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Link G. (Ed) — One Hundred Years of Russell's Paradox: Mathematics, Logic, Philosophy
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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 662

Добавлена в каталог: 19.05.2008

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Предметный указатель
$\beta$-conversion      454
$\Box$ principle      86
$\Delta^1_1$-comprehension      20
$\epsilon$-operator      537f
$\Gamma_0$ (ordinal)      18 200
$\Omega$ Conjecture      37
$\Omega$-logic      29 34 101 113
$\Omega$-proof      36
$\Omega$-soundness      36
$\Sigma$ 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 $\epsilon$-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 $\mathbb{R}$      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$_1$      626 628
Context$_2$      628
Context$_3$      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
1 2 3 4
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