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Link G. (Ed) — One Hundred Years of Russell's Paradox: Mathematics, Logic, Philosophy
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Название: One Hundred Years of Russell's Paradox: Mathematics, Logic, Philosophy
Автор: Link G. (Ed)
Аннотация: These 31 papers come from the June 2001 international conference held to commemorate the centenary of the discover of the famous "Russell's Paradox," and include contributions from Russell scholars, mathematical logicians, set theorists, and scholars in the philosophy of mathematics. Papers include an introduction by Godehard Link that credits Russell with the invention of the new mathematical philosophy, W. Hugh Woodin on set theory after Russell, Harvey Friedman on a way out of Russell's paradox, Sy Friedman on completeness and iteration in modern set theory, and John S. Bell on "Russell's Paradox and Diagonalization in a Constructive Context." Other papers include examinations of aspects of the Principia Mathematica, Russell on method, and critiques of works related to Russell's fields of study.
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Рубрика: Математика /
Статус предметного указателя: Готов указатель с номерами страниц
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Год издания: 2004
Количество страниц: 662
Добавлена в каталог: 19.05.2008
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Предметный указатель
-conversion 454
principle 86
-comprehension 20
-operator 537f
(ordinal) 18 200
Conjecture 37
-logic 29 34 101 113
-proof 36
-soundness 36
operation 119 122
0# exists (large cardinal axiom) 88 90
3-valued semantics 292
Absolute undecidability 525
Absolutism 23
AC see axiom (scheme) of choice
Acceptable ordinal 301
Ackermann, Wilhelm 147n
Acquaintance 450
Act of collection 110
Act of consciousness 104
Act of reflection 110
Actual infinite 166 549 558
Aczel, Peter 149 194 195 232n 261
AD see determinacy axiom
Admissible set theory 121
AFA see anti-foundation axiom
Algebra of logic 507 509
Ambiguity 135
Ambiguity, systematic 135
Ambiguity, typical 135
Anti-foundation axiom (AFA) 19 20 149 194
Antinomy of infinite number 354
Approximate splitting principle 229
Aquinas 192
Aristotle 166 192
Arithmetic in ramified logics 472
Armageddon 186
Armstrong, David M. 592 603 606 607
Assumptions of infinity 162
Axiom (scheme) for propositions and truth 261
Axiom (scheme) for the -operator 537
Axiom (scheme) of anti-foundation (AFA) 19 20 149 194
Axiom (scheme) of choice (AC) 31 438 537
Axiom (scheme) of dependent choice (DC) 198 227
Axiom (scheme) of determinacy (AD) 16 33 537
Axiom (scheme) of extensionality 438 443
Axiom (scheme) of inclusion subtlety 52
Axiom (scheme) of infinity 14n 45 438 451
Axiom (scheme) of projective determinacy (PD) 16 31 32
Axiom (scheme) of reducibility 14 192 418 435 437 438 449 450 469
Axiom (scheme) of reflection 141
Axiom (scheme) of subtlety 50
Axiom (scheme) of weak inclusion subtlety 53
Axiom (scheme), large cardinal 31
Axiom (scheme), multiplicative 438
Axiom (scheme), Newcomp 50 52
Axiom of Solvability 518 529
Axiomatic method 102
Axiomatic program 508
Axiomatization 502
Axiomatization of logic 509
Axiomatization of set theory 509
Ayer, Alfred J. 482
Azzouni, Jody 581
Baire property 35
Balaguer, Mark 551 584
Baltag, Alexandru 149n
Bar induction 520
Barendregt, Henk 236n
Barwise, Jon 149n 194
Basic law V 248
Basic set theory 121
Bealer, George 600 604
Begriffsschrift 247
Bell, John L. 20 568 574 587
Benacerraf, Paul 572
Berkeley, George 497
Berkowski, Hermann 511
Bernays, Paul 142n 193 313
Berry paradox 378
Bishop, Errett 195 227 233n 449
Bisimulation 203
Blackwell, Ken 495
Blass, Andreas 147n
Blau, Ulrich 21
Blumenthal, Otto 504
Bolzano — Weierstrass theorem 519
Boole, George 507 509
Boolos, George 222 248n 563
Bourbaki, Nicolas 565
Bradley, Francis H. 3n 353 427 432
Bradley’s paradox 21 419 426 429 432
Bradley’s regress 423
Bricmont, Jean 546
Bridges, Douglas 242
British hegelianism 353
British idealism 489
Broad, Charles D. 422n 487
Brouwer, Luitzen 449 451 518ff
Brouwer’s intuitionism 517
Brown, James Robert 584
Bunge, Mario 581
Bunn, Robert 352
Burali — Forti paradox 191 349 378
Burali-Forti, Cesare 3n 350n 351
Burgess, John 248n 253 473 570
Buridan, John 464
Cantini, Andrea 20 201
Cantor, Georg 3n 5 93 96 250 375 534 551 553
Cantorian set theory 504
Cantor’s Absolute 96
Cantor’s paradox 1 349 350 378 502f 506
Cantor’s theorem 20 221 249 250 260 350
Cardinal, inaccessible 96
Cardinal, indescribable 18 51 97
Cardinal, large 96
Cardinal, Mahlo 18 51 97
Cardinal, measurable 90 97 112
Cardinal, strong 97
Cardinal, subtle 18 50f
Cardinal, supercompact 97
Cardinal, superstrong 89
Cardinal, weakly compact 51 106
Cardinal, Woodin 33 89 90 97 99 106
Carnap, Rudolf 14 439 442 449 523
