Philosophy of mathematics: a contemporary introduction to the world of proofs and pictures
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Routledge
2008
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Routledge contemporary introductions to philosophy
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 245 S. Ill., graph. Darst. |
| ISBN: | 9780415960489 9780415960472 |
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Datensatz im Suchindex
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| adam_text | PHILOSOPHY OF MATHEMATICS A CONTEMPORARY INTRODUCTION TO THE WORLD OF
PROOFS AND PICTURES SECOND EDITION JAMES ROBERT BROWN ROUTLEDGE TAYLOR
H. FRANCIS CROUP NEW YORK AND LONDON CONTENTS PREFACE AND
ACKNOWLEDGEMENTS XI CHAPTER 1: INTRODUCTION: THE MATHEMATICAL IMAGE 1
FURTHER READING 8 CHAPTER 2: PLATONISM 9 THE ORIGINAL PLATONIST 9 S OME
RECENT VIEW S 10 WHAT IS PLATONISM? 12 THE PROBLEM OF ACCESS 16 THE
PROBLEM OF CERTAINTY 19 PLATONISM AND ITS RIVALS 24 FURTHER READING 25
CHAPTER 3: PICTURE-PROOFS AND PLATONISM 26 BOLZANO S PURELY ANALYTIC
PROOF 26 WHAT DID BOLZANO DO? 29 DIFFERENT THEOREMS, DIFFERENT CONCEPTS?
30 INDUCTIVE MATHEMATICS 31 SPECIAL AND GENERAL CASES 34 INSTRUCTIVE
EXAMPLES 35 REPRESENTATION 38 SEEING INDUCTION? 40 THREE ANALOGIES 44
ARE PICTURES EXPLANATORY? 46 VIII CONTENTS SO WHY WORRY? 47 FURTHER
READING 47 APPENDIX 47 CHAPTER 4: WHAT IS APPLIED MATHEMATICS? 51
REPRESENTATIONS 52 ARTIFACTS 54 BOGUS APPLICATIONS 56 DOES SCIENCE NEED
MATHEMATICS? 57 REPRESENTATION VS. DESCRIPTION 60 STRUCTURALISM 62
FURTHER READING 66 CHAPTER 5: HILBERT AND GODEL 67 THE NOMINALISTIC
INSTINCT 67 EARLY FORMALISM 68 HILBERT S FORMALISM 69 HILBERT S
PROGRAMME 73 SMALL PROBLEMS 75 GODEL S THEOREM 76 GODEL S SECOND THEOREM
80 THE UPSHOT FOR HILBERT S PROGRAMME 82 THE AFTERMATH 82 FURTHER
READING 83 CHAPTER 6: KNOTS AND NOTATION 84 KNOTS 86 THE DOWKER NOTATION
88 THE CONWAY NOTATION 89 POLYNOMIALS 91 CREATION OR REVELATION? 93
SENSE, REFERENCE AND SOMETHING ELSE 97 FURTHER READING 98 CHAPTER 7:
WHAT IS A DEFINITION? 99 THE OFFICIAL VIEW 99 THE FREGE-HILBERT DEBATE
100 REDUCTIONISM 107 GRAPH THEORY 108 CONTENTS IX LAKATOS 113 CONCLUDING
REMARKS 117 FURTHER READING 117 CHAPTER 8: CONSTRUCTIVE APPROACHES 118
FROM KANT TO BROUWER 119 BROUWER S INTUITIONISM 120 BISHOP S
CONSTRUCTIVISM 122 DUMMETT S ANTI-REALISM 123 LOGIC 125 PROBLEMS 127
FURTHER READING 135 CHAPTER 9: PROOFS, PICTURES AND PROCEDURES IN
WITTGENSTEIN 136 A PICTURE AND A PROBLEM 136 FOLLOWING A RULE 138
PLATONISM 142 ALGORITHMS 144 DISPOSITIONS 144 KNOWING OUR OWN INTENTIONS
145 BROUWER S BEETLE 145 RADICAL CONVENTIONALISM 146 BIZARRE EXAMPLES
147 NATURALISM 148 THE SCEPTICAL SOLUTION 150 MODUS PONENS OR MODUS
TOLLENSL 151 WHAT IS A RULE? 152 GRASPING A SENSE 153 PLATONISM VERSUS
REALISM 155 SURVEYABILITY 157 THE SENSE OF A PICTURE 158 FURTHER READING
159 CHAPTER 10: COMPUTATION, PROOF AND CONJECTURE 160 THE FOUR COLOUR
THEOREM 160 FALLIBILITY 161 SURVEYABILITY 163 INDUCTIVE MATHEMATICS 164
X CONTENTS PERFECT NUMBERS 165 COMPUTATION 168 IS N NORMAL? 170 FERMAT S
LAST THEOREM 171 THE RIEMANN HYPOTHESIS 172 CLUSTERS OF CONJECTURES 173
POLYA AND PUTNAM 174 CONJECTURES AND AXIOMS 175 FURTHER READING 177
