Metaphysical myths, mathematical practice: the ontology and epistemology of the exact sciences
This original and exciting study offers a completely new perspective on the philosophy of mathematics. Most philosophers of mathematics try to show either that the sort of knowledge mathematicians have is similar to the sort of knowledge specialists in the empirical sciences have or that the kind of...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
1994
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | This original and exciting study offers a completely new perspective on the philosophy of mathematics. Most philosophers of mathematics try to show either that the sort of knowledge mathematicians have is similar to the sort of knowledge specialists in the empirical sciences have or that the kind of knowledge mathematicians have, although apparently about objects such as numbers, sets, and so on, isn't really about those sorts of things at all Jody Azzouni argues that mathematical knowledge is a special kind of knowledge that must be gathered in its own unique way. He analyzes the linguistic pitfalls and misperceptions philosophers in this field are often prone to, and explores the misapplications of epistemic principles from the empirical sciences to the exact sciences. What emerges is a picture of mathematics sensitive both to mathematical practice and to the ontological and epistemological issues that concern philosophers The book will be of special interest to philosophers of science, mathematics, logic, and language. It should also interest mathematicians themselves |
| Physical Description: | IX, 249 S. |
| ISBN: | 0521442230 |
Staff View
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| 520 | 3 | |a This original and exciting study offers a completely new perspective on the philosophy of mathematics. Most philosophers of mathematics try to show either that the sort of knowledge mathematicians have is similar to the sort of knowledge specialists in the empirical sciences have or that the kind of knowledge mathematicians have, although apparently about objects such as numbers, sets, and so on, isn't really about those sorts of things at all | |
| 520 | |a Jody Azzouni argues that mathematical knowledge is a special kind of knowledge that must be gathered in its own unique way. He analyzes the linguistic pitfalls and misperceptions philosophers in this field are often prone to, and explores the misapplications of epistemic principles from the empirical sciences to the exact sciences. What emerges is a picture of mathematics sensitive both to mathematical practice and to the ontological and epistemological issues that concern philosophers | ||
| 520 | |a The book will be of special interest to philosophers of science, mathematics, logic, and language. It should also interest mathematicians themselves | ||
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Record in the Search Index
| _version_ | 1804124042348724224 |
|---|---|
| adam_text | Contents
Acknowledgments page ix
PART I
MATHEMATICAL PRACTICE AND ITS PUZZLES
§ 1 Metaphysical Inertness 3
§ 2 Metaphysical Inertness and Reference 6
§ 3 The Virtues of (Second Order) Theft 11
§ 4 Intuitions about Reference and Axiom Systems 18
§ 5 Comparing Mathematical Terms and Empirical
Terms I 31
§ 6 Comparing Mathematical Terms and Empirical
Terms II 48
§ 7 The Epistemic Role Puzzle 55
§ 8 Benacerrafs Puzzle 58
§ 9 Comparing Puzzles 60
§ 10 Quine s Approach I 64
§11 Quine s Approach II 71
PART II
THE STUFF OF MATHEMATICS:
POSITS AND ALGORITHMS
§ 1 Introduction 79
§ 2 An Initial Picture 80
§ 3 Application and Truth 88
§ 4 Systems, Application, and Truth 94
§ 5 Quine s Objections to Truth by Convention 105
§6 Grades of Ontological Commitment 118
§ 7 Multiply Interpreting Systems 132
§ 8 Intuitions about Reference Revisited 139
VII
VIII CONTENTS
PART III
THE GEOGRAPHY OF THE A PRIORI
§ 1 Introduction 153
§ 2 Algorithms Again 156
§ 3 Some Observations on Metamathematics 171
§ 4 Incorrigible Co empiricalness 174
§ 5 Why There Are No Incorrigible Co empirical Truths 192
§ 6 Normative Considerations, the Success of Applied
Mathematics, Concluding Thoughts 204
Appendix 215
Bibliography 236
Index 246
|
| any_adam_object | 1 |
| author | Azzouni, Jody 1954- |
| author_GND | (DE-588)142352764 |
| author_facet | Azzouni, Jody 1954- |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | CC 2600 |
