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| Beth E.W. — The foundations of mathematics: A study in the philosophy of science |
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| Предметный указатель |
Lindenbaum, A. 76 159 167 235 250f. 262 345 377f. 435 523 552 599
Linguistic element in mathematical thought 636
Listing, J.B. 58
LJ (Gentzen) 451
LK (Gentzen) 282ff.
Lobachewskij, N.I. 57 154
Locke, J. 38 192 633
Loeb, M. 482
Loewenheim — Skolem — Goedel (theorem of) 193 267 320 435 574 645
Loewenheim, L. 74f. 182 193 230 267 320f. 435 473 482 488ff. 492 518ff. 572 574 584ff. 642f. 645
Logic (combinatory) 363 510
Logic (elementary) 202 215ff. 235
Logic (higher-order) 75 127 202 224 495 655
Logic (inductive) 393
Logic (intuitionistic) 230f. 433ff. 444ff. 549 674ff. 677
Logic (many-sorted) 225 655 666
Logic (many-valued) 230
Logic (modal) xxiif. 18 54 230 435 549
Logic (predicate) v. "Logic (elementary)"
Logic (reduced) 263 267 296 525 527
Logic (sentential) 53 55 73 202 520 652ff.
Logic and mathematics 67 70 636 cf.
Logic with identity 19 221f. 554f. 655
Logica Magna 202 229 504
Logica Magna, identity v. "Identity"
Logica Magna, logical consequence v. "Consequence"
Logicism 67 353ff. 499 504
Logico-mathematical parallelism 172 442 cf.
Loomis, L. 171
Lorenzen, P. xxii xxvi 128 232 472
Los, J. 328
Lotze, H. 353
ls 345ff.
Lukasiewicz, J. 4 23f. 73 192 230 249 293 353 362f. 502 621 627
Lullus, R. 52
Lusin, N. 567 576 608
Lyndon, R.C. 67 293 508
Mach, E. 48 192 644
Maine de Biran, P. 615
Majorant set 386
Malcev, A. 537
Mannoury, G. 69f. 436 439 621 628 630f. 644
Many-sorted logic v. "Logic"
Many-valued logic v. "Logic"
Mapping xx 162 346
Marburg School v. "Kantianism"
Maritain, J. 629
Markoff, A. 392
Martin, R.M. 317 363 471
Marx, K. 11 88
Mates, J. Benson 4
Mathematical truth and provability 340f.
Mathematics (pure and applied) 37 57 637
Mathesis universalis v. "Universal mathematics"
Matrix method xxiii 249ff. 435
Maximal 377 380 539
Maximal, ideal v. "Ideal (prime)"
Mazurkiewicz, S. 552
McColl, H. 69
McKinsey, J.C.C. 67 435 536 549f. 586 674
McLaurin, C. 62
McNaughton, R. 129 508
Meaning 23 76 503 cf. "Interpretation"
Megarics 20 23 32 53f. 464
Melissus 7 8
Menger, K. 172
Mention v. "Use and mention"
Metamathematics 70ff. 411 441f.
Metamathematics, (Chwistek's rational) 509
Metaphysics 32 cf.
Metasystem 336
Method (analytic, synthetic) 44
Metric space 158ff.
Metrisable space 160f.
Meyerson, E. 617f.
Meyerson-Brodie, H.C. 510
Microperfect 112
Midsequent 280
Mill, J. Stuart 58 353
Minimal 380
Minimal, calculus 436
Misch, G. xxii
ML (Quine) 230 497 508f.
Modal logic, logic of modalities v. "Logic"
Model 76 120ff. 181 183ff. 319 360 448 526 542ff. 571ff. 642 666
Model (complete) 538 678
Model (recursive classification) 607ff.
Model (standard, non-standard) 337 342 349 411 490 509 515f. 527 668
modus ponens 71 191 205ff. 208 228 414
Modus ponens, (generalised) 654
Moh Shaw-Kwei 230 482
Montague, R. 164 482 679
Moore, E.H. 143
Moore, G.E. 482 619
Moore, R.L. 377
Morris, C.W. 631f.
