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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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Предметный указатель
Pigeon Hole Principle 476 Planck, Max 2 Plantinga, Alvin 601 Plato 484 Platonism 21 94 311 313 449 538 551 577 Platonism, conditional 32 Platonism, Goedel’s 12 Po/ao paradox 377 388 Poincare, Henri 2 5 12 191 373 533 540 577 Possible world semantics 601 Postulationism 586 Potential infinite 154 166 PRA see primitive recursive arithmetic Pre-utterance 628 Predicable 1 364 Predicate logic 628 Predicate logic, dynamic 628 Predicate logic, fibered view 628 Predicative 252 Predicative analysis 473 Predicative class hierarchy 319 Predicativism 12 200 Predicativism, system W 14 Predicativity 402 Primitive recursive arithmetic (PRA) 19 155 Principle of disjunction (of types) 404 Principles for propositions and truth 261 Problem of the many 612 Probst, Dieter 18 Proclus 102 Projective determinacy axiom (PD) 16 31 32 98 102 112 Projective sets 29 98 Projective sets, measure problem 44 Proof-theoretic ordinal 119 Proof-theoretical reducibility 154 Proper class 306 Property theories 595 Property, Baire 35 Property, natural 309 Property, naturalistic conception 607 Property, semantical conception 591 Property, semantically-conceived 309 Proposition 7 419 450 Proposition, elementary 405ff Proposition, elimination of 406ff Proposition, general 404f Proposition, hierarchy of 404f 410ff Proposition, paradox of 20 Proposition,Propositional function 8 418 450 Propositional object 261 Pudlak, Pavel 158 Putnam, Hilary 14 551 600 Quantification 9 Quantification, objectual 374 Quantification, substitutional 450 459 Quine — Putnam indispensability 14 551 Quine, Willard V. 7 14f 136 149 273 376 495 551 580 597 602 Ramified analysis 272 Ramified second-order logic 457 Ramified theory of types 10 450 Ramified third-order logic 457 Ramified types 457 Ramsey, Frank P. 14n 349 377 379 451 464 512 594 Rao, Vidhyanath 148n Rathjen, Michael 19 232n Rationalism 22 535 538f Real number 324 Real number in constructive analysis 227 Real number, transdefinite 345 Real number, transfinite 329 336 Recurrence paradox 2 Recursively saturated 254 Reducibility, finitistic 154 Reducibility, proof-theoretical 154 Reduction of material objects to sense-data 483 Reductionism 14 Reflected truth 318 Reflection principle 97 111 Reflective universes 141 Reflexion logic (LR) 21 317 Regressive method 15 491 Reinhardt, Wiliam 534 Relations 418 Resnik, Michael 565 Resource consciousness 15 Restricted diagonalization 278 Reverse mathematics 15 Richard paradox 378 Richman, Fred 231n 237 243n Robinson, Abraham 12 Robinson’s arithmetic 253 Rodriguez-Consuegra, Francisco 8n 21 Rouilhan, Philippe de 21 444n 446n Rueede, Christian 119 127 Ruestow, Alexander 512f Ruitenberg, Willem 237 Russell — Zermelo paradox see Russell’s paradox Russell, Bertrand 1ff 29 49 136ff 191ff 247f 259f 264f 311 349ff 373ff 401ff 417ff 435ff 449ff 481ff 501 507 510f 533 543ff 561ff 567 569ff 577ff 585ff 594 605 611 613 615f 619f 639 Russell-the-fallibilist 481 Russell-the-foundationalist 481 Russell’s eliminativism 375 Russell’s method of analysis 487 Russell’s paradox 1 29 49 137 191 221 247 265 285 349 350 501f 505 511 512 534 593 600 605 Russell’s paradox in a constructive context 221 Russell’s paradox, predicational variant 1 364 Russell’s substitutional theory 373ff Russell’s substitutional theory axiom schemata for the 1906 version 390 Russell’s substitutional theory, axiom schemata for the 1905 version 380 Russell’s theory of knowledge 22 482 Satisfaction 306 Schema V 254 Schlick, Moritz 523 Scholz, Heinrich 507 Schroeder, Ernst 507 509 577 Schroeder-Heister, Peter 251 Schuette, Kurt 13 200 Schuster, Peter 20 Schwichtenberg, Helmut 20 Scope of class symbols 439 Scott, Dana 261n 534 Second-order logic 248 Second-order number theory 30 98 Self-application 591 Self-instantiation 591 592 606 Self-predication 1 11 Self-referential imperative 312 324 Self-referential paradox 349 Self-referential truth, Kripke — Feferman 278 Sellars, Wilfrid 599 Semantic paradox 193 317 349 376 464 Semantic pretence 582 Semantical conception of properties 591 Semantically unfounded sentence 317 Semantics 23 592 601 Semantics, 3-valued 292 Semantics, multi-valued 21 292 Semantics, realist 584 Semantics, substitutional 469 Sense-data 