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Gödel's theorem [[electronic resource] ] : an incomplete guide to its use and abuse / / Torkel Franzén
| Gödel's theorem [[electronic resource] ] : an incomplete guide to its use and abuse / / Torkel Franzén |
| Autore | Franzén Torkel |
| Pubbl/distr/stampa | Wellesley, MA, : A K Peters, c2005 |
| Descrizione fisica | x, 172 p |
| Disciplina | 511.3 |
| Soggetto topico |
Gödel's theorem
Incompleteness theorems |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-56881-500-X
1-4398-7692-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 5050 1. Introduction -- 2. The incompleteness theorem : an overview -- 3. Computability, formal systems, and incompleteness -- 4. Incompleteness everywhere -- 5. Skepticism and confidence -- 6. Gödel, minds, and computers -- 7. Gödel's completeness theorem -- 8. Incompleteness, complexity, and infinity |
| Record Nr. | UNINA-9910454403903321 |
Franzén Torkel
|
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| Wellesley, MA, : A K Peters, c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Gödel's theorem [[electronic resource] ] : an incomplete guide to its use and abuse / / Torkel Franzén
| Gödel's theorem [[electronic resource] ] : an incomplete guide to its use and abuse / / Torkel Franzén |
| Autore | Franzén Torkel |
| Pubbl/distr/stampa | Wellesley, MA, : A K Peters, c2005 |
| Descrizione fisica | x, 172 p |
| Disciplina | 511.3 |
| Soggetto topico |
Gödel's theorem
Incompleteness theorems |
| ISBN |
1-56881-500-X
1-4398-7692-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 5050 1. Introduction -- 2. The incompleteness theorem : an overview -- 3. Computability, formal systems, and incompleteness -- 4. Incompleteness everywhere -- 5. Skepticism and confidence -- 6. Gödel, minds, and computers -- 7. Gödel's completeness theorem -- 8. Incompleteness, complexity, and infinity |
| Record Nr. | UNINA-9910782047303321 |
|
Franzén Torkel
|
||
| Wellesley, MA, : A K Peters, c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Gödel's theorem : an incomplete guide to its use and abuse / / Torkel Franzén
| Gödel's theorem : an incomplete guide to its use and abuse / / Torkel Franzén |
| Autore | Franzén Torkel |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Wellesley, MA, : A K Peters, c2005 |
| Descrizione fisica | x, 172 p |
| Disciplina | 511.3 |
| Soggetto topico |
Gödel's theorem
Incompleteness theorems |
| ISBN |
1-56881-500-X
1-4398-7692-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 5050 1. Introduction -- 2. The incompleteness theorem : an overview -- 3. Computability, formal systems, and incompleteness -- 4. Incompleteness everywhere -- 5. Skepticism and confidence -- 6. Gödel, minds, and computers -- 7. Gödel's completeness theorem -- 8. Incompleteness, complexity, and infinity |
| Record Nr. | UNINA-9910828412403321 |
|
Franzén Torkel
|
||
| Wellesley, MA, : A K Peters, c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Gödel's incompleteness theorem / V.A. Uspensky
| Gödel's incompleteness theorem / V.A. Uspensky |
| Autore | Uspenskiĭ, Vladimir Anreevich) |
| Edizione | [Revised 1982 Russian edition] |
| Descrizione fisica | 104 pages ; 20 cm |
| Disciplina | 511.3 |
| Altri autori (Persone) | Koblitz, Neal |
| Collana | Little mathematics library |
| Soggetto topico |
Gödel's theorem
Incompleteness theorems |
| Classificazione | LC QA9.65 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991003532459707536 |
|
Uspenskiĭ, Vladimir Anreevich)
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| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Undecidability, uncomputability, and unpredictability / / Anthony Aguirre, Zeeya Merali, David Sloan, editors
| Undecidability, uncomputability, and unpredictability / / Anthony Aguirre, Zeeya Merali, David Sloan, editors |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (181 pages) |
| Disciplina | 511.3 |
| Collana | Frontiers Collection |
| Soggetto topico |
Decidability (Mathematical logic)
Completeness theorem Incompleteness theorems |
