Philosophy of mathematics: an introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Malden, MA
Wiley- Blackwell
2009
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | X, 332 S. |
| ISBN: | 9781405189927 9781405189910 |
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS PREFACE VIII 1. PLATO VERSUS ARISTOTLE 1 A. PLATO 1 1. THE
SOCRATIC BACKGROUND 1 2. THE THEORY OF RECOLLECTION 3 3. PLATONISM IN
MATHEMATICS 7 4. RETRACTIONS: THE DIVIDED LINE IN REPUBLIC VI
(509D-511E) 9 B. ARISTOTLE 15 5. THE OVERALL POSITION 15 6.
IDEALIZATIONS 17 7. COMPLICATIONS 20 8. PROBLEMS WITH INFINITY 23 C.
PROSPECTS 28 2. FLOM ARISTOTLE TOKANT 33 1. MEDIAEVAL TIMES 33 2.
DESCARTES 35 3. LOCKE, BERKELEY, HUME 38 4. AREMARK ON CONCEPTUALISM 43
5. KANT: THE PROBLEM 44 6. KANT: THE SOLUTION 51 3. REACTIONS TO KANT 62
1. MILL ON GEOMETRY 62 2. MILL VERSUS FREGE ON ARITHMETIC 69 3. ANALYTIC
TRUTHS 74 4. CONDUDING REMARKS 85 VI CONTENTS 4. MATHEMATICS AND ITS
FOUNDATIONS 87 1. GEOMETRY 87 2. DIFFERENT KINDS OF NUMBER 90 3. THE
CALCULUS 93 4. RETURN TO FOUNDATIONS 97 5. INFINITE NUMBERS 103 6.
FOUNDATIONS AGAIN 111 5. LOGICISM 114 1. FREGE 115 2. RUSSELL 122 3.
BORKOWSKI/BOSTOCK 136 4. SET THEORY 140 5. LOGIC 152 6. DEFINITION 160~
6. FORMALISM 167 1. HILBERT 168 2. GOEDEL 175 3. PURE FORMALISM 180 4.
STRUCTURALISM 183 5. SOME COMMENTS 191 7. INTUITIONISM 197 1. BROUWER
197 2. INTUITIONIST LOGIC 201 3. THE IRRELEVANCE OF ONTOLOGY 215 4. THE
ATTACK ON CLASSICALLOGIC 218 8. PREDICATIVISM 224 1. RUSSELL AND THE VCP
224 2. RUSSELL S RAMIFIED THEORY AND THE AXIOM OF REDUCIBILITY 235 3.
PREDICATIVE THEORIES AFTER RUSSELL 244 4. CONCLUDING REMARKS 253 9.
REALISM AND NOMINALISM 261 A. REALISM 262 1. GOEDEL 263 2. NEO- FREGEANS
266 3. QUINE AND PUTNAM B. NOMINALISM 4. REDUCTIVE NOMINALISM 5.
FICTIONALISM 6. CONCLUDING REMARKS REFERENCES INDEX CONTENTS VU 275 282
282 289 304 310 325
In this new introduction to the philosophy of mathematics, David
Bostock
guides the
reader through the basic ideas on the nature of mathematics that have played a major
part in the development of philosophy from antiquity to the present.
The chapters proceed historically, beginning with the earliest serious views on the
interpretation of mathematics, due to Plato and Aristotle.They then move quickly
through the middle ages and the early moderns, but continue with extended
discussions of Kant, Mill and
Frege.
Later chapters explore the main schools of
thought at the start of the twentieth century, i.e. the movements known as logicism,
formalism,
intuiţionism,
and what may be called predicativism.These chapters also
discuss more modern variations on the same basic themes. Finally the book concludes
with a discussion of the most recent debates between realists and nominalists.The
emphasis throughout is not simply to describe, but to offer a critical appraisal of,
the views discussed.The result is an engaging, clear and remarkably comprehensive
panorama of the major issues in the field.
The book assumes no prior knowledge of mathematics, beyond what is commonly
taught in schools, and only a minimal exposure to standard philosophical terminology.
It is aimed at undergraduates in philosophy and mathematics, but will also provide an
important new perspective on the subject for more experienced readers.
David
Bostock
has been a Fellow andTutor in Philosophy at Merton College, and
Lecturer in Philosophy at the University of Oxford.. His recent publications include
Intermediate Logic
(1997),
Aristotle s Ethics
(2000)
and Spacejime, Matter, and Form:
Essays
onAristoÜe s
Physics
(2006).
|
| any_adam_object | 1 |
| author | Bostock, David 1936-2019 |
| author_GND | (DE-588)151039003 |
| author_facet | Bostock, David 1936-2019 |
| author_role | aut |
| author_sort | Bostock, David 1936-2019 |
| author_variant | d b db |
| building | Verbundindex |
| bvnumber | BV035309171 |
| classification_rvk | CC 2600 SG 700 |
| ctrlnum | (OCoLC)470900505 (DE-599)BVBBV035309171 |
| 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 | 3510.1 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV035309171 |
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| indexdate | 2024-07-09T21:30:58Z |
| institution | BVB |
| isbn | 9781405189927 9781405189910 |
| language | English |
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| spelling | Bostock, David 1936-2019 Verfasser (DE-588)151039003 aut Philosophy of mathematics an introduction David Bostock 1. publ. Malden, MA Wiley- Blackwell 2009 X, 332 S. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Mathématiques - Philosophie ram Mathematik Philosophie Mathematics Philosophy Mathematik (DE-588)4037944-9 gnd rswk-swf Philosophie (DE-588)4045791-6 gnd rswk-swf Mathematik (DE-588)4037944-9 s Philosophie (DE-588)4045791-6 s b DE-604 Digitalisierung UB Erlangen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017113935&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017113935&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Bostock, David 1936-2019 Philosophy of mathematics an introduction Mathématiques - Philosophie ram Mathematik Philosophie Mathematics Philosophy Mathematik (DE-588)4037944-9 gnd Philosophie (DE-588)4045791-6 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4045791-6 |
| title | Philosophy of mathematics an introduction |
| title_auth | Philosophy of mathematics an introduction |
| title_exact_search | Philosophy of mathematics an introduction |
| title_full | Philosophy of mathematics an introduction David Bostock |
| title_fullStr | Philosophy of mathematics an introduction David Bostock |
| title_full_unstemmed | Philosophy of mathematics an introduction David Bostock |
| title_short | Philosophy of mathematics |
| title_sort | philosophy of mathematics an introduction |
| title_sub | an introduction |
| topic | Mathématiques - Philosophie ram Mathematik Philosophie Mathematics Philosophy Mathematik (DE-588)4037944-9 gnd Philosophie (DE-588)4045791-6 gnd |
| topic_facet | Mathématiques - Philosophie Mathematik Philosophie Mathematics Philosophy |
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