Platonism and anti-Platonism in mathematics /:
Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible views. Introducing a form of platonism ("full-blooded platonism") that solves all problems traditionally associat...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York :
Oxford University Press,
1998.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible views. Introducing a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, he proceeds to defend anti-platonism (in particular, mathematical fictionalism) against various attacks, most notably the Quine-Putnam indispensability attack. He concludes by arguing that it is not simply that we do not currently have any good argument for or against platonism, but that we could never have such an argument and, indeed, that there is no fact of the matter as to whether platonism is correct |
| Beschreibung: | 1 online resource (x, 217 pages) |
| Bibliographie: | Includes bibliographical references (pages 207-211) and index. |
| ISBN: | 0585245673 9780585245676 0195143981 9780195143980 9780195122305 0195122305 1280470836 9781280470837 |
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| 245 | 1 | 0 | |a Platonism and anti-Platonism in mathematics / |c Mark Balaguer. |
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| 505 | 0 | |a Cover -- Contents -- 1 Introduction -- 1. The Project of This Book -- 2. Mathematical Platonism and Anti-Platonism -- 3. Synopsis of the Book -- ONE: Platonism -- 2 The Epistemological Argument Against Platonism -- 1. Introduction -- 2. Formulating the Epistemological Argument -- 3. A Taxonomy of Platonist Responses -- 4. Contact with Other Worlds: Gödel -- 5. Contact in This World: Maddy -- 6. Knowledge Without Contact -- 3 A New Platonist Epistemology -- 1. Introduction -- 2. Skeleton of the Refutation of the Epistemological Argument -- 3. Internalist vs. Externalist Explanations -- 4. Defending and Motivating FBP -- 5. Consistency -- 4 Non-Uniqueness Embraced -- 1. Introduction -- 2. Trying to Salvage the Numbers -- 3. Structuralism -- 4. The Solution -- 5. Two Loose Ends -- TWO: Anti-Platonism -- 5 The Fregean Argument Against Anti-Platonism -- 1. Introduction -- 2. The Argument -- 3. In Defense of Fictionalism -- 4. Nonfictionalistic Versions of Anti-Realistic Anti-Platonism -- 5. The Refutation of Realistic Anti-Platonism -- 6. Platonism and the Issue of Applicability and Indispensability -- 6 Denying the Existence of Indispensable Applications: Toward a Nominalization of Quantum Mechanics -- 1. Introduction -- 2. How Field Nominalizes -- 3. Malament's Objection -- 4. The Strategy for Nominalizing QM -- 5. The Nominalistic Status of Propensities -- 7 Accounting for Indispensable Applications from a Fictionalist Point of View -- 1. Introduction -- 2. What, Exactly, Needs to Be Accounted For? -- 3. A Fictionalist Account of the Applicability of Mathematics -- 4. Problems with Platonism Revisited -- THREE: Conclusions -- 8 The Unsolvability of the Problem and a Kinder, Gentler Positivism -- 1. Introduction -- 2. The Strong Epistemic Conclusion -- 3. The Metaphysical Conclusion -- 4. My Official View -- Notes -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W. | |
| 520 | |a Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible views. Introducing a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, he proceeds to defend anti-platonism (in particular, mathematical fictionalism) against various attacks, most notably the Quine-Putnam indispensability attack. He concludes by arguing that it is not simply that we do not currently have any good argument for or against platonism, but that we could never have such an argument and, indeed, that there is no fact of the matter as to whether platonism is correct | ||
