In the light of logic:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York
Oxford University Press
©1998
|
| Schriftenreihe: | Logic and computation in philosophy
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| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (pages 309-330) and index In this collection of essays written over a period of twenty years, Solomon Feferman explains advanced results in modern logic and employs them to cast light on significant problems in the foundations of mathematics. Most troubling among these is the revolutionary way in which Georg Cantor elaborated the nature of the infinite, and in doing so helped transform the face of twentieth-century mathematics. Feferman details the development of Cantorian concepts and the foundational difficulties they engendered. He argues that the freedom provided by Cantorian set theory was purchased at a heavy philosophical price, namely adherence to a form of mathematical platonism that is difficult to support I. Foundational Problems - Deciding the undecidable: Wrestling with Hilbert's problems - Infinity in mathematics: Is Cantor necessary? -- - II. Foundational Ways - The logic of mathematical discovery versus the logical structure of mathematics - Foundational ways - Working foundations -- - III. Godel - Godel's life and work - Kurt Godel: Conviction and caution - Introductory note to Godel's 1933 lecture -- - IV. Proof Theory - What does logic have to tell us about mathematical proofs? - What rests on what? The proof-theoretic analysis of mathematics - Godel's Dialectica interpretation and its two-way stretch -- - V. Countably Reducible Mathematics - Infinity in mathematics: Is Cantor necessary? (Conclusion) |
| Beschreibung: | 1 Online-Ressource (xii, 340 pages) |
| ISBN: | 0195080300 058535829X 9780585358291 |
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| author | Feferman, Solomon |
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| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| spelling | Feferman, Solomon Verfasser aut In the light of logic Solomon Feferman New York Oxford University Press ©1998 1 Online-Ressource (xii, 340 pages) txt rdacontent c rdamedia cr rdacarrier Logic and computation in philosophy Includes bibliographical references (pages 309-330) and index In this collection of essays written over a period of twenty years, Solomon Feferman explains advanced results in modern logic and employs them to cast light on significant problems in the foundations of mathematics. Most troubling among these is the revolutionary way in which Georg Cantor elaborated the nature of the infinite, and in doing so helped transform the face of twentieth-century mathematics. Feferman details the development of Cantorian concepts and the foundational difficulties they engendered. He argues that the freedom provided by Cantorian set theory was purchased at a heavy philosophical price, namely adherence to a form of mathematical platonism that is difficult to support I. Foundational Problems - Deciding the undecidable: Wrestling with Hilbert's problems - Infinity in mathematics: Is Cantor necessary? -- - II. Foundational Ways - The logic of mathematical discovery versus the logical structure of mathematics - Foundational ways - Working foundations -- - III. Godel - Godel's life and work - Kurt Godel: Conviction and caution - Introductory note to Godel's 1933 lecture -- - IV. Proof Theory - What does logic have to tell us about mathematical proofs? - What rests on what? The proof-theoretic analysis of mathematics - Godel's Dialectica interpretation and its two-way stretch -- - V. Countably Reducible Mathematics - Infinity in mathematics: Is Cantor necessary? (Conclusion) MATHEMATICS / Infinity bisacsh MATHEMATICS / Logic bisacsh Logic, Symbolic and mathematical fast Logic, Symbolic and mathematical Logik (DE-588)4036202-4 gnd rswk-swf 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content Logik (DE-588)4036202-4 s 2\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=23626 Aggregator 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 |
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| title | In the light of logic |
| title_auth | In the light of logic |
| title_exact_search | In the light of logic |
| title_full | In the light of logic Solomon Feferman |
| title_fullStr | In the light of logic Solomon Feferman |
| title_full_unstemmed | In the light of logic Solomon Feferman |
| title_short | In the light of logic |
| title_sort | in the light of logic |
| topic | MATHEMATICS / Infinity bisacsh MATHEMATICS / Logic bisacsh Logic, Symbolic and mathematical fast Logic, Symbolic and mathematical Logik (DE-588)4036202-4 gnd |
| topic_facet | MATHEMATICS / Infinity MATHEMATICS / Logic Logic, Symbolic and mathematical Logik Aufsatzsammlung |
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