69ff. 82f. 127 136 139 141 143 147f. 150 155 196 202 223f. 227 233 257 260 293 295 321 344 353 411f. 415 489f. 521 535 584 616 622 626 641 655f.
Hintikka, K.J.J. xxii 201 539
Hippocrates of Chios 139
Hobbes, Th. 52 640
Hoelder, O. 192
Hoff-Hansen, E. 65
Hollitscher, W. 628
Homeomorphic mapping 163
Homomorphic image 332
Homorphism 166 171 173 526
Horatius 35
Hume, D. 45f. 192 633
Husserl, E. 192 353
Hypothesis 81 190
IDEA 12
Idea (innate) 36
Idea (principle of the ) 12 16
Ideal 65 133 138 166ff. 522
Ideal (prime) 133 138 167
Ideal (principal) 134
Ideal, number (Plato) 14 196
Idealism 615 617 624 640 643
Identity v. "Equality"
Identity (axioms of) 221 303
Identity (definition of) 226 554 664
Identity (logical) 76 184 190 210 229 319 362 652
Idoneism 624
Immortality 35
Implication 178
Impredicative (classes, definitions) 388 394 407 468 500f. cf. "Vicious-circle
Incommensurable proportions 90 365 492
Incompleteness of higher-order logic 351 412 cf.
Inconsistent 208 cf.
Independence 82ff.
Index functio (designated) xxv 403
INDEX function xxv 247f. 274
Indistinguishable (arithmetically) 543
Induction 34
Induction (principle of complete) 69 73f.
Induction (strong) 123
Induction (transfinite) v. "Recursion"
Inference (logical) 186
Infinite xxvi 380 637
Infinitistic v. "Finitistic"
Infinitum (regressua in) 11 32 82 617
infinity xxvi 20
Infinity (actual) 22 365
Infinity (potential or virtual) 22 365
Infinity, axiom 227 361 382 385 387f. 467 474 499 532
Inherence (theory of) 13f.
Initial formulas in semantic tableau 197ff. 275 508ff.
Initial formulas in semantic tableau, number 379 401 403
Initiation 35
Integers (Gaussian) 132
Integers (rational) 95ff. 238 649f.
Integral domain 136 138 649f.
Intension v. "Extension and intension"
Interpretable, weakly interpretable 600ff. 679
Interpretation of logic (in various senses) 177 342f. 399 679
Interpretation of logic (linguistic) 23
Intersection xviii 366
Intuition, intuitive vision 34 46 56 70 74f.
Intuitionism 70 192 342ff. 364 409ff.
Intuitionistic logic v. "Logic"
Intuitionistic logic and topology 680 cf. closure)"
Intuitionistic logic, mathematics xxv 70 75 196 230f. 409ff. 616
Invariant under permutation 346f.
Irrationalism 617 622
Isomorphic, isomorphism, isomorphy 45 97 99 124 132 149 153 173 327 490 514f. 550f.
Jacobi, C.G.J. 58
Jacobsthal, E. 375
James, W. 515 517
Jaskowski, S. 434f. 605 678
Jevons, W. Stanley 64ff. 196
Johansson, I. 436f.
Johnson, W.E. 69
Jonsson, B. 536
Junctive xxvi 446ff.
Kalmar, L. 128 586
Kanger, S. xxii 201
Kant, I. 11f. 31 33 36 39 41ff. 56f. 69 192 342 353 409 493 626 640 651
Kantianism 17 48 361 409 615 618f. 640
Keill, W. 40
Kelley, J.L. 433 652
Kelsen, H. 4f. 7
Kemeny, J.G. 75
Kepler, J. 640
Khintchine, A. 433
Kierkegaard, S. 615
Kleene's theorem 593 679
Kleene, S.C. xv 75 128 193 196 202 233 282 297 328 365 436 442 444 510 557 588 592f. 607f. 675 679
Klein, F. 172
Knowledge (theory of) 33
Kochen, S. xxvii 580
Koenig, D. 263 377
Koenig, J. 70 482 488 492 495 503 521 569
Kolmogorov, A.N. 433
Korselt, A. 663f.
Korteweg, D.J. 69
Korzybski, A. 76 632
Kotarbinski, T. 502
Kreisel, G. xv xxii xxvi 75 461 482 608
Krijgsman, Ph.H. 39
Kripke, S. xxiii
Kroman, K. 192
Kronecker, L. 128f. 409 619
Kuerschak, J. 110
Kummer, E. 58
Kuratowski — Tarski (method of) 562 566 568 589
Kuratowski, K. 160 162f. 227f. 335 377 557f. 562 566 568 589f. 669
Kurepa, D. 670
Ladd-Franklin, C. 67
Lambda-conversion 510
Lambert, J.H. 52 63 92 638
Langford, C.H. 185 321 584 586
Lattice v. "Partial order"
Least number principle 123 418
Least upper bound 104 499 547
Lebesgue, H. 482 521 569
Leibniz, G.W. 36 38f. 44ff. 52 55 226 229 583 627 636 659
Length of expression 258
Lesniewski, S. 76 226 230 353 363 471f. 502 510 621
Leucippus 33
Levi, Beppo 376
Lewis, C.I. 61 230f. 549 586
Limes number (limit number) xxiv 374 398 402 560 567
Limitation of size 401 497
Limited means of expression of formalised theories 345ff.
Lindeloef, E. 161 562
Lindenbaum's theorem on existence of adequate matrix 250 435
Lindenbaum's theorem on existence of complete extension 209 235 262 523 552 596 597
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