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| contents | Cover -- Contents -- 1 Introduction -- 1. The Project of This Book -- 2. Mathematical Platonism and Anti-Platonism -- 3. Synopsis of the Book -- ONE: Platonism -- 2 The Epistemological Argument Against Platonism -- 1. Introduction -- 2. Formulating the Epistemological Argument -- 3. A Taxonomy of Platonist Responses -- 4. Contact with Other Worlds: Gödel -- 5. Contact in This World: Maddy -- 6. Knowledge Without Contact -- 3 A New Platonist Epistemology -- 1. Introduction -- 2. Skeleton of the Refutation of the Epistemological Argument -- 3. Internalist vs. Externalist Explanations -- 4. Defending and Motivating FBP -- 5. Consistency -- 4 Non-Uniqueness Embraced -- 1. Introduction -- 2. Trying to Salvage the Numbers -- 3. Structuralism -- 4. The Solution -- 5. Two Loose Ends -- TWO: Anti-Platonism -- 5 The Fregean Argument Against Anti-Platonism -- 1. Introduction -- 2. The Argument -- 3. In Defense of Fictionalism -- 4. Nonfictionalistic Versions of Anti-Realistic Anti-Platonism -- 5. The Refutation of Realistic Anti-Platonism -- 6. Platonism and the Issue of Applicability and Indispensability -- 6 Denying the Existence of Indispensable Applications: Toward a Nominalization of Quantum Mechanics -- 1. Introduction -- 2. How Field Nominalizes -- 3. Malament's Objection -- 4. The Strategy for Nominalizing QM -- 5. The Nominalistic Status of Propensities -- 7 Accounting for Indispensable Applications from a Fictionalist Point of View -- 1. Introduction -- 2. What, Exactly, Needs to Be Accounted For? -- 3. A Fictionalist Account of the Applicability of Mathematics -- 4. Problems with Platonism Revisited -- THREE: Conclusions -- 8 The Unsolvability of the Problem and a Kinder, Gentler Positivism -- 1. Introduction -- 2. The Strong Epistemic Conclusion -- 3. The Metaphysical Conclusion -- 4. My Official View -- Notes -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W. |
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| dewey-ones | 510 - Mathematics |
| dewey-raw | 510/.1 |
| dewey-search | 510/.1 |
| dewey-sort | 3510 11 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (x, 217 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Oxford University Press, |
| record_format | marc |
| spelling | Balaguer, Mark. Platonism and anti-Platonism in mathematics / Mark Balaguer. New York : Oxford University Press, 1998. 1 online resource (x, 217 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 207-211) and index. Cover -- Contents -- 1 Introduction -- 1. The Project of This Book -- 2. Mathematical Platonism and Anti-Platonism -- 3. Synopsis of the Book -- ONE: Platonism -- 2 The Epistemological Argument Against Platonism -- 1. Introduction -- 2. Formulating the Epistemological Argument -- 3. A Taxonomy of Platonist Responses -- 4. Contact with Other Worlds: Gödel -- 5. Contact in This World: Maddy -- 6. Knowledge Without Contact -- 3 A New Platonist Epistemology -- 1. Introduction -- 2. Skeleton of the Refutation of the Epistemological Argument -- 3. Internalist vs. Externalist Explanations -- 4. Defending and Motivating FBP -- 5. Consistency -- 4 Non-Uniqueness Embraced -- 1. Introduction -- 2. Trying to Salvage the Numbers -- 3. Structuralism -- 4. The Solution -- 5. Two Loose Ends -- TWO: Anti-Platonism -- 5 The Fregean Argument Against Anti-Platonism -- 1. Introduction -- 2. The Argument -- 3. In Defense of Fictionalism -- 4. Nonfictionalistic Versions of Anti-Realistic Anti-Platonism -- 5. The Refutation of Realistic Anti-Platonism -- 6. Platonism and the Issue of Applicability and Indispensability -- 6 Denying the Existence of Indispensable Applications: Toward a Nominalization of Quantum Mechanics -- 1. Introduction -- 2. How Field Nominalizes -- 3. Malament's Objection -- 4. The Strategy for Nominalizing QM -- 5. The Nominalistic Status of Propensities -- 7 Accounting for Indispensable Applications from a Fictionalist Point of View -- 1. Introduction -- 2. What, Exactly, Needs to Be Accounted For? -- 3. A Fictionalist Account of the Applicability of Mathematics -- 4. Problems with Platonism Revisited -- THREE: Conclusions -- 8 The Unsolvability of the Problem and a Kinder, Gentler Positivism -- 1. Introduction -- 2. The Strong Epistemic Conclusion -- 3. The Metaphysical Conclusion -- 4. My Official View -- Notes -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W. Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible views. Introducing a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, he proceeds to defend anti-platonism (in particular, mathematical fictionalism) against various attacks, most notably the Quine-Putnam indispensability attack. He concludes by arguing that it is not simply that we do not currently have any good argument for or against platonism, but that we could never have such an argument and, indeed, that there is no fact of the matter as to whether platonism is correct Print version record. Mathematics Philosophy. http://id.loc.gov/authorities/subjects/sh85082153 Platonists. http://id.loc.gov/authorities/subjects/sh85103327 Mathématiques Philosophie. MATHEMATICS History & Philosophy. bisacsh Mathematics Philosophy fast Platonists fast Wiskunde. gtt Platonisme. gtt has work: Platonism and anti-Platonism in mathematics (Text) https://id.oclc.org/worldcat/entity/E39PCGXG8CFgCKCQdtYd8hPWQm https://id.oclc.org/worldcat/ontology/hasWork Print version: Balaguer, Mark. Platonism and anti-Platonism in mathematics. New York : Oxford University Press, 1998 0195122305 (DLC) 97033108 (OCoLC)37580365 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=23569 Volltext |
| spellingShingle | Balaguer, Mark Platonism and anti-Platonism in mathematics / Cover -- Contents -- 1 Introduction -- 1. The Project of This Book -- 2. Mathematical Platonism and Anti-Platonism -- 3. Synopsis of the Book -- ONE: Platonism -- 2 The Epistemological Argument Against Platonism -- 1. Introduction -- 2. Formulating the Epistemological Argument -- 3. A Taxonomy of Platonist Responses -- 4. Contact with Other Worlds: Gödel -- 5. Contact in This World: Maddy -- 6. Knowledge Without Contact -- 3 A New Platonist Epistemology -- 1. Introduction -- 2. Skeleton of the Refutation of the Epistemological Argument -- 3. Internalist vs. Externalist Explanations -- 4. Defending and Motivating FBP -- 5. Consistency -- 4 Non-Uniqueness Embraced -- 1. Introduction -- 2. Trying to Salvage the Numbers -- 3. Structuralism -- 4. The Solution -- 5. Two Loose Ends -- TWO: Anti-Platonism -- 5 The Fregean Argument Against Anti-Platonism -- 1. Introduction -- 2. The Argument -- 3. In Defense of Fictionalism -- 4. Nonfictionalistic Versions of Anti-Realistic Anti-Platonism -- 5. The Refutation of Realistic Anti-Platonism -- 6. Platonism and the Issue of Applicability and Indispensability -- 6 Denying the Existence of Indispensable Applications: Toward a Nominalization of Quantum Mechanics -- 1. Introduction -- 2. How Field Nominalizes -- 3. Malament's Objection -- 4. The Strategy for Nominalizing QM -- 5. The Nominalistic Status of Propensities -- 7 Accounting for Indispensable Applications from a Fictionalist Point of View -- 1. Introduction -- 2. What, Exactly, Needs to Be Accounted For? -- 3. A Fictionalist Account of the Applicability of Mathematics -- 4. Problems with Platonism Revisited -- THREE: Conclusions -- 8 The Unsolvability of the Problem and a Kinder, Gentler Positivism -- 1. Introduction -- 2. The Strong Epistemic Conclusion -- 3. The Metaphysical Conclusion -- 4. My Official View -- Notes -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W. Mathematics Philosophy. http://id.loc.gov/authorities/subjects/sh85082153 Platonists. http://id.loc.gov/authorities/subjects/sh85103327 Mathématiques Philosophie. MATHEMATICS History & Philosophy. bisacsh Mathematics Philosophy fast Platonists fast Wiskunde. gtt Platonisme. gtt |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85082153 http://id.loc.gov/authorities/subjects/sh85103327 |
| title | Platonism and anti-Platonism in mathematics / |
| title_auth | Platonism and anti-Platonism in mathematics / |
| title_exact_search | Platonism and anti-Platonism in mathematics / |
| title_full | Platonism and anti-Platonism in mathematics / Mark Balaguer. |
| title_fullStr | Platonism and anti-Platonism in mathematics / Mark Balaguer. |
| title_full_unstemmed | Platonism and anti-Platonism in mathematics / Mark Balaguer. |
| title_short | Platonism and anti-Platonism in mathematics / |
| title_sort | platonism and anti platonism in mathematics |
| topic | Mathematics Philosophy. http://id.loc.gov/authorities/subjects/sh85082153 Platonists. http://id.loc.gov/authorities/subjects/sh85103327 Mathématiques Philosophie. MATHEMATICS History & Philosophy. bisacsh Mathematics Philosophy fast Platonists fast Wiskunde. gtt Platonisme. gtt |
| topic_facet | Mathematics Philosophy. Platonists. Mathématiques Philosophie. MATHEMATICS History & Philosophy. Mathematics Philosophy Platonists Wiskunde. Platonisme. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=23569 |
| work_keys_str_mv | AT balaguermark platonismandantiplatonisminmathematics |