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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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Friedman, Sy D. 18 Fries, Jacob F. 510 Fulfillment 107 Functor category 146 Fundamental assumption of contemporary physics 554 Fundamental theorem of algebra 236 Galilei, Galileo 4 16 Garciadiego, Alejandro 350 Gentzen, Gerhard 455 Gentzen’s Hauptsatz 475 Gestalt-qualities 111 Geuvers, Herman 236n Goedel fixed point 182 Goedel, Kurt 2 6f 12f 18 85 93 97 98 101 142n 146n 449 587 Goedel’s completeness theorem 37 Goedel’s incompleteness theorems 2 159 182 Goesch, Heinrich 511f Goldfarb, Warren 252 Goodman, Nelson 15 449 617 Grattan-Guinness, Ivor 350 Grelling, Kurt 510n 511f Grelling’s paradox 510n 512 Griffin, Nicholas 2n 21 489 Grim, Peter 261 Grishin, V.N. 275 Grothendieck, Alexander 148 Grundgesetze 248 Gupta, Anil 595 Hacker, Peter M.S. 496 Haecceities 570 Hale, Robert 248n Hauser, Kai 18 Hazen, Allen P. 10n 22 452 Heck, Richard 248n 251 Hellinger, Ernst 506 Hellman, Geoffrey 23 Helmholtz, Hermann von 529 Hempel, Carl G. 496 497 Hermeneutic circle 193 Hersh, Reuben 578 Herzberger, Hans 595 Hessenberg, Gerhard 5n 510f Hilbert circle 507 Hilbert, David 2f 93 102 159f 162 351 455 517 533 551 Hilbert’s paradox 2 22 504ff 510f Hilbert’s program 159 517ff 551 Hodes, Harold 581 Huerter, Tobias 19 Hume’s Principle 11n Husserl, Edmund 18 104 110 507f Hylton, Peter 393n 489 490 496 Idealist 524 527 Identity statement 582 Ignorabimus 22 523 Impredicative 254 Impredicative class theory 313 Impredicative definitions 191 Inclusion subtlety 52 Incomplete symbol 8 385 419 436 453 Inconsistent multiplicities 350 Indescribable cardinal 18 51 Individuals 407f 410 Infinitaercalcael 522 Infinitary mathematics 551 Infinite game 30 98 Infinite game, determined 31 98 Infinite, actual 549 558 Infinite, the actual 166 Infinite, the potential 154 166 Infinitesimal number 320 Infinitesimals 522 525 527 Infinity axiom 45 438 451 Inscrutability of reference 612 621 Inseparability 268 Insolubilia 376 Intensional interpretation 435 Intensional logic 12 464 594 Intentional paradox 464 Intentionality 104 Interactive prover Coq 236 Intermediate theory (Russell) 21 401ff Intermediate theory (Russell), formal language of 408f Intermediate Value Theorem 234 Intra-sentential 631 Intrinsic evidence 102 Intuition 94 542 Intuitionism 22 517 530 540 543 Intuitive act 107 Inwagen, Peter van 581 Irvine, Andrew D. 15 22 Isaacson, Daniel 587 Iterative concept of set 95 111 Jaeger, Gerhard 14 18 Jane, Ignacio 586 Jensen, Ronald 86 149f Jonsson, Olafur 617 621 Jordan, Camille 612 Jubien, Michael 592 Justification of extrapolation 553 558 Kaiser, Karl 510 Kant, Immanuel 4 102 Kaplan, David 395n Keraenen, Jukka 570 Klaua, Dietrich 321n Kleene, Stephen 288n Klein, Felix 5 Kneser, Martin 236 Knowledge by acquaintance 483 Knowledge by description 483 Koenig/Dixon paradox 378 Kotarbinski, Tadeusz 537 kp see Kripke — Platek set theory Kreisel, Georg 200 585n Kripke — Feferman self-referential truth 278 Kripke — Platek set theory (KP) 18 120 199 Kripke, Saul 193 288 317n Kripke’s theory of truth 21 193 288 317n 595 Kunen, Kenneth 87 534 L 112 Lambda abstraction 261 Landini, Gregory 8n 11n 21f 439 442n 452 472 476 Large cardinal 96 Large cardinal axioms 31 Large cardinal hierarchy 100 Large ordinal 315 Largest fixed point 209 Lavine, Shaughan 15 19 22 153 163 165f 173 177n Law of excluded middle 289 Lebesgue measurability 16 30 Leblanc, Hugues 462 Lehman, Hugh 586 Leibniz, Gottfried 96n 484 489 Leonard, Henry 617 Lesniewski, Stanislaw 165n 617 Levy, Azriel 141 Lewis, David 193 600 601 613n 619 Liar paradox 2 191 317 379 505 512 Limit ordinal 315 Lindstroem, Ingrid 202 Linguistic paradox 349 Link, Godehard 136n 138n 140n 150 183n Linsky, Bernard 21 435n Litorial 315 Locally finite theory Fin(T ) 163 Locke, John 96n Logical atomism 8 21 417 485 Logical paradox 376 Logical product 259 Logical syntax 7 Logicism 14 543 Lorenzen, Paul 167 200 LR see reflexion logic Lycan, Bill 490 Mac Lane, Saunders 