Mathematics and its logics: philosophical essays
In these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appear to be contradictions between different systems, and positing different frameworks serving different legitimate purposes. The essays refin...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2021
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| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBG01 Volltext |
| Zusammenfassung: | In these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appear to be contradictions between different systems, and positing different frameworks serving different legitimate purposes. The essays refine and extend Hellman's modal-structuralist account of mathematics, developing a height-potentialist view of higher set theory which recognizes indefinite extendability of models and stages at which sets occur. In the first of three new essays written for this volume, Hellman shows how extendability can be deployed to derive the axiom of Infinity and that of Replacement, improving on earlier accounts; he also shows how extend]ability leads to attractive, novel resolutions of the set-theoretic paradoxes. Other essays explore advantages and limitations of restrictive systems - nominalist, predicativist, and constructivist. Also included are two essays, with Solomon Feferman, on predicative foundations of arithmetic |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Feb 2021) |
| Beschreibung: | 1 Online-Ressource (vii, 286 Seiten) |
| ISBN: | 9781108657419 |
| DOI: | 10.1017/9781108657419 |
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Datensatz im Suchindex
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| author | Hellman, Geoffrey 1943- |
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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 |
| discipline_str_mv | Mathematik |
| doi_str_mv | 10.1017/9781108657419 |
| format | Electronic eBook |
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| index_date | 2024-07-03T16:44:57Z |
| indexdate | 2024-07-10T09:04:48Z |
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| isbn | 9781108657419 |
| language | English |
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| spelling | Hellman, Geoffrey 1943- (DE-588)1169845142 aut Mathematics and its logics philosophical essays Geoffrey Hellman Cambridge Cambridge University Press 2021 1 Online-Ressource (vii, 286 Seiten) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 05 Feb 2021) In these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appear to be contradictions between different systems, and positing different frameworks serving different legitimate purposes. The essays refine and extend Hellman's modal-structuralist account of mathematics, developing a height-potentialist view of higher set theory which recognizes indefinite extendability of models and stages at which sets occur. In the first of three new essays written for this volume, Hellman shows how extendability can be deployed to derive the axiom of Infinity and that of Replacement, improving on earlier accounts; he also shows how extend]ability leads to attractive, novel resolutions of the set-theoretic paradoxes. Other essays explore advantages and limitations of restrictive systems - nominalist, predicativist, and constructivist. Also included are two essays, with Solomon Feferman, on predicative foundations of arithmetic Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s DE-604 Erscheint auch als Druck-Ausgabe 978-1-108-49418-2 https://doi.org/10.1017/9781108657419 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Hellman, Geoffrey 1943- Mathematics and its logics philosophical essays Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4037951-6 |
| title | Mathematics and its logics philosophical essays |
| title_auth | Mathematics and its logics philosophical essays |
| title_exact_search | Mathematics and its logics philosophical essays |
| title_exact_search_txtP | Mathematics and its logics philosophical essays |
| title_full | Mathematics and its logics philosophical essays Geoffrey Hellman |
| title_fullStr | Mathematics and its logics philosophical essays Geoffrey Hellman |
| title_full_unstemmed | Mathematics and its logics philosophical essays Geoffrey Hellman |
| title_short | Mathematics and its logics |
| title_sort | mathematics and its logics philosophical essays |
| title_sub | philosophical essays |
| topic | Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Logic, Symbolic and mathematical Mathematische Logik |
| url | https://doi.org/10.1017/9781108657419 |
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