Philosophy of Mathematics:
The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2018]
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| Schriftenreihe: | De Gruyter STEM
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| Schlagworte: | |
| Online-Zugang: | DE-1043 DE-1046 DE-858 DE-Aug4 DE-898 DE-859 DE-860 DE-91 DE-706 DE-739 Volltext |
| Zusammenfassung: | The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems connected with the concept of a number, with the infinity, the continuum and the infinitely small, with the applicability of mathematics as well as with sets, logic, provability and truth and with the axiomatic approach to mathematics are considered. In Chapter 6 the meaning of infinitesimals to mathematics and to the elements of analysis is presented. The authors of the present book are mathematicians. Their aim is to introduce mathematicians and teachers of mathematics as well as students into the philosophy of mathematics. The book is suitable also for professional philosophers as well as for students of philosophy, just because it approaches philosophy from the side of mathematics. The knowledge of mathematics needed to understand the text is elementary. Reports on historical conceptions. Thinking about today‘s mathematical doing and thinking. Recent developments. Based on the third, revised German edition. For mathematicians - students, teachers, researchers and lecturers - and readersinterested in mathematics and philosophy. Contents On the way to the reals On the history of the philosophy of mathematics On fundamental questions of the philosophy of mathematics Sets and set theories Axiomatic approach and logic Thinking and calculating infinitesimally – First nonstandard steps Retrospection |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed 23. Nov 2018) |
| Beschreibung: | 1 online resource (474 pages) |
| ISBN: | 9783110468335 |
| DOI: | 10.1515/9783110468335 |
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Datensatz im Suchindex
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| author | Bedürftig, Thomas 1943- Murawski, Roman 1949- |
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| ctrlnum | (ZDB-23-DGG)9783110468335 (OCoLC)1199725768 (DE-599)BVBBV045879550 |
| discipline | Mathematik Philosophie |
| doi_str_mv | 10.1515/9783110468335 |
| format | Electronic eBook |
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| isbn | 9783110468335 |
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| spelling | Bedürftig, Thomas 1943- Verfasser (DE-588)108217876 aut Philosophy of Mathematics Thomas Bedürftig, Roman Murawski Berlin ; Boston De Gruyter [2018] © 2018 1 online resource (474 pages) txt rdacontent c rdamedia cr rdacarrier De Gruyter STEM Description based on online resource; title from PDF title page (publisher's Web site, viewed 23. Nov 2018) The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems connected with the concept of a number, with the infinity, the continuum and the infinitely small, with the applicability of mathematics as well as with sets, logic, provability and truth and with the axiomatic approach to mathematics are considered. In Chapter 6 the meaning of infinitesimals to mathematics and to the elements of analysis is presented. The authors of the present book are mathematicians. Their aim is to introduce mathematicians and teachers of mathematics as well as students into the philosophy of mathematics. The book is suitable also for professional philosophers as well as for students of philosophy, just because it approaches philosophy from the side of mathematics. The knowledge of mathematics needed to understand the text is elementary. Reports on historical conceptions. Thinking about today‘s mathematical doing and thinking. Recent developments. Based on the third, revised German edition. For mathematicians - students, teachers, researchers and lecturers - and readersinterested in mathematics and philosophy. Contents On the way to the reals On the history of the philosophy of mathematics On fundamental questions of the philosophy of mathematics Sets and set theories Axiomatic approach and logic Thinking and calculating infinitesimally – First nonstandard steps Retrospection In English Axiomatik Logik Mathematik Mengenlehre Philosophie Philosophie (DE-588)4045791-6 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematik (DE-588)4037944-9 s Philosophie (DE-588)4045791-6 s DE-604 Murawski, Roman 1949- (DE-588)103247831 aut Erscheint auch als Druck-Ausgabe 978-3-11-046830-4 https://doi.org/10.1515/9783110468335 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Bedürftig, Thomas 1943- Murawski, Roman 1949- Philosophy of Mathematics Axiomatik Logik Mathematik Mengenlehre Philosophie Philosophie (DE-588)4045791-6 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4045791-6 (DE-588)4037944-9 |
| title | Philosophy of Mathematics |
| title_auth | Philosophy of Mathematics |
| title_exact_search | Philosophy of Mathematics |
| title_full | Philosophy of Mathematics Thomas Bedürftig, Roman Murawski |
| title_fullStr | Philosophy of Mathematics Thomas Bedürftig, Roman Murawski |
| title_full_unstemmed | Philosophy of Mathematics Thomas Bedürftig, Roman Murawski |
| title_short | Philosophy of Mathematics |
| title_sort | philosophy of mathematics |
| topic | Axiomatik Logik Mathematik Mengenlehre Philosophie Philosophie (DE-588)4045791-6 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Axiomatik Logik Mathematik Mengenlehre Philosophie |
| url | https://doi.org/10.1515/9783110468335 |
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