Brouwer meets Husserl: on the phenomenology of choice sequences
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht
Springer
2007
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "This is an analysis, using Husserl's methods, of Brouwer's main contribution to the ontology of mathematics" (preface) |
| Physical Description: | XIII, 191 S. |
| ISBN: | 1402050860 9781402050862 |
Staff View
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Record in the Search Index
| _version_ | 1804135457950269440 |
|---|---|
| adam_text | CONTENTS PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . .. IX
ACKNOWLEDGEMENTS XI 1 AN INFORMAL INTRODUCTION. . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 1 2 INTRODUCTION. . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 5 2.1 THE AIM . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 5 2.2 THE THESIS 5 2.3
MOTIVATION 5 2.4 METHOD, AND AN ASSUMPTION . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 7 2.5 THE LITERATURE . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 THE
ARGUMENT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 9 3.1
PRESENTATION............................................ 9 3.2
COMMENTS.............................................. 9 4 THE ORIGINAL
POSITIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . .. 11 4.1 THE INEOMPATIBILITY OF HUSSERL S AND BROUWER S
POSITIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.. 11 4.2 TWO SOURCES OF MUTUAL PRESSURE . . . . . . . . . . . . . . . .
. . . . . . . . . .. 17 4.2.1 SIMILARITY OF METHODS . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .. 18 4.2.2 INITIAL PLAUSIBILITY OF
BOTH POSITIONS . . . . . . . . . . . . . . . .. 27 4.3 RESOLVING THE
CONFIIET: THE OPTIONS, AND A PROPOSAL. . . . . . . .. 37 4.3.1 DENY THAT
SOME MATHEMATIEAL OBJECTS ARE INTRATEMPORAL, DYNAMIE AND UNBOUNDED 37
4.3.2 DENY THAT MATHEMATIEAL OBJEETS ARE OMNITEMPORAL. .. 39 4.3.3 DENY
THAT MATHEMATIEAL OBJEETS ARE WITHIN THE TEMPORAL REALM 40 4.3.4 DENY
THAT MATHEMATIES IS ABOUT OBJEETS . . . . . . . . . . .. 40 4.3.5
APROPOSAL: THE HETEROGENEOUS UNIVERSE 51 VII VIII CONTENTS 5 THE
PHENOMENOLOGICAL INCORRECTNESS OF THE ORIGINAL ARGUMENTS . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . .. 53 5.1 THE
PHENOMENOLOGICAL STANDARD FOR A CORRECT ARGUMENT IN ONTOLOGY . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. .. 53 5.2 HUSSERL S WEAK REVISIONISM . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . .. 55 5.3 HUSSERL S IMPLIED STRANG REVISIONISM
59 5.4 THE INCOMPLETENESS OF HUSSERL S ARGUMENT. . . . . . . . . . . . .
. . . .. 67 5.4.1 FROM ATEMPORALITY TO OMNITEMPORALITY . . . . . . . . .
. . . .. 67 5.4.2 POSSIBLE INFLUENCE OF HUSSERL S INFORMANTS. . . . . .
. . . . . .. 72 5.5 THE IRREFLEXIVITY OF BRAUWER S PHILOSOPHY 74 6 THE
CONSTITUTION OF CHOICE SEQUENCES . . . . . . . . . . . . . . . . . . .
.. 85 6.1 A MOTIVATION FOR CHOICE SEQUENCES . . . . . . . . . . . . . .
. . . . . . . . .. 85 6.2 CHOICE SEQUENCES AS OBJECTS . . . . . . . . .
. . . . . . . . . . . . . . . . . . . .. 89 6.3 CHOICE SEQUENCES AS
MATHEMATICAL OBJECTS . . . . . . . . . . . . . . . .. 95 6.3.1 THE
TEMPORALITY OF CHOICE SEQUENCES . . . . . . . . . . . . . . .. 96 6.3.2
THE FORMAL CHARACTER OF CHOICE SEQUENCES . . . . . . . . . .. 97 6.3.3
THE SUBJECT-DEPENDENCY OF CHOICE SEQUENCES . . . . . . . .. 98 7
APPLICATION: AN ARGUMENT FOR WEAK CONTINUITY 103 7.1 THE WEAK CONTINUITY
PRINCIPLE 103 7.2 AN ARGUMENT THAT DOES NOT WORK 105 7.3 A
PHENOMENOLOGICAL ARGUMENT 106 8 CONCLUDING REMARKS 111 APPENDIX:
INTUITIONISTIC REMARKS ON HUSSERL S ANALYSIS OF FINITE N UMBER IN THE
PHILOSOPHY OF A RITHMETIC 113 NOTES 127 REFERENCES 169 NAME AND CITATION
INDEX 181 SUBJEET INDEX 187
|
| adam_txt |
CONTENTS PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . IX
ACKNOWLEDGEMENTS XI 1 AN INFORMAL INTRODUCTION. . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 1 2 INTRODUCTION. . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 5 2.1 THE AIM . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 5 2.2 THE THESIS 5 2.3
MOTIVATION 5 2.4 METHOD, AND AN ASSUMPTION . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 7 2.5 THE LITERATURE . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 THE
ARGUMENT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 9 3.1
PRESENTATION. 9 3.2
COMMENTS. 9 4 THE ORIGINAL
POSITIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 11 4.1 THE INEOMPATIBILITY OF HUSSERL'S AND BROUWER'S
POSITIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 11 4.2 TWO SOURCES OF MUTUAL PRESSURE . . . . . . . . . . . . . . . .