483ff Sentence 640 Sentence, definition of 634 Sentential expansion 632 Sequential completeness 231 234 Set continuous class operator 208 Set theory New Foundations (NF) 535 Set theory with universes 141 Set theory, admissible 121 Set theory, axiomatization of 509 Set theory, basic 121 Set theory, Cantorian 504 Set theory, constructive 195 Set theory, constructive, CZFA 198 Set theory, constructive, Zermelo — Fraenkel (CZF) 196 Set theory, descriptive 16 89 Set theory, Kripke — Platek (KP) 18 120 199 Set theory, Kripke — Platek (KP), KPi 18 120 Set theory, Morse — Kelley 308 Set theory, Neumann — Bernays — Goedel (NBG) 12 86 308 Set theory, New Foundations (NF) 19 20 136 273 Set theory, New Foundations (NF), subsystems 275ff Set theory, New Foundations (NF), with urelements (NFU) 149 260 Set theory, Zermelo Z 11 Set theory, Zermelo — Fraenkel (ZF) 11 13 33 141 596 Set theory, Zermelo — Fraenkel (ZF), with choice (ZFC) 34 Set theory, Zermelo — Fraenkel (ZF), with reflective universes 141 Set theory, Zermelo — Fraenkel (ZF), with the Axiom of Choice (ZFC) 141 Set, constructible 85 99 103 Set, non-well-founded 193 Set, projective 29 44 98 Set, virtual 49 61 Set-theoretic paradox 464 Shapiro, Stewart 551 565 Sharp operation 18 Shoemaker, Sidney 607 Signitive act 107 Simple theory of types 11 137 438 606 Simultaneous dual substitution 385 Single-candidate thesis 617ff Skolem paradox 534 Skolem, Thoralf 452 Slupecki, Jerzy 537 Sokal, Alan 546 Solovay, Robert 13 Solution lemma 207 212 Specker, Ernst 136 150 275 St Paul 349 Steinhaus, Hugo 534 Stout, George F. 424 Stratification 273 Stratified comprehension 273 Stratified explicit comprehension 274 Stratified T-schema 280 Stratified truth 273 streams 213 Structural realism 374 Structuralism 23 587 Structuralism, ante rem 565 Structuralism, Dedekind’s 23 562 569 Structuralism, eliminative 565 Structuralism, modal 565 587 Structuralism, set-theoretic 565 Sturm, Holger 23 Subcountable 223 Subject and predicate 426 430 Subjective 112 Subjectivity 104 Substitution 7 376 Substitution, simultaneous dual 385 Substitutional interpretation 452 Substitutional quantification 450 459 Substitutional semantics 469 Substitutional theory (Russell) 21 373ff 402 404 Subtle cardinal 18 50f Subtle ordinal 52 Successor ordinal 315 Superstrong cardinal 89 Swoyer, Chris 600 Symbolic explicitness 6 Syncategorematical 641 T-schema, stratified 280 Tait, William 159n 569 Tarski, Alfred 13 404n 537 614 Tertium non datur 519 Theory of intuition 542 Theory of judgment 406ff 418 426 Theory of properties 23 Theory of properties, naive 285 Theory of truth 13 20 595 Theory of truth, Kripke 21 193 288 317n 595 Theory of types 10 Theory of types of attributes, axiom schemata for 384 Theory of types, Martin — Loef 12 196 202 629 Theory of types, ramified 10 402 450 Theory of types, simple 11 137 438 606 Theory of types, simple, extensional 451 Third truth value 317 Thomas, Robert S.D. 23 Thomson, James 168 Thomson, Judith J. 617n 621 Thought-objects 533 Tooley, Michael 592 607 Topoi 567 Transcendence 109 Transcendental 113 Transcendental predicate 594 Transdefinite ordinal 315 Transdefinite real numbers 345 Transdefinite well-ordering 314 Transfinite real numbers 329 336 Troelstra, Anne 236n 243 Truistic context principle 631 Truth 541 Truth value gaps 614 Truth, hierarchy 319 Truth, reflected 318 Truth, self-referential 278 Truth, stratified 273 Truth, theory of 595 Truth, unreflected 318 Twardowski, Kazimierz 537 Twofold nature of relations 426 TYPE 403f Type free language 595 Type of level n 467 Type symbol 383 Type, ramified 457 Type, simple 466 Typed 456 Types, doctrine of 401 Types, ramified theory of 402 Typical ambiguity 19 135 Uncountable 223 Unfounded sentence 317 Unger, Peter 611ff 617n Unit of meaning 23 630 637 Universalism 403f Universally Baire 35 Universals 424 Unreflected truth 318 Urmson, J.O. 496 V 95 103 113 V = L 61 86 Vagueness 23 613 Value-range 248 Van Bendegem, Jean Paul 582n van Dalen, Dirk 243 Van Inwagen, Peter 613n Vaught, Robert L. 141 Veblen function 19n 201 Veblen function, ternary 129 Vicious circle principle 10 12 192 374 377 402ff Vicious regress 192 Virtual class 49 Virtual set 49 61 Visser, Albert 23 von Mises, Richard 523 Von Neumann hierarchy 85 von Neumann, John 352 Wadge hierarchy 36 Waismann, Friedrich 171
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