Mostowski, A. xv xxvi xxvii 124 279 385 393f. 412 435 449 536 551 571f. 574 580 586 588 593 604ff. 608 680
Multiplication v. "Product"
Multitude 407f. 465
Mutakallimun 493
Myhill, J. 74 510
Mystical doctrines, mysticism 34 619
Nagata, J. 161
NAME 20 188 354 490 516
Natorp, P. 618f.
Natural deduction 193 198ff. 248 527
Nature 4
NB (von Neumann — Bernays — Goedel) 386ff. 407 497 508 668
Needham, J. xxii
Negation 64 177 516 cf.
Negation (choice, exclusion) 631
Negationless intuitionistic mathematics (Griss) 70 436ff. 631 674 cf. "Stable"
Neighbourhood 111 156ff. 523 680
Neighbourhood, space (Hausdorff) 156 168 173 523 651
Nelson, D. 75 430 442
Nelson, L. 413 482 584 626
Neo-criticism (Baden school of) v. "Kantianism"
Neo-kantians v. "Kantianism"
Neumann, B.H. 539
Newton, I. 11 44
NF (Quine) 230f. 497 507ff.
Nietzsche, Fr. 615
Nieuwentyt, B. 38ff.
NJ (Gentzen) 451 463
NK (Gentzen) 280ff.
No-counterexample interpretation (Kreisel) 200
Noether, E. 136 172
Nominalism 363 408 464ff.
Nomos 5
Non-categoricity v. "Categoricity"
Non-constructive methods 233 418ff.
Non-predicative v. "Impredicative"
Normal forms (of logical formulas) 282 658 662
Normal matrix 250
Normal space 160
Normal valuation xxviii 263 525
Notation in mathematics 636
Novak, I.L. 392
Null-class xvii 62
Number (complex) 137
Number (natural) 90 113ff.
Number (p-adic) 149
Number (prime) 132
Number (rational) 98f. 649 cf.
Number (real) 99ff. 128 423 649
Number in intuitionistic mathematics 420ff. 671ff.
Number theory v. "Arithmetic"
Number, number concept 90 357
Numeral xx 238 246 258 298
Numeralwise represented 307ff. 345 587ff.
| Object 354 366 cf.
Object of mathematical thought 636
Object, system 336
Occurrence 296 cf.
Ockham, William 54
Ontological interpretation of logic and mathematics 364 613ff.
Ontology 644ff.
Open set 156 432 680
Operation 221 263 cf.
Operation (infinite) 169
Operator (of elementary logic) 216
Opposites 16
Order (continuous) 330
Order (dense) 100 321ff. 555
Order (of a constructible set) 403
Order (partial) v. "Partial order"
Order (simple) xvii 262
Order, order relation, ordered set 100 123 127f. 139f. 152 185 238 370 565ff. 669
Order, relations in intuitionistic mathematics 672
Order, types (operations on) 670
Ordering principle 262 378
Ordinal numbers, ordinals 366 370f. 394ff.
Ordinal sum 333
Orey, S. xxv 580
Ostrowski, A. 110
P ("Peano") 311ff. 587ff. 615
Padoa's method 87 151f. 292 651 667 669
Padoa, A. 69 87f. 151 379 651 667 669
Pair (ordered) xvii 227
Pappus 145 150
Paradox (Berry) 486 512
Paradox (Burali — Forti) 397 484 496
Paradox (Cantor) 484 495
Paradox (Grelling) 486
Paradox (Liar) 20 24 343 482 485 493
Paradox (Richard) 473 487 513 521 569
Paradox (Russell) 68 361f. 482f.
Paradox (Skolem — Loewenheim) 75 488ff. 513ff. 643
Paradox (Sorites) 21
Paradox (Zermelo — Koenig) 488 521 569
Paradox of symmetric solids (Kant) 651
Paradoxes 8f. 14 20 70 341 481ff. 625 630 641
Paradoxes (cantorist views on) 494ff.
Paradoxes (intuitionistic interpretation of) 494
Paradoxes (semantical) 76 501 510
Paradoxes (Zeno's) 8 365 492ff.
