Interpreting Gödel: critical essays
The logician Kurt Gödel (1906–1978) published a paper in 1931 formulating what have come to be known as his 'incompleteness theorems', which prove, among other things, that within any formal system with resources sufficient to code arithmetic, questions exist which are neither provable nor...
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| Format: | Electronic eBook |
| Language: | English |
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| Online Access: | BSB01 FHN01 UBG01 Volltext |
| Summary: | The logician Kurt Gödel (1906–1978) published a paper in 1931 formulating what have come to be known as his 'incompleteness theorems', which prove, among other things, that within any formal system with resources sufficient to code arithmetic, questions exist which are neither provable nor disprovable on the basis of the axioms which define the system. These are among the most celebrated results in logic today. In this volume, leading philosophers and mathematicians assess important aspects of Gödel's work on the foundations and philosophy of mathematics. Their essays explore almost every aspect of Godel's intellectual legacy including his concepts of intuition and analyticity, the Completeness Theorem, the set-theoretic multiverse, and the state of mathematical logic today. This groundbreaking volume will be invaluable to students, historians, logicians and philosophers of mathematics who wish to understand the current thinking on these issues |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xi, 279 pages) |
| ISBN: | 9780511756306 |
| DOI: | 10.1017/CBO9780511756306 |
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| 505 | 8 | |a 1. Introduction: Gödel and analytic philosophy: how did we get here? / Juliette Kennedy -- Part I. Gödel on Intuition: 2. Intuitions of three kinds in Gödel's views on the continuum / John P. Burgess; 3. Gödel on how to have your mathematics and know it too / Janet Folina -- Part II. The Completeness Theorem: 4. Completeness and the ends of axiomatization / Michael Detlefsen; 5. Logical completeness, form, and content: an archaeology / Curtis Franks -- Part III. Computability and Analyticity: 6. Gödel's 1946 Princeton bicentennial lecture: an appreciation / Juliette Kennedy; 7. Analyticity for realists / Charles Parsons -- Part IV. The Set-theoretic Multiverse: 8. Gödel's program / John R. Steel; 9. Multiverse set theory and absolutely undecidable propositions / Jouko Väänänen -- Part V. The Legacy: 10. Undecidable problems: a sampler / Bjorn Poonen; 11. Reflecting on logical dreams / Saharon Shelah | |
| 520 | |a The logician Kurt Gödel (1906–1978) published a paper in 1931 formulating what have come to be known as his 'incompleteness theorems', which prove, among other things, that within any formal system with resources sufficient to code arithmetic, questions exist which are neither provable nor disprovable on the basis of the axioms which define the system. These are among the most celebrated results in logic today. In this volume, leading philosophers and mathematicians assess important aspects of Gödel's work on the foundations and philosophy of mathematics. Their essays explore almost every aspect of Godel's intellectual legacy including his concepts of intuition and analyticity, the Completeness Theorem, the set-theoretic multiverse, and the state of mathematical logic today. This groundbreaking volume will be invaluable to students, historians, logicians and philosophers of mathematics who wish to understand the current thinking on these issues | ||
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| contents | 1. Introduction: Gödel and analytic philosophy: how did we get here? / Juliette Kennedy -- Part I. Gödel on Intuition: 2. Intuitions of three kinds in Gödel's views on the continuum / John P. Burgess; 3. Gödel on how to have your mathematics and know it too / Janet Folina -- Part II. The Completeness Theorem: 4. Completeness and the ends of axiomatization / Michael Detlefsen; 5. Logical completeness, form, and content: an archaeology / Curtis Franks -- Part III. Computability and Analyticity: 6. Gödel's 1946 Princeton bicentennial lecture: an appreciation / Juliette Kennedy; 7. Analyticity for realists / Charles Parsons -- Part IV. The Set-theoretic Multiverse: 8. Gödel's program / John R. Steel; 9. Multiverse set theory and absolutely undecidable propositions / Jouko Väänänen -- Part V. The Legacy: 10. Undecidable problems: a sampler / Bjorn Poonen; 11. Reflecting on logical dreams / Saharon Shelah |
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| discipline | Mathematik Philosophie |