CHAPTER 11: HOW TO REFUTE THE CONTINUUM HYPOTHESIS 178 WHAT IS THE
CONTINUUM HYPOTHESIS? 179 HOW COULD WE DETERMINE THE TRUTH OF CH? 183
KREISEL S ANALOGY 185 FREILING S REFUTATION OF CH 186 WHAT MIGHT THE
CONTINUUM BE? 191 TWO OBJECTIONS 192 WHAT DID THE THOUGHT EXPERIMENT
CONTRIBUTE? 195 TWO MORALS 196 APPENDIX: FREILING S VERSION 196 FURTHER
READING 197 CHAPTER 12: CALLING THE BLUFF 198 CALLING THE BLUFF 205 MATH
WARS: A REPORT FROM THE FRONT 207 ONCE MORE: THE MATHEMATICAL IMAGE 217
FURTHER READING 219 NOTES 220 BIBLIOGRAPHY 226 INDEX 236
|
| adam_txt |
PHILOSOPHY OF MATHEMATICS A CONTEMPORARY INTRODUCTION TO THE WORLD OF
PROOFS AND PICTURES SECOND EDITION JAMES ROBERT BROWN ROUTLEDGE TAYLOR
H. FRANCIS CROUP NEW YORK AND LONDON CONTENTS PREFACE AND
ACKNOWLEDGEMENTS XI CHAPTER 1: INTRODUCTION: THE MATHEMATICAL IMAGE 1
FURTHER READING 8 CHAPTER 2: PLATONISM 9 THE ORIGINAL PLATONIST 9 S OME
RECENT VIEW S 10 WHAT IS PLATONISM? 12 THE PROBLEM OF ACCESS 16 THE
PROBLEM OF CERTAINTY 19 PLATONISM AND ITS RIVALS 24 FURTHER READING 25
CHAPTER 3: PICTURE-PROOFS AND PLATONISM 26 BOLZANO'S 'PURELY ANALYTIC
PROOF 26 WHAT DID BOLZANO DO? 29 DIFFERENT THEOREMS, DIFFERENT CONCEPTS?
30 INDUCTIVE MATHEMATICS 31 SPECIAL AND GENERAL CASES 34 INSTRUCTIVE
EXAMPLES 35 REPRESENTATION 38 SEEING INDUCTION? 40 THREE ANALOGIES 44
ARE PICTURES EXPLANATORY? 46 VIII CONTENTS SO WHY WORRY? 47 FURTHER
READING 47 APPENDIX 47 CHAPTER 4: WHAT IS APPLIED MATHEMATICS? 51
REPRESENTATIONS 52 ARTIFACTS 54 BOGUS APPLICATIONS 56 DOES SCIENCE NEED
MATHEMATICS? 57 REPRESENTATION VS. DESCRIPTION 60 STRUCTURALISM 62
FURTHER READING 66 CHAPTER 5: HILBERT AND GODEL 67 THE NOMINALISTIC
INSTINCT 67 EARLY FORMALISM 68 HILBERT'S FORMALISM 69 HILBERT'S
PROGRAMME 73 SMALL PROBLEMS 75 GODEL'S THEOREM 76 GODEL'S SECOND THEOREM
80 THE UPSHOT FOR HILBERT'S PROGRAMME 82 THE AFTERMATH 82 FURTHER
READING 83 CHAPTER 6: KNOTS AND NOTATION 84 KNOTS 86 THE DOWKER NOTATION
88 THE CONWAY NOTATION 89 POLYNOMIALS 91 CREATION OR REVELATION? 93
SENSE, REFERENCE AND SOMETHING ELSE 97 FURTHER READING 98 CHAPTER 7:
WHAT IS A DEFINITION? 99 THE OFFICIAL VIEW 99 THE FREGE-HILBERT DEBATE
100 REDUCTIONISM 107 GRAPH THEORY 108 CONTENTS IX LAKATOS 113 CONCLUDING
REMARKS 117 FURTHER READING 117 CHAPTER 8: CONSTRUCTIVE APPROACHES 118
FROM KANT TO BROUWER 119 BROUWER'S INTUITIONISM 120 BISHOP'S
CONSTRUCTIVISM 122 DUMMETT'S ANTI-REALISM 123 LOGIC 125 PROBLEMS 127
FURTHER READING 135 CHAPTER 9: PROOFS, PICTURES AND PROCEDURES IN
WITTGENSTEIN 136 A PICTURE AND A PROBLEM 136 FOLLOWING A RULE 138
PLATONISM 142 ALGORITHMS 144 DISPOSITIONS 144 KNOWING OUR OWN INTENTIONS
145 BROUWER'S BEETLE 145 RADICAL CONVENTIONALISM 146 BIZARRE EXAMPLES
147 NATURALISM 148 THE SCEPTICAL SOLUTION 150 MODUS PONENS OR MODUS
TOLLENSL 151 WHAT IS A RULE? 152 GRASPING A SENSE 153 PLATONISM VERSUS
REALISM 155 SURVEYABILITY 157 THE SENSE OF A PICTURE 158 FURTHER READING
159 CHAPTER 10: COMPUTATION, PROOF AND CONJECTURE 160 THE FOUR COLOUR
THEOREM 160 FALLIBILITY 161 SURVEYABILITY 163 INDUCTIVE MATHEMATICS 164
X CONTENTS PERFECT NUMBERS 165 COMPUTATION 168 IS N NORMAL? 170 FERMAT'S
LAST THEOREM 171 THE RIEMANN HYPOTHESIS 172 CLUSTERS OF CONJECTURES 173
