Mathematical structuralism / Geoffrey Hellman, Stewart Shapiro.
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...
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Full Text (via Cambridge) |
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| Main Authors: | , |
| Format: | Electronic eBook |
| Language: | No linguistic content |
| Published: |
Cambridge :
Cambridge University Press,
2019.
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| Series: | Cambridge elements. Elements in the philosophy of mathematics.
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| Subjects: |
| Summary: | 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. |
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| Physical Description: | 1 online resource (92 pages) |
| ISBN: | 9781108582933 1108582931 |
| ISSN: | 2399-2883 |
| DOI: | 10.1017/9781108582933 |
| Source of Description, Etc. Note: | Vendor-supplied metadata. |