Representation and productive ambiguity in mathematics and the sciences:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2007
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XVIII, 313 S. Ill., graph. Darst. |
| ISBN: | 9780199299737 |
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| adam_text | REPRESENTATION AND PRODUCTIVE AMBIGUITY IN MATHEMATICS AND THE SCIENCES
EMILY R. GROSHOLZ OXPORD UNIVERSITY PRESS CONTENTS PREFACE XI
ACKNOWLEDGMENTS XV PART I: INTRODUCTORY CHAPTERS I 1. PRODUCTIVE
AMBIGUITY: GALILEO CONTRA CARNAP 3 1.1. GALILEO S DEMONSTRATION OF
PROJECTILE MOTION 5 1.2. CARNAP ON LANGUAGE AND THOUGHT 16 1.3. FROM THE
SYNTACTIC TO THE SEMANTIC TO THE PRAGMATIC APPROACH 19 1.4. A PRAGMATIC
ACCOUNT OF BERZELIAN FORMULAS 24 2. ANALYSIS AND EXPERIENCE 33 2.1.
ANALYSIS 33 2.2. MATHEMATICAL EXPERIENCE 47 PART II: CHEMISTRY AND
GEOMETRY 61 3. BIOORGANIC CHEMISTRY AND BIOLOGY 63 3.1. WHAT LIES
BETWEEN REPRESENTING AND INTERVENING 64 3.2. THE REDUCTION OF A
BIOLOGICAL ITEM TO A CHEMICAL ITEM 68 3.3. FORMULATING THE PROBLEM 71
3.4. CONSTRUCTING THE ANTIBODY MIMIC 74 3.5. TESTING THE ANTIBODY MIMIC
84 3.6. CONCLUSIONS 89 4. GENETICS AND MOLECULAR BIOLOGY 91 4.1.
OBJECTIONS TO HEMPEL S MODEL OF THEORY REDUCTION 92 4.2. THE
TRANSPOSITION OF GENES: MCCLINTOCK AND FEDOROFF 97 4.3. MCCLINTOCK S
STUDIES OF MAIZE 103 4.4. J. D. WATSON S TEXTBOOK 111 4.5. FEDOROFFS
TRANSLATION OF MCCLINTOCK 113 4.6. THE FUTURE OF MOLECULAR BIOLOGY 123
VLLL CONTENTS 5. CHEMISTRY, QUANTUM MECHANICS, AND GROUP THEORY 126 5.1.
SYMBOLS, ICONS, AND ICONICITY 126 5.2. REPRESENTATION THEORY 128 5.3.
MOLECULES, SYMMETRY, AND GROUPS 131 5.4. SYMMETRY GROUPS,
REPRESENTATIONS, AND CHARACTER TABLES 135 5.5. THE BENZENE RING AND
CARBOCYCLIC SYSTEMS 139 5.6. MEASURING DELOCALIZATION ENERGY IN THE
BENZENE MOLECULE 147 PART III: GEOMETRY AND SEVENTEENTH CENTURY
MECHANICS 157 6. DESCARTES S GEOMETRY 159 6.1. LOCKE S CRITICISM OF
SYLLOGISTIC 159 6.2. DESCARTES GEOMETRY AS THE EXEMPLAR OF CARTESIAN
METHOD 165 6.3. DIAGRAMS AS PROCEDURES 169 6.4. GENERALIZATION TO THE
CONSTRUCTION OF A LOCUS 171 6.5. GENERALIZATION TO HIGHER ALGEBRAIC
CURVES 177 7. NEWTON S PRINCIPIA 184 7.1. PHILIP KITCHER ON HISTORY 187
7.2. JEAN CAVAILLES ON HISTORY 189 7.3. BOOK I, PROPOSITIONS I AND VI IN
NEWTON S PRINCIPIA 192 7.4. BOOK I, PROPOSITION XI IN NEWTON S PRINCIPIA
198 8. LEIBNIZ ON TRANSCENDENTAL CURVES 204 8.1. THE PRINCIPLE OF
CONTINUITY 205 8.2. STUDIES FOR THE INFINITESIMAL CALCULUS 207 8.3. THE
PRINCIPLE OF PERFECTION 213 8.4. THE ISOCHRONE AND THE TRACTRIX 215 8.5.
THE CATENARY OR LA CHAINETTE 221 PART IV: GEOMETRY AND TWENTIETH CENTURY
TOPOLOGY 225 9. GEOMETRY, ALGEBRA, AND TOPOLOGY 227 9.1. VUILLEMIN ON
THE RELATION OF MATHEMATICS AND PHILOSOPHY 227 9.2. EUCLID S ELEMENTS
AND DESCARTES GEOMETRY REVISITED 230 CONTENTS 9.3. KANT S
TRANSCENDENTAL AESTHETIC: EXTRINSIC AND INTRINSIC INTUITION 9.4. THE
FIRST PAGES OF SINGER AND THORPE 9.5. DE RHAM S THEOREM 9.6. NANCY
CARTWRIGHT ON THE ABSTRACT AND CONCRETE 10. LOGIC AND TOPOLOGY 10.1.