Paradoxes of denotation and analysis 21 356 482 490 516ff.
Paradoxes of set-theory 75 465 492 495
Paradoxes of the infinite (Bolzano's) 493
Parallelism v. "Logico-mathematical"
Parameters 221
Parmenides 7f. 54 632
Partial order 77 135 166 171f. 377
Particularisation 178
Pascal's condition 505
Pascal, B. 145 505 615
Pasch, M. 139f. 641
Paulsen, F. 48
Peacock, G. 58
Peano, G. 63 68ff. 113 126 128 139 293 297 311 342 348 353 355 360f. 376 410ff. 502 605
Pedigree 178 204f. 235 237f. 652
Peirce, C.S. 63f. 66f. 73 92 113 172 355 360 383 617 638 662
Pepis, J. 586
Perfect 111
Peter, R. xxvi 128
Phantasma 635
Philitas of Cos 492
Philolaos 5
Philosophy 33 613ff.
Physis 5
Piaget, J. 632
Pieri, M. 68ff. 139 344
Plato 5 7 11ff. 20 22f. 25 31 35ff. 40 54 90 196 223 354 493 629 632 637 644
Platonism 362f. 407 421 464ff. 627 638ff.
Plotinus 16 640
Ploucquet, G. 63
Plurality 7
Plutarchus 36 54
Poincare, H. 64 69f. 73 85 114f. 147ff. 156f. 409 471 481 497 500 513 619 641f.
Pontrjagin, L. 111f.
Popper, K.R. 4 193
Poretskij, P. 69
Pos, H.J. 643
Posidonius 52
Positivism (logical) 362f.
Post, E.L. 73 230 584 593 608 659
Postulate 81
Pragmatism 614 618f.
Prantl, C. xxii 32
Predicate (quantification of the) 53
Predicate, predicate logic 67 73 cf.
Predicative v. "Impredicative"
Premiss 190 198
Prenex formula v. "Normal forms"
Presburger, M. 74 127 238 584 586
Price, D. xxii
primitive elements 382
Primitive elements, notion or term 81 150ff. 173
Primitive elements, notions of Euclidean geometry 150f. 339
Primitive elements, recursive 299f.
Principle 10f. 15 32
Probability theory 363
Proclus 139
Product (Cartesian) xix 576 651
Product (direct) 333ff.
Product (logical) xviii 61 164
Product (relative) 92 665
Projective set 576ff.
Proof from assumptions 204 219
Proof from assumptions by exposition 192
Proof from assumptions, theory 233ff. cf.
Proportions (theory of) 15 37 90 365 492 cf.
Proposition, propositional v. "Sentence" "Sentential"
Provable 86 cf. "Derivation" "Inference" "Proof"
Psellus, M. 35
Pseudo-definition 226
Pseudo-problem 628
Pseudo-valuation 681
Psychologism, psychology 353 628 632ff.
Punctuation 203
Pythagoras 33 40 147
Q (R.M. Robinson) 243 247ff. 306ff. 604 614
Quantification v. "Predicate" "Quantifier"
Quantification (double) 190
Quantification (theory of) 202
Quantifier 67 178
Quantifier (definition of) 218 223f.
Quantifier (elimination of) 324
Quantifier (relativising) 602 666
Quine, W.V. 113 193 202 230f. 297 356 363 437 471f. 491 497 507f. 512
Quotation marks 259ff. 490 516f.
Ramification 502 509
Ramsey, F.P. 497 502ff.
Range (of variable) 179
Rasiowa, H. 75 435f. 536 675 680
Rational science 47
Rationalism 38 615 632
Realism 619ff. 624 621ff. 644
reality 40 622
Reality (spheres of) 644
Reality, postulate 32 47
Reason (World) 34
Recursion v. "Induction"
Recursion (course-of-values) 123
Recursion (definition by) 115 122 129ff. 345
Recursion (proof by) 113 122 126 204f. 285ff.
Recursion (transfinite) xxiv 74 372 395 402
Recursion for rational integers 658
Recursive functions and predicates 297ff. 375 436 583ff. cf. "Primitive
Recursively enumerable xxvii 592f. 596 599
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