Fixing Frege:
The great logician Gottlob Frege attempted to provide a purely logical foundation for mathematics. His system collapsed when Bertrand Russell discovered a contradiction in it. Thereafter, mathematicians and logicians, beginning with Russell himself, turned in other directions to look for a framework...
Saved in:
| Main Author: | |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Princeton, NJ
Princeton University Press
[2018]
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| Series: | Princeton Monographs in Philosophy
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| Subjects: | |
| Online Access: | DE-859 DE-860 DE-739 DE-473 DE-1046 DE-1043 DE-858 URL des Erstveröffentlichers |
| Summary: | The great logician Gottlob Frege attempted to provide a purely logical foundation for mathematics. His system collapsed when Bertrand Russell discovered a contradiction in it. Thereafter, mathematicians and logicians, beginning with Russell himself, turned in other directions to look for a framework for modern abstract mathematics. Over the past couple of decades, however, logicians and philosophers have discovered that much more is salvageable from the rubble of Frege's system than had previously been assumed. A variety of repaired systems have been proposed, each a consistent theory permitting the development of a significant portion of mathematics. This book surveys the assortment of methods put forth for fixing Frege's system, in an attempt to determine just how much of mathematics can be reconstructed in each. John Burgess considers every proposed fix, each with its distinctive philosophical advantages and drawbacks. These systems range from those barely able to reconstruct the rudiments of arithmetic to those that go well beyond the generally accepted axioms of set theory into the speculative realm of large cardinals. For the most part, Burgess finds that attempts to fix Frege do less than advertised to revive his system. This book will be the benchmark against which future analyses of the revival of Frege will be measured |
| Item Description: | Description based on online resource; title from PDF title page (publisher's Web site, viewed 23. Nov 2018) |
| Physical Description: | 1 online resource |
| ISBN: | 9780691187068 |
| DOI: | 10.1515/9780691187068 |
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| dewey-ones | 511 - General principles of mathematics |
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| isbn | 9780691187068 |
| language | English |
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| spelling | Burgess, John P. Verfasser aut Fixing Frege John P. Burgess Princeton, NJ Princeton University Press [2018] © 2005 1 online resource txt rdacontent c rdamedia cr rdacarrier Princeton Monographs in Philosophy Description based on online resource; title from PDF title page (publisher's Web site, viewed 23. Nov 2018) The great logician Gottlob Frege attempted to provide a purely logical foundation for mathematics. His system collapsed when Bertrand Russell discovered a contradiction in it. Thereafter, mathematicians and logicians, beginning with Russell himself, turned in other directions to look for a framework for modern abstract mathematics. Over the past couple of decades, however, logicians and philosophers have discovered that much more is salvageable from the rubble of Frege's system than had previously been assumed. A variety of repaired systems have been proposed, each a consistent theory permitting the development of a significant portion of mathematics. This book surveys the assortment of methods put forth for fixing Frege's system, in an attempt to determine just how much of mathematics can be reconstructed in each. John Burgess considers every proposed fix, each with its distinctive philosophical advantages and drawbacks. These systems range from those barely able to reconstruct the rudiments of arithmetic to those that go well beyond the generally accepted axioms of set theory into the speculative realm of large cardinals. For the most part, Burgess finds that attempts to fix Frege do less than advertised to revive his system. This book will be the benchmark against which future analyses of the revival of Frege will be measured In English Frege, Gottlob 1848-1925 (DE-588)118535161 gnd rswk-swf Logic, Symbolic and mathematical Logik (DE-588)4036202-4 gnd rswk-swf Widerspruchsfreiheit (DE-588)4189803-5 gnd rswk-swf Frege, Gottlob 1848-1925 (DE-588)118535161 p Logik (DE-588)4036202-4 s Widerspruchsfreiheit (DE-588)4189803-5 s 1\p DE-604 https://doi.org/10.1515/9780691187068 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Burgess, John P. Fixing Frege Frege, Gottlob 1848-1925 (DE-588)118535161 gnd Logic, Symbolic and mathematical Logik (DE-588)4036202-4 gnd Widerspruchsfreiheit (DE-588)4189803-5 gnd |
| subject_GND | (DE-588)118535161 (DE-588)4036202-4 (DE-588)4189803-5 |
| title | Fixing Frege |
| title_auth | Fixing Frege |
| title_exact_search | Fixing Frege |
| title_full | Fixing Frege John P. Burgess |
| title_fullStr | Fixing Frege John P. Burgess |
| title_full_unstemmed | Fixing Frege John P. Burgess |
| title_short | Fixing Frege |
| title_sort | fixing frege |
| topic | Frege, Gottlob 1848-1925 (DE-588)118535161 gnd Logic, Symbolic and mathematical Logik (DE-588)4036202-4 gnd Widerspruchsfreiheit (DE-588)4189803-5 gnd |
| topic_facet | Frege, Gottlob 1848-1925 Logic, Symbolic and mathematical Logik Widerspruchsfreiheit |
| url | https://doi.org/10.1515/9780691187068 |
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