PENELOPE MADDY ON SET THEORY 10.2. A BRIEF RECONSIDERATION OF ARITHMETIC
10.3. THE APPLICATION OF LOGIC TO GENERAL TOPOLOGY 10.4. LOGICAL
HIERARCHIES AND THE BOREL HIERARCHY 10.5. MODEL THEORY AND TOPOLOGICAL
LOGICS 10.6. CODA LIST OF ILLUSTRATIONS GLOSSARY BIBLIOGRAPHY BOOKS
ARTICLES INDEX IX 232 235 243 254 257 259 262 268 273 279 283 285 291
293 293 299 307
|
| adam_txt |
REPRESENTATION AND PRODUCTIVE AMBIGUITY IN MATHEMATICS AND THE SCIENCES
EMILY R. GROSHOLZ OXPORD UNIVERSITY PRESS CONTENTS PREFACE XI
ACKNOWLEDGMENTS XV PART I: INTRODUCTORY CHAPTERS I 1. PRODUCTIVE
AMBIGUITY: GALILEO CONTRA CARNAP 3 1.1. GALILEO'S DEMONSTRATION OF
PROJECTILE MOTION 5 1.2. CARNAP ON LANGUAGE AND THOUGHT 16 1.3. FROM THE
SYNTACTIC TO THE SEMANTIC TO THE PRAGMATIC APPROACH 19 1.4. A PRAGMATIC
ACCOUNT OF BERZELIAN FORMULAS 24 2. ANALYSIS AND EXPERIENCE 33 2.1.
ANALYSIS 33 2.2. MATHEMATICAL EXPERIENCE 47 PART II: CHEMISTRY AND
GEOMETRY 61 3. BIOORGANIC CHEMISTRY AND BIOLOGY 63 3.1. WHAT LIES
BETWEEN REPRESENTING AND INTERVENING 64 3.2. THE REDUCTION OF A
BIOLOGICAL ITEM TO A CHEMICAL ITEM 68 3.3. FORMULATING THE PROBLEM 71
3.4. CONSTRUCTING THE ANTIBODY MIMIC 74 3.5. TESTING THE ANTIBODY MIMIC
84 3.6. CONCLUSIONS 89 4. GENETICS AND MOLECULAR BIOLOGY 91 4.1.
OBJECTIONS TO HEMPEL'S MODEL OF THEORY REDUCTION 92 4.2. THE
TRANSPOSITION OF GENES: MCCLINTOCK AND FEDOROFF 97 4.3. MCCLINTOCK'S
STUDIES OF MAIZE 103 4.4. J. D. WATSON'S TEXTBOOK 111 4.5. FEDOROFFS
TRANSLATION OF MCCLINTOCK 113 4.6. THE FUTURE OF MOLECULAR BIOLOGY 123
VLLL CONTENTS 5. CHEMISTRY, QUANTUM MECHANICS, AND GROUP THEORY 126 5.1.
SYMBOLS, ICONS, AND ICONICITY 126 5.2. REPRESENTATION THEORY 128 5.3.
MOLECULES, SYMMETRY, AND GROUPS 131 5.4. SYMMETRY GROUPS,
REPRESENTATIONS, AND CHARACTER TABLES 135 5.5. THE BENZENE RING AND
CARBOCYCLIC SYSTEMS 139 5.6. MEASURING DELOCALIZATION ENERGY IN THE
BENZENE MOLECULE 147 PART III: GEOMETRY AND SEVENTEENTH CENTURY
MECHANICS 157 6. DESCARTES'S GEOMETRY 159 6.1. LOCKE'S CRITICISM OF
SYLLOGISTIC 159 6.2. DESCARTES' GEOMETRY AS THE EXEMPLAR OF CARTESIAN
METHOD 165 6.3. DIAGRAMS AS PROCEDURES 169 6.4. GENERALIZATION TO THE
CONSTRUCTION OF A LOCUS 171 6.5. GENERALIZATION TO HIGHER ALGEBRAIC
CURVES 177 7. NEWTON'S PRINCIPIA 184 7.1. PHILIP KITCHER ON HISTORY 187
7.2. JEAN CAVAILLES ON HISTORY 189 7.3. BOOK I, PROPOSITIONS I AND VI IN
NEWTON'S PRINCIPIA 192 7.4. BOOK I, PROPOSITION XI IN NEWTON'S PRINCIPIA
198 8. LEIBNIZ ON TRANSCENDENTAL CURVES 204 8.1. THE PRINCIPLE OF
CONTINUITY 205 8.2. STUDIES FOR THE INFINITESIMAL CALCULUS 207 8.3. THE
PRINCIPLE OF PERFECTION 213 8.4. THE ISOCHRONE AND THE TRACTRIX 215 8.5.
