Explaining beauty in mathematics: an aesthetic theory of mathematics
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham [u.a.]
Springer
2014
|
| Series: | Synthese library
370 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 220 S. |
| ISBN: | 9783319034515 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | Titel: Explaining beauty in mathematics
Autor: Montano, Ulianov
Jahr: 2014
Contents
Part I Antecedents
1 On Non-Iiteral Approaches 3
1.1 The Two Cultures, Shaftesbury and Hutchenson 3
1.1.1 Unsound Divide 4
1.1.2 Shaftesbury 5
1.1.3 Hutchenson 6
1.2 The Epistemic Character of Mathematics 8
1.2.1 Rota s Interpretation of Mathematical Beauty 9
1.2.2 Rota s Problems 11
1.3 The Rational Character of Mathematics 15
1.3.1 Rational Reinterpretations 16
2 Beautiful, Literally 21
2.1 Metaphor and Aesthetic Terms 21
2.2 McAllister s Approach 23
2.2.1 McAllister s Aesthetic Theory 24
2.2.2 Aesthetic Properties, Aesthetic Criteria
and Aesthetic Canon 25
2.2.3 The Aesthetic Canon 26
2.2.4 The Aesthetic Induction 27
2.2.5 Aesthetic Induction in Mathematics 29
2.2.6 McAllister in Summary 30
3 Ugly, Literally 33
3.1 Ugliness in Mathematics 33
3.2 Computer-Assisted Proofs 36
3.3 Phenomenological Factors 38
3.3.1 Intentional Objects 39
3.3.2 Intentional Proofs 40
3.3.3 Why the Conflict? 42
v
vi Contents
4 Problems of the Aesthetic Induction 45
4.1 Two Kinds of Problems 45
4.1.1 Anomalies 45
4.2 Theoretical Tensions 51
4.2.1 Induction 52
4.2.2 Beauty and Aesthetic 54
4.2.3 Objectivism/Projectivismlnconsistency 55
4.2.4 Theory and Modelling 55
5 Naturalizing the Aesthetic Induction 57
5.1 The Mere-Exposure Effect and the Nature
of the Aesthetic Induction 57
5.1.1 Naturalizing Preference Evolution 58
5.1.2 Naturalizing the Aesthetic Induction 60
5.1.3 Preference, Affection and Emotion 60
5.1.4 Constraints of Affective Plasticity 62
5.2 Conceptualizing Preference Evolution 63
5.2.1 The Aesthetic Canon as a System 64
5.2.2 Critical Adequacy 65
5.2.3 Robustness of Critical Adequacy 65
5.2.4 Dynamics of the New Model 66
5.3 The New Model: Constrained Aesthetic Induction 68
5.3.1 Constrained Aesthetic Induction (CAI) 68
5.3.2 Problems Addressed 68
Part II An Aesthetics of Mathematics
6 Introduction to a Naturalistic Aesthetic Theory 73
6.1 The Mark of the Aesthetic 76
6.1.1 Phases of an Aesthetic-Process 79
7 Aesthetic Experience 85
7.1 Characterizing Aesthetic Experience 85
7.2 Aesthetic Intentional Objects 87
7.3 Mathematical Intentional Objects 88
7.4 A Notion of Aesthetic Mathematical Intentional Object 89
7.4.1 Dimensions and Properties 89
7.4.2 Activities and Relations 92
7.4.3 A Model of Aesthetic Mathematical
Intentional Objects 96
7.4.4 Aesthetic Form 97
7.5 Types of Experience 98
7.5.1 Basic Appreciation Response 98
7.5.2 Non Inductive Response 100
Contents vii
7.5.3 Performative Appreciation Responses 101
7.5.4 Adaptive Appreciation Response 107
7.6 The Pleasure-Relation 111
7.6.1 Formalization 112
8 Aesthetic Value 117
8.1 Extension of Aesthetic Value 118
8.2 Typical Positive Aesthetic Criterion 121
8.3 Dynamics 122
8.3.1 Value and Aesthetic Canon 122
8.4 Aesthetic Canon Evolution 124
8.4.1 Naturalistic Evolution Rule II (NERII) 124
8.4.2 Positive Value 126
8.4.3 Negative Value 128
8.4.4 Aesthetic Experience and the Application of
Value Repositories 129
9 Aesthetic Judgement I: Concept 131
9.1 On Aesthetic Terms 131
9.1.1 Sibley 131
9.1.2 Hungerland 133
9.1.3 Kivy 134
9.1.4 De Clercq 135
9.1.5 Zangwill 135
9.2 A New Model of Aesthetic Terms 136
9.2.1 Metaphor 137
9.2.2 Metaphorical Terms and Aesthetic Terms 138
9.2.3 Experience and Response Spaces 139
