Plato's problem: an introduction to mathematical platonism
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basingstoke [u.a.]
Palgrave Macmillan
2013
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| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 306 S. |
| ISBN: | 9780230365483 9780230365490 |
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MARC
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Record in the Search Index
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| adam_text | Titel: Plato s problem
Autor: Panza, Marco
Jahr: 2013
Contents
Preface vii
Acknowledgements xii
Terminological Conventions xiii
Introduction 1
Platonism in the Philosophy of Mathematics 1
Nominalism in the Philosophy of Mathematics 9
The Indispensability Argument 14
1 The Origins 16
1.1 Plato as a Piatonist? 17
1.2 Aristotle Between Platonism and Anti-platonism 27
1.3 Proclus: The Neoplatonic Interpretation of
Euclid s Geometry 32
1.4 Kant: The Transcendental Interpretation of
Classical Arithmetic and Geometry 36
2 From Frege to Gödel (Through Hubert) 45
2.1 Frege s Logicist Platonism 45
2.2 Russell and the Separation of Logicism and
Platonism 66
2.3 Set Theory 69
2.4 The Problem of Foundations 73
2.5 Gödel s Platonism and the Rise of
Mathematical Intuition 90
3 Benacerraf s Arguments 99
3.1 What Natural Numbers Could Not Be
(According to Benacerraf) 101
3.2 Benacerraf s Dilemma 107
3.3 A Map of Responses to Benacerraf s Dilemma:
Contemporary Solutions to Plato s Problem 110
4 Non-conservative Responses to Benacerraf s Dilemma 112
4.1 Field s Nominalism: Mathematics Without Truth and
Science Without Numbers 112
4.2 Mathematics as Fiction: Field and Yablo 125
vi Contents
4.3 Eliminative Structuralism and its Modal Version 136
4.4 Maddy and the Cognitive Origins of Set Theory 144
5 Conservative Responses to Benacerraf s Dilemma 149
5.1 Neo-logicism: A Revised Version of Frege s Programme 149
5.2 Linsky, Zalta and Object Theory : Mathematics
and Logic (or Metaphysics) of Abstract Objects 165
5.3 A First Version of Non-eliminative Structuralism:
Ante Rem Structuralism 177
5.4 A Second Version of Non-eliminative Structuralism:
Parsons and the Role of Intuition 187
6 The Indispensability Argument: Structure and
Basic Notions 196
6.1 Four Versions of ia 197
6.2 The Quine-Putnam Argument and Colyvan s
Argument 201
6.3 (In)dispensability 203
6.4 Quine s Criterion of Ontological Commitment 210
6.5 Naturalism 212
6.6 Confirmational Holism 214
6.7 The Dispensability of Naturalism and
Confirmational Holism 215
7 The Indispensability Argument: The Debate 217
7.1 Against Indispensability 217
7.2 Against Ontological Commitment 224
7.3 Against Naturalism and Scientific Realism 235
7.4 Against Confirmational Holism 241
Concluding Remarks 250
Notes 255
References 273
Index 296
|
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| id | DE-604.BV040738351 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:32:52Z |
| institution | BVB |
| isbn | 9780230365483 9780230365490 |
| language | English |
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| physical | XVI, 306 S. |
| publishDate | 2013 |
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| spelling | Panza, Marco Verfasser aut Il problema di Platone Plato's problem an introduction to mathematical platonism Marco Panza and Andrea Sereni 1. publ. Basingstoke [u.a.] Palgrave Macmillan 2013 XVI, 306 S. txt rdacontent n rdamedia nc rdacarrier Platonismus (DE-588)4046303-5 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Platonismus (DE-588)4046303-5 s Mathematik (DE-588)4037944-9 s b DE-604 Sereni, Andrea Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025718330&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Panza, Marco Sereni, Andrea Plato's problem an introduction to mathematical platonism Platonismus (DE-588)4046303-5 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4046303-5 (DE-588)4037944-9 |
| title | Plato's problem an introduction to mathematical platonism |
| title_alt | Il problema di Platone |
| title_auth | Plato's problem an introduction to mathematical platonism |
| title_exact_search | Plato's problem an introduction to mathematical platonism |
| title_full | Plato's problem an introduction to mathematical platonism Marco Panza and Andrea Sereni |
| title_fullStr | Plato's problem an introduction to mathematical platonism Marco Panza and Andrea Sereni |
| title_full_unstemmed | Plato's problem an introduction to mathematical platonism Marco Panza and Andrea Sereni |
| title_short | Plato's problem |
| title_sort | plato s problem an introduction to mathematical platonism |
| title_sub | an introduction to mathematical platonism |
| topic | Platonismus (DE-588)4046303-5 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Platonismus Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025718330&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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