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| spelling | Interpreting Gödel critical essays edited by Juliette Kennedy, University of Helsinki Cambridge Cambridge University Press 2014 1 online resource (xi, 279 pages) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 05 Oct 2015) 1. Introduction: Gödel and analytic philosophy: how did we get here? / Juliette Kennedy -- Part I. Gödel on Intuition: 2. Intuitions of three kinds in Gödel's views on the continuum / John P. Burgess; 3. Gödel on how to have your mathematics and know it too / Janet Folina -- Part II. The Completeness Theorem: 4. Completeness and the ends of axiomatization / Michael Detlefsen; 5. Logical completeness, form, and content: an archaeology / Curtis Franks -- Part III. Computability and Analyticity: 6. Gödel's 1946 Princeton bicentennial lecture: an appreciation / Juliette Kennedy; 7. Analyticity for realists / Charles Parsons -- Part IV. The Set-theoretic Multiverse: 8. Gödel's program / John R. Steel; 9. Multiverse set theory and absolutely undecidable propositions / Jouko Väänänen -- Part V. The Legacy: 10. Undecidable problems: a sampler / Bjorn Poonen; 11. Reflecting on logical dreams / Saharon Shelah The logician Kurt Gödel (1906–1978) published a paper in 1931 formulating what have come to be known as his 'incompleteness theorems', which prove, among other things, that within any formal system with resources sufficient to code arithmetic, questions exist which are neither provable nor disprovable on the basis of the axioms which define the system. These are among the most celebrated results in logic today. In this volume, leading philosophers and mathematicians assess important aspects of Gödel's work on the foundations and philosophy of mathematics. Their essays explore almost every aspect of Godel's intellectual legacy including his concepts of intuition and analyticity, the Completeness Theorem, the set-theoretic multiverse, and the state of mathematical logic today. This groundbreaking volume will be invaluable to students, historians, logicians and philosophers of mathematics who wish to understand the current thinking on these issues Gödel, Kurt Gödel, Kurt 1906-1978 (DE-588)11869569X gnd rswk-swf Mathematik Philosophie Logic, Symbolic and mathematical Mathematics / Philosophy 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content Gödel, Kurt 1906-1978 (DE-588)11869569X p 2\p DE-604 Kennedy, Juliette 1955- (DE-588)1023532948 edt Erscheint auch als Druckausgabe 978-1-107-00266-1 https://doi.org/10.1017/CBO9780511756306 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Interpreting Gödel critical essays 1. Introduction: Gödel and analytic philosophy: how did we get here? / Juliette Kennedy -- Part I. Gödel on Intuition: 2. Intuitions of three kinds in Gödel's views on the continuum / John P. Burgess; 3. Gödel on how to have your mathematics and know it too / Janet Folina -- Part II. The Completeness Theorem: 4. Completeness and the ends of axiomatization / Michael Detlefsen; 5. Logical completeness, form, and content: an archaeology / Curtis Franks -- Part III. Computability and Analyticity: 6. Gödel's 1946 Princeton bicentennial lecture: an appreciation / Juliette Kennedy; 7. Analyticity for realists / Charles Parsons -- Part IV. The Set-theoretic Multiverse: 8. Gödel's program / John R. Steel; 9. Multiverse set theory and absolutely undecidable propositions / Jouko Väänänen -- Part V. The Legacy: 10. Undecidable problems: a sampler / Bjorn Poonen; 11. Reflecting on logical dreams / Saharon Shelah Gödel, Kurt Gödel, Kurt 1906-1978 (DE-588)11869569X gnd Mathematik Philosophie Logic, Symbolic and mathematical Mathematics / Philosophy |
| subject_GND | (DE-588)11869569X (DE-588)4143413-4 |
| title | Interpreting Gödel critical essays |
| title_auth | Interpreting Gödel critical essays |
| title_exact_search | Interpreting Gödel critical essays |
| title_full | Interpreting Gödel critical essays edited by Juliette Kennedy, University of Helsinki |
| title_fullStr | Interpreting Gödel critical essays edited by Juliette Kennedy, University of Helsinki |
| title_full_unstemmed | Interpreting Gödel critical essays edited by Juliette Kennedy, University of Helsinki |
| title_short | Interpreting Gödel |
| title_sort | interpreting godel critical essays |
| title_sub | critical essays |
| topic | Gödel, Kurt Gödel, Kurt 1906-1978 (DE-588)11869569X gnd Mathematik Philosophie Logic, Symbolic and mathematical Mathematics / Philosophy |
| topic_facet | Gödel, Kurt Gödel, Kurt 1906-1978 Mathematik Philosophie Logic, Symbolic and mathematical Mathematics / Philosophy Aufsatzsammlung |
| url | https://doi.org/10.1017/CBO9780511756306 |
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