POLYA AND PUTNAM 174 CONJECTURES AND AXIOMS 175 FURTHER READING 177
CHAPTER 11: HOW TO REFUTE THE CONTINUUM HYPOTHESIS 178 WHAT IS THE
CONTINUUM HYPOTHESIS? 179 HOW COULD WE DETERMINE THE TRUTH OF CH? 183
KREISEL'S ANALOGY 185 FREILING'S REFUTATION OF CH 186 WHAT MIGHT THE
CONTINUUM BE? 191 TWO OBJECTIONS 192 WHAT DID THE THOUGHT EXPERIMENT
CONTRIBUTE? 195 TWO MORALS 196 APPENDIX: FREILING'S VERSION 196 FURTHER
READING 197 CHAPTER 12: CALLING THE BLUFF 198 CALLING THE BLUFF 205 MATH
WARS: A REPORT FROM THE FRONT 207 ONCE MORE: THE MATHEMATICAL IMAGE 217
FURTHER READING 219 NOTES 220 BIBLIOGRAPHY 226 INDEX 236 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
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| discipline | Mathematik Philosophie |
| discipline_str_mv | Mathematik Philosophie |
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| language | English |
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| spelling | Brown, James Robert Verfasser aut Philosophy of mathematics a contemporary introduction to the world of proofs and pictures James Robert Brown 2. ed. New York [u.a.] Routledge 2008 XIV, 245 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Routledge contemporary introductions to philosophy Mathematics / Philosophy Mathematik Philosophie Mathematics Philosophy Philosophie (DE-588)4045791-6 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Mathematik (DE-588)4037944-9 s Philosophie (DE-588)4045791-6 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016263426&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brown, James Robert Philosophy of mathematics a contemporary introduction to the world of proofs and pictures Mathematics / Philosophy Mathematik Philosophie Mathematics Philosophy Philosophie (DE-588)4045791-6 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4045791-6 (DE-588)4037944-9 (DE-588)4151278-9 |
| title | Philosophy of mathematics a contemporary introduction to the world of proofs and pictures |
| title_auth | Philosophy of mathematics a contemporary introduction to the world of proofs and pictures |
| title_exact_search | Philosophy of mathematics a contemporary introduction to the world of proofs and pictures |
| title_exact_search_txtP | Philosophy of mathematics a contemporary introduction to the world of proofs and pictures |
| title_full | Philosophy of mathematics a contemporary introduction to the world of proofs and pictures James Robert Brown |
| title_fullStr | Philosophy of mathematics a contemporary introduction to the world of proofs and pictures James Robert Brown |
| title_full_unstemmed | Philosophy of mathematics a contemporary introduction to the world of proofs and pictures James Robert Brown |
| title_short | Philosophy of mathematics |
| title_sort | philosophy of mathematics a contemporary introduction to the world of proofs and pictures |
| title_sub | a contemporary introduction to the world of proofs and pictures |
| topic | Mathematics / Philosophy Mathematik Philosophie Mathematics Philosophy Philosophie (DE-588)4045791-6 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Mathematics / Philosophy Mathematik Philosophie Mathematics Philosophy Einführung |
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