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...
Gespeichert in:
| Beteilige Person: | |
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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2021
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| Links: | https://doi.org/10.1017/9781108657419 |
| 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. |
| Umfang: | 1 Online-Ressource (vii, 286 Seiten) |
| ISBN: | 9781108657419 |
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| spelling | Hellman, Geoffrey Mathematics and Its logics philosophical essays Geoffrey Hellman Cambridge Cambridge University Press 2021 1 Online-Ressource (vii, 286 Seiten) txt c cr 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. Erscheint auch als Druck-Ausgabe 9781108494182 Erscheint auch als Druck-Ausgabe 9781108714006 |
| spellingShingle | Hellman, Geoffrey Mathematics and Its logics philosophical essays |
| 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_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 |
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