| ctrlnum | (OCoLC)28026812 (DE-599)BVBBV009696178 |
| dewey-full | 510/.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510/.1 |
| dewey-search | 510/.1 |
| dewey-sort | 3510 11 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| edition | 1. publ. |
| format | Book |
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| spelling | Azzouni, Jody 1954- Verfasser (DE-588)142352764 aut Metaphysical myths, mathematical practice the ontology and epistemology of the exact sciences Jody Azzouni 1. publ. Cambridge Cambridge Univ. Press 1994 IX, 249 S. txt rdacontent n rdamedia nc rdacarrier This original and exciting study offers a completely new perspective on the philosophy of mathematics. Most philosophers of mathematics try to show either that the sort of knowledge mathematicians have is similar to the sort of knowledge specialists in the empirical sciences have or that the kind of knowledge mathematicians have, although apparently about objects such as numbers, sets, and so on, isn't really about those sorts of things at all Jody Azzouni argues that mathematical knowledge is a special kind of knowledge that must be gathered in its own unique way. He analyzes the linguistic pitfalls and misperceptions philosophers in this field are often prone to, and explores the misapplications of epistemic principles from the empirical sciences to the exact sciences. What emerges is a picture of mathematics sensitive both to mathematical practice and to the ontological and epistemological issues that concern philosophers The book will be of special interest to philosophers of science, mathematics, logic, and language. It should also interest mathematicians themselves ALGORITMOS larpcal FILOSOFIA larpcal Filosofie gtt MATEMÁTICA larpcal METAFÍSICA larpcal Mathématiques - Philosophie ram Theorie en praktijk gtt Wiskunde gtt Mathematik Philosophie Mathematics Philosophy Mathematik (DE-588)4037944-9 gnd rswk-swf Philosophie (DE-588)4045791-6 gnd rswk-swf Erkenntnistheorie (DE-588)4070914-0 gnd rswk-swf Ontologie (DE-588)4075660-9 gnd rswk-swf Mathematik (DE-588)4037944-9 s Philosophie (DE-588)4045791-6 s Erkenntnistheorie (DE-588)4070914-0 s Ontologie (DE-588)4075660-9 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006413225&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Azzouni, Jody 1954- Metaphysical myths, mathematical practice the ontology and epistemology of the exact sciences ALGORITMOS larpcal FILOSOFIA larpcal Filosofie gtt MATEMÁTICA larpcal METAFÍSICA larpcal Mathématiques - Philosophie ram Theorie en praktijk gtt Wiskunde gtt Mathematik Philosophie Mathematics Philosophy Mathematik (DE-588)4037944-9 gnd Philosophie (DE-588)4045791-6 gnd Erkenntnistheorie (DE-588)4070914-0 gnd Ontologie (DE-588)4075660-9 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4045791-6 (DE-588)4070914-0 (DE-588)4075660-9 |
| title | Metaphysical myths, mathematical practice the ontology and epistemology of the exact sciences |
| title_auth | Metaphysical myths, mathematical practice the ontology and epistemology of the exact sciences |
| title_exact_search | Metaphysical myths, mathematical practice the ontology and epistemology of the exact sciences |
| title_full | Metaphysical myths, mathematical practice the ontology and epistemology of the exact sciences Jody Azzouni |
| title_fullStr | Metaphysical myths, mathematical practice the ontology and epistemology of the exact sciences Jody Azzouni |
| title_full_unstemmed | Metaphysical myths, mathematical practice the ontology and epistemology of the exact sciences Jody Azzouni |
| title_short | Metaphysical myths, mathematical practice |
| title_sort | metaphysical myths mathematical practice the ontology and epistemology of the exact sciences |
| title_sub | the ontology and epistemology of the exact sciences |
| topic | ALGORITMOS larpcal FILOSOFIA larpcal Filosofie gtt MATEMÁTICA larpcal METAFÍSICA larpcal Mathématiques - Philosophie ram Theorie en praktijk gtt Wiskunde gtt Mathematik Philosophie Mathematics Philosophy Mathematik (DE-588)4037944-9 gnd Philosophie (DE-588)4045791-6 gnd Erkenntnistheorie (DE-588)4070914-0 gnd Ontologie (DE-588)4075660-9 gnd |
| topic_facet | ALGORITMOS FILOSOFIA Filosofie MATEMÁTICA METAFÍSICA Mathématiques - Philosophie Theorie en praktijk Wiskunde Mathematik Philosophie Mathematics Philosophy Erkenntnistheorie Ontologie |
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