Mathematical structuralism:
The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose with...
Gespeichert in:
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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2019
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| Schriftenreihe: | Elements in the philosophy of mathematics
Cambridge elements |
| Links: | https://doi.org/10.1017/9781108582933 |
| Zusammenfassung: | The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself. After exposing a number of problems, the book considers three further perspectives formulated by logicians and philosophers of mathematics: sui generis, treating structures as abstract universals, modal, eliminating structures as objects in favor of freely entertained logical possibilities, and finally, modal-set-theoretic, a sort of synthesis of the set-theoretic and modal perspectives. |
| Umfang: | 1 Online-Ressource (92 Seiten) |
| ISBN: | 9781108582933 |
| ISSN: | 2399-2883 |
Internformat
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| id | ZDB-20-CTM-CR9781108582933 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-03T11:58:02Z |
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| isbn | 9781108582933 |
| issn | 2399-2883 |
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| spelling | Hellman, Geoffrey Mathematical structuralism Geoffrey Hellman, Stewart Shapiro Cambridge Cambridge University Press 2019 1 Online-Ressource (92 Seiten) txt c cr Elements in the philosophy of mathematics 2399-2883 Cambridge elements The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself. After exposing a number of problems, the book considers three further perspectives formulated by logicians and philosophers of mathematics: sui generis, treating structures as abstract universals, modal, eliminating structures as objects in favor of freely entertained logical possibilities, and finally, modal-set-theoretic, a sort of synthesis of the set-theoretic and modal perspectives. Shapiro, Stewart 1951- Erscheint auch als Druck-Ausgabe 9781108456432 |
| spellingShingle | Hellman, Geoffrey Mathematical structuralism |
| title | Mathematical structuralism |
| title_auth | Mathematical structuralism |
| title_exact_search | Mathematical structuralism |
| title_full | Mathematical structuralism Geoffrey Hellman, Stewart Shapiro |
| title_fullStr | Mathematical structuralism Geoffrey Hellman, Stewart Shapiro |
| title_full_unstemmed | Mathematical structuralism Geoffrey Hellman, Stewart Shapiro |
| title_short | Mathematical structuralism |
| title_sort | mathematical structuralism |
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