Mathematical intuition: phenomenology and mathematical knowledge
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer
1989
|
| Series: | Synthese library
203 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 209 S. |
| ISBN: | 0792301315 |
Staff View
MARC
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Record in the Search Index
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TABLE OF CONTENTS
PREFACE xi
ABBREVIATIONS FOR WORKS OF HUSSERL xv
CHAPTER 1. THE CONCEPT OF INTUITION IN MATHEMATICS 1
1. Introduction 1
2. Knowledge, Evidence, and Intuition 2
3. Intuition "of and Intuition "that" 5
4. Some Recent Views of Mathematical Intuition 6
5. Hilbert and Bernays 6
6. Parsons 8
7. Brouwer 12
8. Some "Extended" Proof Theoretic Views 13
9. GOdel on Sets 14
10. Platonism and Constructivism 16
11. Mathematical Truth and Mathematical Knowledge 17
12. Principal Objections to Mathematical Intuition 18
CHAPTER 2. THE PHENOMENOLOGICAL VIEW OF INTUITION 21
1. Introduction 21
2. Intentionality and Intuition 22
3. Intuition of Abstract Objects 25
4. Acts of Abstraction and Abstract Objects 31
5. Acts of Reflection 36
6. Types and Degrees of Evidence 38
7. Comparison with Kant 43
8. Intuition and the Theory of Meaning 45
viii TABLE OF CONTENTS
CHAPTER 3. PERCEPTION 48
1. Introduction 48
2. Sequences of Perceptual Acts 49
3. The Horizon of Perceptual Acts 51
4. The Possibilities of Perception 56
5. The "Determinable X" in Perception and Indexicals 58
6. Perceptual Evidence 61
7. Phenomenological Reduction and the Problem of Realism /
Idealism 63
CHAPTER 4. MATHEMATICAL INTUITION 66
1. Introduction 66
2. Objections About Analogies Between Perceptual and
Mathematical Intuition 67
3. Objections Based on Structuralism 71
4. Objections About Founding 75
5. A Logic Compatible With Mathematical Intuition and
the Notion of Construction 79
6. Is Classical Mathematics to be Rejected? 89
CHAPTER 5. NATURAL NUMBERS I 92
1. Introduction 92
2. The Concept of Number Cannot Be Explicitly Defined 93
3. The Origin of the Concept of Number 96
4. Intuition of Natural Numbers 99
5. Ordinals 101
6. Ordinals and Cardinals 105
7. Constructing Units and the Role of Reflection and Abstraction 111
8. Syntax and Representations of Numbers 116
CHAPTER 6. NATURAL NUMBERS II 119
1. Introduction 119
2. Oandl 121
3. Numbers Formed by Arithmetic Operations 122
4. Small Numbers and Singular Statements About Them 124
5. Large Numbers and Mathematical Induction 128
6. The Possibilities of Intuition 131
7. Summary of the Argument for Large Numbers 135
8. Further Comments on Mathematical Induction 137
TABLE OF CONTENTS ix
9. Intuition and Axioms of Elementary Number Theory 140
CHAPTER 7. FINITE SETS 143
1. Introduction 143
2. A Theory of Finite Sets 145
3. The Origin of the Concept of Finite Set 147
4. Intuition of Finite Sets 153
5. Comparison with GOdel and Wang 156
6. Unit Sets, the Empty Set, and Mereology vs. Set Theory 161
r 7. Large Sets and a Hierarchy of Sets 164
8. Illusion in Set Theory 169
9. Concluding Remarks 170
CHAPTER 8. CRITICAL REFLECTIONS AND CONCLUSION 172
1. Introduction 172
2. Summary of the Account 172
3. Areas for Further Work 175
4. Platonism, Constructivism, and Benacerraf s Dilemma 177
NOTES 183
BIBLIOGRAPHY 194
INDEX 201 |
| any_adam_object | 1 |
| author | Tieszen, Richard L. 1951-2017 |
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| classification_rvk | CC 2600 CC 4400 |
| ctrlnum | (OCoLC)18984017 (DE-599)BVBBV002522094 |
| 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 |
| format | Book |
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| id | DE-604.BV002522094 |
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| indexdate | 2024-11-11T09:11:55Z |
| institution | BVB |
| isbn | 0792301315 |
| language | English |
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| physical | XIV, 209 S. |
| publishDate | 1989 |
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| publisher | Kluwer |
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| series2 | Synthese library |
| spelling | Tieszen, Richard L. 1951-2017 Verfasser (DE-588)1013625196 aut Mathematical intuition phenomenology and mathematical knowledge Richard L. Tieszen Dordrecht u.a. Kluwer 1989 XIV, 209 S. txt rdacontent n rdamedia nc rdacarrier Synthese library 203 Intuition Mathématiques - Philosophie Mathematik Philosophie Mathematics Philosophy Phänomenologie (DE-588)4045660-2 gnd rswk-swf Philosophie (DE-588)4045791-6 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Phänomenologie (DE-588)4045660-2 s Mathematik (DE-588)4037944-9 s DE-604 Philosophie (DE-588)4045791-6 s Synthese library 203 (DE-604)BV000005044 203 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001622384&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tieszen, Richard L. 1951-2017 Mathematical intuition phenomenology and mathematical knowledge Synthese library Intuition Mathématiques - Philosophie Mathematik Philosophie Mathematics Philosophy Phänomenologie (DE-588)4045660-2 gnd Philosophie (DE-588)4045791-6 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4045660-2 (DE-588)4045791-6 (DE-588)4037944-9 |
| title | Mathematical intuition phenomenology and mathematical knowledge |
| title_auth | Mathematical intuition phenomenology and mathematical knowledge |
| title_exact_search | Mathematical intuition phenomenology and mathematical knowledge |
| title_full | Mathematical intuition phenomenology and mathematical knowledge Richard L. Tieszen |
| title_fullStr | Mathematical intuition phenomenology and mathematical knowledge Richard L. Tieszen |
| title_full_unstemmed | Mathematical intuition phenomenology and mathematical knowledge Richard L. Tieszen |
| title_short | Mathematical intuition |
| title_sort | mathematical intuition phenomenology and mathematical knowledge |
| title_sub | phenomenology and mathematical knowledge |
| topic | Intuition Mathématiques - Philosophie Mathematik Philosophie Mathematics Philosophy Phänomenologie (DE-588)4045660-2 gnd Philosophie (DE-588)4045791-6 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Intuition Mathématiques - Philosophie Mathematik Philosophie Mathematics Philosophy Phänomenologie |
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