THE CATENARY OR LA CHAINETTE 221 PART IV: GEOMETRY AND TWENTIETH CENTURY
TOPOLOGY 225 9. GEOMETRY, ALGEBRA, AND TOPOLOGY 227 9.1. VUILLEMIN ON
THE RELATION OF MATHEMATICS AND PHILOSOPHY 227 9.2. EUCLID'S ELEMENTS
AND DESCARTES' GEOMETRY REVISITED 230 CONTENTS 9.3. KANT'S
TRANSCENDENTAL AESTHETIC: EXTRINSIC AND INTRINSIC INTUITION 9.4. THE
FIRST PAGES OF SINGER AND THORPE 9.5. DE RHAM'S THEOREM 9.6. NANCY
CARTWRIGHT ON THE ABSTRACT AND CONCRETE 10. LOGIC AND TOPOLOGY 10.1.
PENELOPE MADDY ON SET THEORY 10.2. A BRIEF RECONSIDERATION OF ARITHMETIC
10.3. THE APPLICATION OF LOGIC TO GENERAL TOPOLOGY 10.4. LOGICAL
HIERARCHIES AND THE BOREL HIERARCHY 10.5. MODEL THEORY AND TOPOLOGICAL
LOGICS 10.6. CODA LIST OF ILLUSTRATIONS GLOSSARY BIBLIOGRAPHY BOOKS
ARTICLES INDEX IX 232 235 243 254 257 259 262 268 273 279 283 285 291
293 293 299 307 |
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| spelling | Grosholz, Emily 1950- Verfasser (DE-588)135716071 aut Representation and productive ambiguity in mathematics and the sciences Emily R. Grosholz 1. publ. Oxford [u.a.] Oxford Univ. Press 2007 XVIII, 313 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Ambiguity in science Knowledge, Theory of Mathematics - Philosophy Science - Philosophy Mathematik Naturwissenschaft Philosophie Mathematics Philosophy Science Philosophy Mathematik (DE-588)4037944-9 gnd rswk-swf Darstellung Mathematik (DE-588)4128289-9 gnd rswk-swf Philosophie (DE-588)4045791-6 gnd rswk-swf Naturwissenschaften (DE-588)4041421-8 gnd rswk-swf Ambiguität (DE-588)4138525-1 gnd rswk-swf Darstellung Mathematik (DE-588)4128289-9 s Ambiguität (DE-588)4138525-1 s DE-604 Mathematik (DE-588)4037944-9 s Philosophie (DE-588)4045791-6 s Naturwissenschaften (DE-588)4041421-8 s b DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016065366&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grosholz, Emily 1950- Representation and productive ambiguity in mathematics and the sciences Ambiguity in science Knowledge, Theory of Mathematics - Philosophy Science - Philosophy Mathematik Naturwissenschaft Philosophie Mathematics Philosophy Science Philosophy Mathematik (DE-588)4037944-9 gnd Darstellung Mathematik (DE-588)4128289-9 gnd Philosophie (DE-588)4045791-6 gnd Naturwissenschaften (DE-588)4041421-8 gnd Ambiguität (DE-588)4138525-1 gnd |
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| title | Representation and productive ambiguity in mathematics and the sciences |
| title_auth | Representation and productive ambiguity in mathematics and the sciences |
| title_exact_search | Representation and productive ambiguity in mathematics and the sciences |
| title_exact_search_txtP | Representation and productive ambiguity in mathematics and the sciences |
| title_full | Representation and productive ambiguity in mathematics and the sciences Emily R. Grosholz |
| title_fullStr | Representation and productive ambiguity in mathematics and the sciences Emily R. Grosholz |
| title_full_unstemmed | Representation and productive ambiguity in mathematics and the sciences Emily R. Grosholz |
| title_short | Representation and productive ambiguity in mathematics and the sciences |
| title_sort | representation and productive ambiguity in mathematics and the sciences |
| topic | Ambiguity in science Knowledge, Theory of Mathematics - Philosophy Science - Philosophy Mathematik Naturwissenschaft Philosophie Mathematics Philosophy Science Philosophy Mathematik (DE-588)4037944-9 gnd Darstellung Mathematik (DE-588)4128289-9 gnd Philosophie (DE-588)4045791-6 gnd Naturwissenschaften (DE-588)4041421-8 gnd Ambiguität (DE-588)4138525-1 gnd |
| topic_facet | Ambiguity in science Knowledge, Theory of Mathematics - Philosophy Science - Philosophy Mathematik Naturwissenschaft Philosophie Mathematics Philosophy Science Philosophy Darstellung Mathematik Naturwissenschaften Ambiguität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016065366&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT grosholzemily representationandproductiveambiguityinmathematicsandthesciences |