Introducing philosophy of mathematics

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1. Verfasser: Friend, Michèle (VerfasserIn)
Format: Buch
Sprache:English
Veröffentlicht: Stocksfield Acumen 2007
Ausgabe:1. publ.
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Datensatz im Suchindex

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adam_text INTRODUCING PHILOSOPHY OF MATHEMATICS MICHELE FRIEND ACUMEN CONTENTS ACKNOWLEDGEMENTS VII PREFACE IX 1. INFINITY 1 1. INTRODUCTION 1 2. ZENO S PARADOXES 2 3. POTENTIAL VERSUS ACTUAL INFINITY 7 4. THE ORDINAL NOTION OF INFINITY 12 5. THE CARDINAL NOTION OF INFINITY 13 6. SUMMARY 22 2. MATHEMATICAL PLATONISM AND REALISM 23 1. INTRODUCTION 23 2. HISTORICAL ORIGINS 23 3. REALISM IN GENERAL 26 4. KURTGODEL 35 5. PENELOPE MADDY 37 6. GENERAL PROBLEMS WITH SET-THEORETIC REALISM 41 7. CONCLUSION 46 8. SUMMARY 47 3. LOGICISM 49 1. INTRODUCTION 49 2. FREGE S LOGICISM: TECHNICAL ACCOMPLISHMENTS 52 3. FREGE S LOGICISM: PHILOSOPHICAL ACCOMPLISHMENTS 58 4. PROBLEMS WITH FREGE S LOGICISM 63 5. WHITEHEAD AND RUSSELL S LOGICISM 66 6. PHILOSOPHICALLY, WHAT IS WRONG WITH WHITEHEAD AND 71 RUSSELL S TYPE THEPRY? CONTENTS 7. OTHER ATTEMPTS AT LOGICISM 78 8. CONCLUSION 78 9. SUMMARY 79 4. STRUCTURALISM 81 1. INTRODUCTION 81 2. THE MOTIVATION FOR STRUCTURALISM: BENACERRAF S PUZZLE 83 3. THE PHILOSOPHY OF STRUCTURALISM: HELLMAN 85 4. THE PHILOSOPHY OF STRUCTURALISM: RESNIK AND SHAPIRO 90 5. CRITIQUE 96 6. SUMMARY 100 5. CONSTRUCTIVISM 101 1. INTRODUCTION 101 2. INTUITIONIST LOGIC 106 3. PRIMA FACIE MOTIVATIONS FOR CONSTRUCTIVISM 113 4. DEEPER MOTIVATIONS FOR CONSTRUCTIVISM 114 5. THE SEMANTICS OF INTUITIONIST LOGIC: DUMMETT 121 6. PROBLEMS WITH CONSTRUCTIVISM 123 7. SUMMARY * 124 6. A POT-POURRI OF PHILOSOPHIES OF MATHEMATICS 127 1. INTRODUCTION 127 2. EMPIRICISM AND NATURALISM 130 3. FICTIONALISM 134 4. PSYCHOLOGISM 137 5. HUSSERL 141 6. FORMALISM 147 7. HILBERT 153 8. MEINONGIAN PHILOSOPHY OF MATHEMATICS 157 9. LAKATOS 163 APPENDIX: PROOF: EX FALSO QUOD LIBET 167 GLOSSARY 169 NOTES 177 GUIDE TO FURTHER READING 191 BIBLIOGRAPHY 195 INDEX 201 VI INTRODUCING PHILOSOPHY OF MATHEMATICS
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spellingShingle Friend, Michèle
Introducing philosophy of mathematics
Philosophie (DE-588)4045791-6 gnd
Mathematik (DE-588)4037944-9 gnd
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(DE-588)4037944-9
title Introducing philosophy of mathematics
title_auth Introducing philosophy of mathematics
title_exact_search Introducing philosophy of mathematics
title_full Introducing philosophy of mathematics Michèle Friend
title_fullStr Introducing philosophy of mathematics Michèle Friend
title_full_unstemmed Introducing philosophy of mathematics Michèle Friend
title_short Introducing philosophy of mathematics
title_sort introducing philosophy of mathematics
topic Philosophie (DE-588)4045791-6 gnd
Mathematik (DE-588)4037944-9 gnd
topic_facet Philosophie
Mathematik
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