| ISBN | 3-030-70354-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Introduction -- Reference -- 2 Undecidability and Unpredictability: Not Limitations, but Triumphs of Science -- 2.1 The Pessimistic View -- 2.2 On Axiomatic Theories and Structural Differentiation -- 2.3 The Physical World: Every Thing Must Go -- 2.4 Ontic Structural Realism -- 2.5 Quantum-Optimistic Conclusions -- References -- 3 Indeterminism and Undecidability -- 3.1 Introduction: Gödel and Bell -- 3.2 Randomness and Its Unprovability -- 3.3 Rethinking Bell's Theorem -- 3.4 Are Deterministic Hidden Variable Theories Deterministic? -- 3.5 Conclusion and Discussion -- References -- 4 Unpredictability and Randomness -- 4.1 Introduction -- 4.2 CA a Closer Look -- 4.3 Conditional Branching -- 4.3.1 Conditional Branching Candidates -- 4.4 Measuring Randomness -- 4.4.1 Random Oracle -- 4.4.2 BCA -- 4.4.3 Distinguishing Chances -- 4.5 Speculations -- References -- 5 Indeterminism, Causality and Information: Has Physics Ever Been Deterministic? -- 5.1 When Did Physics Become Unpredictable? -- 5.2 The ``Orthodox Interpretation'' of Classical Physics -- 5.3 An Alternative, Indeterministic Interpretation of Classical Physics -- 5.3.1 Determinism at Odds with Information Principles -- 5.3.2 ``Finite Information Quantities'' (FIQs) -- 5.3.3 The Classical ``Measurement Problem'' -- 5.4 (In)determinism and Causality -- 5.5 Concluding Remarks -- References -- 6 Undecidability, Fractal Geometry and the Unity of Physics -- 6.1 The Disunity of 20th Century Physics -- 6.2 Chaos and the Undecidable Geometry of Fractal Attractors -- 6.3 Towards a Unification of 21st Century Physics -- 6.3.1 Chaos Theory and Relativity Theory -- 6.3.2 Chaos Theory and Quantum Theory -- 6.3.3 Quantum Theory and General Relativity Theory -- 6.4 Discussion -- References -- 7 A Gödelian Hunch from Quantum Theory -- 7.1 Introduction.
7.2 A Gödelian Hunch from Quantum Contextuality -- 7.2.1 Counterfactual Undecidability -- 7.2.2 Topological Undecidability -- 7.3 A Gödelian Hunch from the Measurement Problem -- 7.3.1 Wigner's Friend, Universality, Meta-Contextuality and Measurement -- 7.3.2 ``Wigner's Friendifications'' -- 7.3.3 The Heirs of Copenhagen -- 7.4 Conclusion: Is Physics Paradoxical? -- 7.5 Epilogue: A Gödelian Hunch from Time -- References -- 8 Epistemic Horizons: This Sentence Is 1sqrt2(|truerangle + |falserangle) -- 8.1 Introduction: Interpretation Versus Reconstruction -- 8.2 Horizons of Our Understanding -- 8.2.1 Superposition -- 8.2.2 Entanglement -- 8.3 Does This Ring a Bell? -- 8.4 EPistemic HoRizons: Incomplete Quantum Mechanics? -- 8.5 Hardy's Paradox -- 8.6 The Frauchiger-Renner Argument -- 8.7 Conclusion -- References -- 9 Why Is the Universe Comprehensible? -- 9.1 Introduction -- 9.2 Comprehensibility -- 9.3 The Price of Comprehensibility -- 9.4 Limitations -- References -- 10 Noisy Deductive Reasoning: How Humans Construct Math, and How Math Constructs Universes -- 10.1 Introduction -- 10.2 Formal Systems -- 10.3 A Stochastic Mathematical Reasoner -- 10.4 Connections to Actual Mathematical Practice -- 10.4.1 Generating New Research Questions -- 10.4.2 Bayesian Models of Heuristics of Human Mathematicians-General Considerations -- 10.4.3 A Bayesian Justification of Abduction in Mathematical Reasoning -- 10.4.4 A Bayesian Formulation of the Value of Multiple Proof Paths in Mathematical Reasoning -- 10.5 Measures over Multiverses -- 10.6 Future Research Directions -- 10.7 Conclusion -- References -- 11 Computational Complexity as Anthropic Principle: A Fable -- 11.1 Laplace Builds a Demon -- 11.2 The Science that Destroys Demons -- References -- Appendix List of Winners -- First Prizes -- Second Prize -- Third Prizes -- Fourth Prizes. Prize for an Interesting Literary Discourse -- Prize for a Creative Approach to the Problem. |
| Record Nr. | UNISA-996466752403316 |
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Undecidability, uncomputability, and unpredictability / / Anthony Aguirre, Zeeya Merali, David Sloan, editors
| Undecidability, uncomputability, and unpredictability / / Anthony Aguirre, Zeeya Merali, David Sloan, editors |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (181 pages) |