Categorematical 641
Categorial grammar 12
Category of all categories 145
Category theory 19 23 140 145 587
Category theory, axiomatic foundations 146
Category theory, naive 148
Category theory, structuralism based on 565
Church, Alonzo 12n 13 435n 453
Chwistek, Leon 442n 446n
Circularity 192
Class of all classes 359
Class symbol in Russell’s substitutional theory 387
Class symbol, scope of 439
Class theory, impredicative 313
Class, proper 306
Class, virtual 49
Cocchiarella, Nino 389n 595
Coffa, Alberto 350
Cohen, Paul 29 33 85 93 101
Coinduction principle 215
Combinatory logic 261
Common knowledge 193
Complemented subset 222
Complex of entities 419
Comprehension 248 384
Comprehension, elementary 266
Comprehension, naive 285
Comprehension, stratified 273
Comprehension, stratified explicit 274
Computer science 11
Concept 248
Conceptual realism 587
Conceptualist approach 9
Conditional platonism 32
Conditional, material 288
Consciousness 104
Consistency proof 251
Consistency proof for arithmetic 509
Constituents 430
Constitution 105
Constitution of sets 110
Constitution of the concept of set 110
Constructible hierarchy 75
Constructible sets 85 99 103
Constructible universe 13
Constructible universe, relativized to 33
Constructionalism 449
Constructive AFA set theory (CZFA) 198
Constructive analysis 227
Constructive set theory 195
Constructive Zermelo — Fraenkel set theory (CZF) 196
Constructivism 12 22 412 540
Contemporary physics 554
Contemporary physics, fundamental assumption of 554
context 626
Context in language 626
Context in logic and computer science 628
Context principle 23
Context principle, Frege’s 625 629
Context principle, truistic 631
Context 626 628
Context 628
Context 629
Context/content duality 628
Context/text duality 628
Contextual definition 393 453
Continuum 322
Continuum Hypothesis 18 29 44 99
Continuum problem 93 100 113 504
Continuum, nonstandard 526
Conway, John 311 321
Corecursion principle 215
Course-of-values 248
Crimmins, Mark 581
Cumulative hierarchy 95
Curry paradox 286
Curry property 290 298
Cusanus, Nicolaus 96n
Cut-elimination 462
CZF see constructive Zermelo — Fraenkel set theory
CZFA see constructive AFA set theory
Davoren, Jen M. 22 452
dc see dependent choice axiom
de Morgan, Augustus 577
Dedekind infinite 396
Dedekind real in constructive analysis 241
Dedekind, Richard 350 375 412 511 553 562 569
Definite description 436 453 639
Dependent choice axiom (DC) 198 227
Descartes, Rene 96n 112 497
Descriptive set theory 16 89
Detachable subset 222
Determinacy axiom (AD) 16 33 537
Determinately (sentential operator) 614 615
Diagonal argument 522
Diagonalization 20 223 527
Diagonalization, restricted 278
Disambiguation 135
Disambiguation, conventions 139 143
Discourse 23 637
Discourse representation theory (DRT) 638
Donnellan, Keith 639n
DRT see discourse representation theory
du Bois-Reymond, Emil 22 523 529
Du Bois-Reymond, Paul 22 522ff
Dummett, Michael 248 630
Dynamic predicate logic 628
Eames, Elizabeth 496 585
EFA see exponential function arithmetic
Effective topos 224
Ehrenfeucht — Mostowski theorem 150
Elementary comprehension 266
Elementary extension 254
Empiricist 524 527
Endless regress 424 429
Epistemic paradox 464
Ernest, Paul 578
Ersatz properties 296
Etchemendy, John 601
Euclid 102
Evans, Gareth 580 616
evidence 102
Excluded Middle 289
Expansion, sentential 632
Explicit mathematics 148 193
Exponential function arithmetic (EFA) 50
Extender model 88
Extensional simple type theory 451
Extensionality 468
Extensionality axiom 438 443
Extra sentential 631
Extrapolation 22 549
Extrapolation, justification of 553 558
Extrinsic evidence 102
Fallibilism 22
Fechner, Gustav 529
Feferman, Solomon 12n 13f 19 148n 154n 161f 193 200 268n 272 594
Fernando, Tim 150
Ferreira, Fernando 251
Feyerabend, Paul 17n
Fibered view on predicate logic 628
Fiction, logical 401f
Fictionalism 584
Field, Hartry 15 20 584
Figural moment 111
filling 109 112
Fin(T ) 153 163 549 557
Fin(ZF) 153
Final coalgebra theorem 217
Fine structure theory 86
Fine, Kit 10n 248n
Finitarily justified system 161
Finite mathematics 154 165 549 557
Finite mathematics of the indefinitely large 22
Finite mathematics, of the indefinitely large 549
Finitistic theory 19 153 158ff 177
Finitistically reducible 153 154ff
Finsler, Paul 193
Fixed point approach to the semantic paradoxes 288
Fixed point lemma 186
Fleischer, Heinrich 508
Forcing 31 93 101
Form of a complex 429
Formal concept 425
Formalism 534 538 543 577
Foundationalism 22 481 491
Founding 107
Four storey truth hierarchy 319
Free logic 595
Frege Arithmetic 11n
Frege structure 261
Frege — Russell definition of number 562
Frege, Gottlob 2 5 9f 11n 20 247ff 350 375 412 507ff 534 561 579 625
Frege’s context principle 625 629
Friedman, Harvey M. 18
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