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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, PhilosophyАвтор: 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: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2004Количество страниц: 662Добавлена в каталог: 19.05.2008Операции: Положить на полку |
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454 86 20 537f 18 200 37 29 34 101 113 36 36 119 122 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 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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