| Disciplina | 511.3 |
| Collana | Frontiers Collection |
| Soggetto topico |
Decidability (Mathematical logic)
Completeness theorem Incompleteness theorems |
| ISBN | 3-030-70354-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Introduction -- Reference -- 2 Undecidability and Unpredictability: Not Limitations, but Triumphs of Science -- 2.1 The Pessimistic View -- 2.2 On Axiomatic Theories and Structural Differentiation -- 2.3 The Physical World: Every Thing Must Go -- 2.4 Ontic Structural Realism -- 2.5 Quantum-Optimistic Conclusions -- References -- 3 Indeterminism and Undecidability -- 3.1 Introduction: Gödel and Bell -- 3.2 Randomness and Its Unprovability -- 3.3 Rethinking Bell's Theorem -- 3.4 Are Deterministic Hidden Variable Theories Deterministic? -- 3.5 Conclusion and Discussion -- References -- 4 Unpredictability and Randomness -- 4.1 Introduction -- 4.2 CA a Closer Look -- 4.3 Conditional Branching -- 4.3.1 Conditional Branching Candidates -- 4.4 Measuring Randomness -- 4.4.1 Random Oracle -- 4.4.2 BCA -- 4.4.3 Distinguishing Chances -- 4.5 Speculations -- References -- 5 Indeterminism, Causality and Information: Has Physics Ever Been Deterministic? -- 5.1 When Did Physics Become Unpredictable? -- 5.2 The ``Orthodox Interpretation'' of Classical Physics -- 5.3 An Alternative, Indeterministic Interpretation of Classical Physics -- 5.3.1 Determinism at Odds with Information Principles -- 5.3.2 ``Finite Information Quantities'' (FIQs) -- 5.3.3 The Classical ``Measurement Problem'' -- 5.4 (In)determinism and Causality -- 5.5 Concluding Remarks -- References -- 6 Undecidability, Fractal Geometry and the Unity of Physics -- 6.1 The Disunity of 20th Century Physics -- 6.2 Chaos and the Undecidable Geometry of Fractal Attractors -- 6.3 Towards a Unification of 21st Century Physics -- 6.3.1 Chaos Theory and Relativity Theory -- 6.3.2 Chaos Theory and Quantum Theory -- 6.3.3 Quantum Theory and General Relativity Theory -- 6.4 Discussion -- References -- 7 A Gödelian Hunch from Quantum Theory -- 7.1 Introduction.
7.2 A Gödelian Hunch from Quantum Contextuality -- 7.2.1 Counterfactual Undecidability -- 7.2.2 Topological Undecidability -- 7.3 A Gödelian Hunch from the Measurement Problem -- 7.3.1 Wigner's Friend, Universality, Meta-Contextuality and Measurement -- 7.3.2 ``Wigner's Friendifications'' -- 7.3.3 The Heirs of Copenhagen -- 7.4 Conclusion: Is Physics Paradoxical? -- 7.5 Epilogue: A Gödelian Hunch from Time -- References -- 8 Epistemic Horizons: This Sentence Is 1sqrt2(|truerangle + |falserangle) -- 8.1 Introduction: Interpretation Versus Reconstruction -- 8.2 Horizons of Our Understanding -- 8.2.1 Superposition -- 8.2.2 Entanglement -- 8.3 Does This Ring a Bell? -- 8.4 EPistemic HoRizons: Incomplete Quantum Mechanics? -- 8.5 Hardy's Paradox -- 8.6 The Frauchiger-Renner Argument -- 8.7 Conclusion -- References -- 9 Why Is the Universe Comprehensible? -- 9.1 Introduction -- 9.2 Comprehensibility -- 9.3 The Price of Comprehensibility -- 9.4 Limitations -- References -- 10 Noisy Deductive Reasoning: How Humans Construct Math, and How Math Constructs Universes -- 10.1 Introduction -- 10.2 Formal Systems -- 10.3 A Stochastic Mathematical Reasoner -- 10.4 Connections to Actual Mathematical Practice -- 10.4.1 Generating New Research Questions -- 10.4.2 Bayesian Models of Heuristics of Human Mathematicians-General Considerations -- 10.4.3 A Bayesian Justification of Abduction in Mathematical Reasoning -- 10.4.4 A Bayesian Formulation of the Value of Multiple Proof Paths in Mathematical Reasoning -- 10.5 Measures over Multiverses -- 10.6 Future Research Directions -- 10.7 Conclusion -- References -- 11 Computational Complexity as Anthropic Principle: A Fable -- 11.1 Laplace Builds a Demon -- 11.2 The Science that Destroys Demons -- References -- Appendix List of Winners -- First Prizes -- Second Prize -- Third Prizes -- Fourth Prizes. Prize for an Interesting Literary Discourse -- Prize for a Creative Approach to the Problem. |
| Record Nr. | UNINA-9910741175803321 |
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