146 147 578 Mach, Ernst 523 Maddy, Penelope 288n Mahlo cardinal 18 51 97 Many-valued logic 614 Martin — Loef type theory 12 196 202 629 Martin, Donald 440 Material conditional 288 Material conditional, paraconsistent approach 288 Mathematical induction 22 Mathematical induction, Russell’s proof of 452 472 Mathematical object 23 105 584 Mathematical practice 579 Mathematics, explicit 148 193 Mathematics, finite 154 165 549 557 Mathematics, infinitary 551 Mathematics, reverse 15 McCarty, David Charles 22 394 McGee, Vann 23 McLaughlin, Brian P. 613 621 Measurable cardinal 90 Measurement 552 555ff Measurement, scientific 22 Meinong, Alexius 579 Mellor, D.H. 592 Menne, Albert 584 Mental construction 535 Mental mechanism 536 Mereology 617 Metapredicative Mahlo 19 119 122 Metatheory 7 Meyerhof, Otto 511 Mines, Ray 233 Mirimanoff, Dimitry 193 Modal operators 168 Modal paradox 260 Monism 419 Montague, Richard 141 594 Moore, George E. 421 432 489 577 Moore, Gregory 3n 350 Morse — Kelley set theory 308 Moss, Lawrence 149n 194 Move in the language-game 630 Mueller, Johannes 529 Muller, Frederik 147n Multi-valued semantics 21 292 Multiple relation theory of judgement 420 431 453 Multiplicative axiom 438 Mycielski, Jan 15 19 22 153 163f 173 177n 549 552n Mycielski-translation into Fin(ZF) 173 Myhill, John 195 Naive category theory 148 Naive comprehension 285 Naive theory of properties 285 Natural language philosophy 495 Natural ontology 592 606 Natural property 309 Naturalistic conception of properties 607 Naturalized epistemology 495 NBG see Neumann — Bernays — Goedel set theory Nelson circle 509f Nelson, Edward 181 Nelson, Leonard 22 509ff Neo-Hegelian 4 Neue Fries’sche Schule 510 Neumann — Bernays — Goedel set theory (NBG) 12 86 308 Neurath, Otto 496 497 Neutral monism 375 New Foundations (NF) 19 20 136 273 535 New Foundations (NF) subsystems 275ff New Foundations (NF) with urelements (NFU) 149 260 Newcomp (comprehension axiom scheme) 50 52 NF see New Foundations NFU see New Foundations with urelements Niebergall, Karl-Georg 19 150 No-classes theory 9 192 265 435 Noema 105 109 114 Nominalism 15 597 Non-standard analysis 12 Non-well-founded sets 193 Nonstandard continuum 526 Number 0, definition of 441 Object sense 105 106 Objective 112 Objective world 554 Objectivity 104 Objectual quantification 374 Ockham’s razor 8 Ontological atom 484 Ontological commitment 597 Ontological development 466 Ontological eliminativism 374 Ontology 21 Open (truth value) 317 Order (vs. type) 405 Order completeness 232 234 Order indiscernibles 556 Ordinal analysis 18 Ordinal, 18 200 Ordinal, acceptable 301 Ordinal, large 315 Ordinal, limit 315 Ordinal, proof-theoretic 119 Ordinal, subtle 52 Ordinal, successor 315 Ordinal, transdefinite 315 Palmgren, Erik 232n Paradox of propositions 401 Paradox, Berry 378 Paradox, Bradley 21 419 426 429 432 Paradox, Burali — Forti (greatest ordinal) 191 349 378 Paradox, Cantor (greatest cardinal) 1 349 350 378 502f 506 Paradox, Curry 286 Paradox, epistemic 464 Paradox, Grelling 510n 512 Paradox, Hilbert 2 22 504ff 510f Paradox, intentional 464 Paradox, Koenig/Dixon 378 Paradox, liar 2 191 317 379 505 512 Paradox, linguistic 349 Paradox, logical 376 Paradox, modal 260 Paradox, of propositions 20 377 Paradox, po/ao 377 388 Paradox, recurrence 2 Paradox, Richard 378 Paradox, Russell 1 29 49 137 191 247 265 285 349 350 501f 505 511 512 593 600 605 Paradox, Russell, in a constructive context 221 Paradox, Russell, predicational variant 364 Paradox, selfreferential 349 Paradox, semantic 317 349 376 464 Paradox, semantic, fixed point approach 288 Paradox, set-theoretic 464 Paradox, Skolem 534 Paradox, Zermelo 501 505 507 510 Parsons, Charles 578 Parsons, Terence 251 Patterns, mathematical structures as 565 Pawlikowski, Janusz 549 pd see projective determinacy axiom Peano, Giuseppe 351 379 412 508 Peckhaus, Volker 2n 5 6n 22 Peirce, Charles S. 453 577 Perception 106 Perspective variations 106 Phenomenology 104 114 Physical quantity 554 556
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