Philosophy of mathematics:
Mathematics is one of humanity's most successful yet puzzling endeavors. It is a model of precision and objectivity, but appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton ; Oxford
Princeton University Press
[2017]
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| Schriftenreihe: | Princeton foundations of contemporary philosophy
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Mathematics is one of humanity's most successful yet puzzling endeavors. It is a model of precision and objectivity, but appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic yet accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Written by Oystein Linnebo, one of the world's leading scholars on the subject, the book introduces all of the classical approaches to the field, including logicism, formalism, intuitionism, empiricism, and structuralism. It also contains accessible introductions to some more specialized issues, such as mathematical intuition, potential infinity, the iterative conception of sets, and the search for new mathematical axioms. The groundbreaking work of German mathematician and philosopher Gottlob Frege, one of the founders of analytic philosophy, figures prominently throughout the book. Other important thinkers whose work is introduced and discussed include Immanuel Kant, John Stuart Mill, David Hilbert, Kurt Godel, W. V. Quine, Paul Benacerraf, and Hartry H. Field. Sophisticated but clear and approachable, this is an essential introduction for all students and teachers of philosophy, as well as mathematicians and others who want to understand the foundations of mathematics |
| Beschreibung: | vi, 203 Seiten 23 cm |
| ISBN: | 0691161402 9780691161402 |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents Acknowledgments vii Introduction 1 CHAPTER ONE Mathematics as a Philosophical Challenge 4 CHAPTER TWO Frege’s Logicism 21 CHAPTER THREE Formalism and Deductivism 38 CHAPTER FOUR Hilbert’s Program 56 CHAPTER FIVE Intuiționism 73 CHAPTER SIX Empiricism about Mathematics 88 CHAPTER SEVEN Nominalism 101 CHAPTER EIGHT Mathematical Intuition 116 CHAPTER NINE Abstraction Reconsidered 126 CHAPTER TEN The Iterative Conception of Sets 139 CHAPTER ELEVEN Structuralism 154 CHAPTER TWELVE The Quest for New Axioms 170
Contents vi Concluding Remarks 183 Bibliography 189 Index 199
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| author | Linnebo, Øystein |
| author_GND | (DE-588)1135819009 |
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| bvnumber | BV044339544 |
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| discipline | Mathematik Philosophie |
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| id | DE-604.BV044339544 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:50:12Z |
| institution | BVB |
| isbn | 0691161402 9780691161402 |
| language | English |
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| physical | vi, 203 Seiten 23 cm |
| publishDate | 2017 |
| publishDateSearch | 2017 |
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| publisher | Princeton University Press |
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| series2 | Princeton foundations of contemporary philosophy |
| spelling | Linnebo, Øystein Verfasser (DE-588)1135819009 aut Philosophy of mathematics Øystein Linnebo Princeton ; Oxford Princeton University Press [2017] © 2017 vi, 203 Seiten 23 cm txt rdacontent n rdamedia nc rdacarrier Princeton foundations of contemporary philosophy Mathematics is one of humanity's most successful yet puzzling endeavors. It is a model of precision and objectivity, but appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic yet accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Written by Oystein Linnebo, one of the world's leading scholars on the subject, the book introduces all of the classical approaches to the field, including logicism, formalism, intuitionism, empiricism, and structuralism. It also contains accessible introductions to some more specialized issues, such as mathematical intuition, potential infinity, the iterative conception of sets, and the search for new mathematical axioms. The groundbreaking work of German mathematician and philosopher Gottlob Frege, one of the founders of analytic philosophy, figures prominently throughout the book. Other important thinkers whose work is introduced and discussed include Immanuel Kant, John Stuart Mill, David Hilbert, Kurt Godel, W. V. Quine, Paul Benacerraf, and Hartry H. Field. Sophisticated but clear and approachable, this is an essential introduction for all students and teachers of philosophy, as well as mathematicians and others who want to understand the foundations of mathematics Mathematik Philosophie Mathematik (DE-588)4037944-9 gnd rswk-swf Philosophie (DE-588)4045791-6 gnd rswk-swf Strukturalismus (DE-588)4058129-9 gnd rswk-swf Logik (DE-588)4036202-4 gnd rswk-swf Empirismus (DE-588)4014610-8 gnd rswk-swf Formalismus Mathematik (DE-588)4154995-8 gnd rswk-swf Mathematics / Philosophy Philosophie (DE-588)4045791-6 s Mathematik (DE-588)4037944-9 s Logik (DE-588)4036202-4 s Formalismus Mathematik (DE-588)4154995-8 s Empirismus (DE-588)4014610-8 s Strukturalismus (DE-588)4058129-9 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029742614&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Linnebo, Øystein Philosophy of mathematics Mathematik Philosophie Mathematik (DE-588)4037944-9 gnd Philosophie (DE-588)4045791-6 gnd Strukturalismus (DE-588)4058129-9 gnd Logik (DE-588)4036202-4 gnd Empirismus (DE-588)4014610-8 gnd Formalismus Mathematik (DE-588)4154995-8 gnd |
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| title | Philosophy of mathematics |
| title_auth | Philosophy of mathematics |
| title_exact_search | Philosophy of mathematics |
| title_full | Philosophy of mathematics Øystein Linnebo |
| title_fullStr | Philosophy of mathematics Øystein Linnebo |
| title_full_unstemmed | Philosophy of mathematics Øystein Linnebo |
| title_short | Philosophy of mathematics |
| title_sort | philosophy of mathematics |
| topic | Mathematik Philosophie Mathematik (DE-588)4037944-9 gnd Philosophie (DE-588)4045791-6 gnd Strukturalismus (DE-588)4058129-9 gnd Logik (DE-588)4036202-4 gnd Empirismus (DE-588)4014610-8 gnd Formalismus Mathematik (DE-588)4154995-8 gnd |
| topic_facet | Mathematik Philosophie Strukturalismus Logik Empirismus Formalismus Mathematik |
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