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, aros...
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge ; New York ; Port Melbourne ; New Delhi ; Singapore
Cambridge University Press
2019
|
| Series: | Cambridge elements. Elements in the philosophy of mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| 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 they encounter, Geoffrey Hellman and Steward Shapiro consider 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"--Back cover |
| Physical Description: | 92 Seiten 23 cm |
| ISBN: | 9781108456432 110845643X 9781108697286 1108697283 |
Staff View
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Record in the Search Index
| _version_ | 1804180590992293888 |
|---|---|
| adam_text | Contents 1 Introduction 1 2 Historical Background 7 3 Set-Theoretic Structuralism 33 4 Category Theory as a Framework for Mathematical Structuralism 43 5 Structures as Sui Generis Structuralism 51 6 The Modal-Structural Perspective 61 7 Modal Set-Theoretic Structuralism 73 References 86
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| author | Hellman, Geoffrey 1943- Shapiro, Stewart 1951- |
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| author_sort | Hellman, Geoffrey 1943- |
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| id | DE-604.BV046205255 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:38:11Z |
| institution | BVB |
| isbn | 9781108456432 110845643X 9781108697286 1108697283 |
| language | English |
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| owner | DE-12 |
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| physical | 92 Seiten 23 cm |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge elements. Elements in the philosophy of mathematics |
| spelling | Hellman, Geoffrey 1943- Verfasser (DE-588)1169845142 aut Mathematical structuralism Geoffrey Hellman (University of Minnesota), Stewart Shapiro (The Ohio State University) Cambridge ; New York ; Port Melbourne ; New Delhi ; Singapore Cambridge University Press 2019 92 Seiten 23 cm txt rdacontent n rdamedia nc rdacarrier Cambridge elements. Elements in the philosophy of mathematics "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 they encounter, Geoffrey Hellman and Steward Shapiro consider 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"--Back cover Mathematik (DE-588)4037944-9 gnd rswk-swf Strukturalismus (DE-588)4058129-9 gnd rswk-swf Philosophie (DE-588)4045791-6 gnd rswk-swf Mathematics / Philosophy Structuralism Mathematik (DE-588)4037944-9 s Strukturalismus (DE-588)4058129-9 s Philosophie (DE-588)4045791-6 s DE-604 Shapiro, Stewart 1951- Verfasser (DE-588)131540564 aut Online version Hellman, Geoffrey Mathematical structuralism Cambridge : Cambridge University Press, 2019 9781108582933 Digitalisierung BSB München - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031584270&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hellman, Geoffrey 1943- Shapiro, Stewart 1951- Mathematical structuralism Mathematik (DE-588)4037944-9 gnd Strukturalismus (DE-588)4058129-9 gnd Philosophie (DE-588)4045791-6 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4058129-9 (DE-588)4045791-6 |
| title | Mathematical structuralism |
| title_auth | Mathematical structuralism |
| title_exact_search | Mathematical structuralism |
| title_full | Mathematical structuralism Geoffrey Hellman (University of Minnesota), Stewart Shapiro (The Ohio State University) |
| title_fullStr | Mathematical structuralism Geoffrey Hellman (University of Minnesota), Stewart Shapiro (The Ohio State University) |
| title_full_unstemmed | Mathematical structuralism Geoffrey Hellman (University of Minnesota), Stewart Shapiro (The Ohio State University) |
| title_short | Mathematical structuralism |
| title_sort | mathematical structuralism |
| topic | Mathematik (DE-588)4037944-9 gnd Strukturalismus (DE-588)4058129-9 gnd Philosophie (DE-588)4045791-6 gnd |
| topic_facet | Mathematik Strukturalismus Philosophie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031584270&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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