9.2.4 A New Model of Aesthetic Terms 140
9.2.5 Genuine Aesthetic Terms 141
9.2.6 Definitions of Aesthetic Term, Description
and Judgement 145
9.2.7 Always and Only Aesthetic Terms; The
Spectrum of Aesthetic Terms 146
10 Aesthetic Judgement II: Functions 149
10.1 Concept and Function 149
10.1.1 Emphases and Perspectives 150
10.2 Articulation 150
10.2.1 Definition of Articulation 152
10.3 Broadcasting Function 154
10.3.1 Locally Terminal Aesthetic Terms 156
10.4 Unifying Approaches 157
11 Mathematical Aesthetic Judgements 161
viii
Contents
Part III Applications
12 Case Analysis I: Beauty 167
12.1 Knowledge, Beauty and Isolated Pearls 168
12.2 Case 1, Beauty: y — ex 169
12.2.1 Experience 169
12.2.2 Value 172
12.3 Dynamics 173
12.4 Judgement 174
12.5 The Process in Summary 177
13 Case Analysis II: Elegance 179
13.1 Experience 179
13.1.1 Step-Series Interpretation 182
13.1.2 Single-Object Interpretation 183
13.1.3 Affective Response in Step-Series Interpretation 186
13.1.4 Affective Response in the Single-Object Interpretation.. 188
13.2 Value 189
13.3 Judgement 192
13.4 The Process in Summary 195
14 Case Analysis III: Ugliness, Revisited 197
14.1 TheProof 197
14.2 Experience 199
14.3 Value 201
14.3.1 Scenario 1: Change by Aesthetic Induction 201
14.3.2 Scenario 2: Change in the Nature of Our Experience .... 201
Part IV Closing Remarks
15 Issues of Mathematical Beauty, Revisited 207
Conclusion 211
Bibliography 217
|
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| institution | BVB |
| isbn | 9783319034515 |
| language | English |
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| physical | XVIII, 220 S. |
| publishDate | 2014 |
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| spelling | Montano, Ulianov Verfasser (DE-588)104657809X aut Explaining beauty in mathematics an aesthetic theory of mathematics Ulianov Montano Cham [u.a.] Springer 2014 XVIII, 220 S. txt rdacontent n rdamedia nc rdacarrier Synthese library 370 Geschichte 1800-2010 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Ästhetik (DE-588)4000626-8 gnd rswk-swf Mathematik (DE-588)4037944-9 s Ästhetik (DE-588)4000626-8 s Geschichte 1800-2010 z b DE-604 Synthese library 370 (DE-604)BV000005044 370 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027097111&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Montano, Ulianov Explaining beauty in mathematics an aesthetic theory of mathematics Synthese library Mathematik (DE-588)4037944-9 gnd Ästhetik (DE-588)4000626-8 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4000626-8 |
| title | Explaining beauty in mathematics an aesthetic theory of mathematics |
| title_auth | Explaining beauty in mathematics an aesthetic theory of mathematics |
| title_exact_search | Explaining beauty in mathematics an aesthetic theory of mathematics |
| title_full | Explaining beauty in mathematics an aesthetic theory of mathematics Ulianov Montano |
| title_fullStr | Explaining beauty in mathematics an aesthetic theory of mathematics Ulianov Montano |
| title_full_unstemmed | Explaining beauty in mathematics an aesthetic theory of mathematics Ulianov Montano |
| title_short | Explaining beauty in mathematics |
| title_sort | explaining beauty in mathematics an aesthetic theory of mathematics |
| title_sub | an aesthetic theory of mathematics |
| topic | Mathematik (DE-588)4037944-9 gnd Ästhetik (DE-588)4000626-8 gnd |
| topic_facet | Mathematik Ästhetik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027097111&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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