. . . . . . . . . . 17 4.2.1 SIMILARITY OF METHODS . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 18 4.2.2 INITIAL PLAUSIBILITY OF
BOTH POSITIONS . . . . . . . . . . . . . . . . 27 4.3 RESOLVING THE
CONFIIET: THE OPTIONS, AND A PROPOSAL. . . . . . . . 37 4.3.1 DENY THAT
SOME MATHEMATIEAL OBJECTS ARE INTRATEMPORAL, DYNAMIE AND UNBOUNDED 37
4.3.2 DENY THAT MATHEMATIEAL OBJEETS ARE OMNITEMPORAL. . 39 4.3.3 DENY
THAT MATHEMATIEAL OBJEETS ARE WITHIN THE TEMPORAL REALM 40 4.3.4 DENY
THAT MATHEMATIES IS ABOUT OBJEETS . . . . . . . . . . . 40 4.3.5
APROPOSAL: THE HETEROGENEOUS UNIVERSE 51 VII VIII CONTENTS 5 THE
PHENOMENOLOGICAL INCORRECTNESS OF THE ORIGINAL ARGUMENTS . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 53 5.1 THE
PHENOMENOLOGICAL STANDARD FOR A CORRECT ARGUMENT IN ONTOLOGY . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 53 5.2 HUSSERL'S WEAK REVISIONISM . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 55 5.3 HUSSERL'S IMPLIED STRANG REVISIONISM
59 5.4 THE INCOMPLETENESS OF HUSSERL'S ARGUMENT. . . . . . . . . . . . .
. . . . 67 5.4.1 FROM ATEMPORALITY TO OMNITEMPORALITY . . . . . . . . .
. . . . 67 5.4.2 POSSIBLE INFLUENCE OF HUSSERL'S INFORMANTS. . . . . .
. . . . . . 72 5.5 THE IRREFLEXIVITY OF BRAUWER'S PHILOSOPHY 74 6 THE
CONSTITUTION OF CHOICE SEQUENCES . . . . . . . . . . . . . . . . . . .
. 85 6.1 A MOTIVATION FOR CHOICE SEQUENCES . . . . . . . . . . . . . .
. . . . . . . . . 85 6.2 CHOICE SEQUENCES AS OBJECTS . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 89 6.3 CHOICE SEQUENCES AS
MATHEMATICAL OBJECTS . . . . . . . . . . . . . . . . 95 6.3.1 THE
TEMPORALITY OF CHOICE SEQUENCES . . . . . . . . . . . . . . . 96 6.3.2
THE FORMAL CHARACTER OF CHOICE SEQUENCES . . . . . . . . . . 97 6.3.3
THE SUBJECT-DEPENDENCY OF CHOICE SEQUENCES . . . . . . . . 98 7
APPLICATION: AN ARGUMENT FOR WEAK CONTINUITY 103 7.1 THE WEAK CONTINUITY
PRINCIPLE 103 7.2 AN ARGUMENT THAT DOES NOT WORK 105 7.3 A
PHENOMENOLOGICAL ARGUMENT 106 8 CONCLUDING REMARKS 111 APPENDIX:
INTUITIONISTIC REMARKS ON HUSSERL'S ANALYSIS OF FINITE N UMBER IN THE
PHILOSOPHY OF A RITHMETIC 113 NOTES 127 REFERENCES 169 NAME AND CITATION
INDEX 181 SUBJEET INDEX 187 |
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| index_date | 2024-07-02T15:03:07Z |
| indexdate | 2024-07-09T20:40:49Z |
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| isbn | 1402050860 9781402050862 |
| language | English |
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| physical | XIII, 191 S. |
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| spelling | Atten, Mark van Verfasser aut Brouwer meets Husserl on the phenomenology of choice sequences by Mark van Atten Dordrecht Springer 2007 XIII, 191 S. txt rdacontent n rdamedia nc rdacarrier "This is an analysis, using Husserl's methods, of Brouwer's main contribution to the ontology of mathematics" (preface) Brouwer, L. E. J <1881-1966> (Luitzen Egbertus Jan) Husserl, Edmund <1859-1938> Brouwer, Luitzen E. J. 1881-1966 (DE-588)118988131 gnd rswk-swf Husserl, Edmund 1859-1938 (DE-588)118555006 gnd rswk-swf Phänomenologie - Wahlfolge Intuitionistic mathematics Phenomenology Sequences (Mathematics) Phänomenologie (DE-588)4045660-2 gnd rswk-swf Ontologie (DE-588)4075660-9 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Husserl, Edmund 1859-1938 (DE-588)118555006 p Brouwer, Luitzen E. J. 1881-1966 (DE-588)118988131 p Phänomenologie (DE-588)4045660-2 s Mathematik (DE-588)4037944-9 s Ontologie (DE-588)4075660-9 s DE-604 V:DE-604 application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014865978&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Atten, Mark van Brouwer meets Husserl on the phenomenology of choice sequences Brouwer, L. E. J <1881-1966> (Luitzen Egbertus Jan) Husserl, Edmund <1859-1938> Brouwer, Luitzen E. J. 1881-1966 (DE-588)118988131 gnd Husserl, Edmund 1859-1938 (DE-588)118555006 gnd Phänomenologie - Wahlfolge Intuitionistic mathematics Phenomenology Sequences (Mathematics) Phänomenologie (DE-588)4045660-2 gnd Ontologie (DE-588)4075660-9 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)118988131 (DE-588)118555006 (DE-588)4045660-2 (DE-588)4075660-9 (DE-588)4037944-9 |
| title | Brouwer meets Husserl on the phenomenology of choice sequences |
| title_auth | Brouwer meets Husserl on the phenomenology of choice sequences |
| title_exact_search | Brouwer meets Husserl on the phenomenology of choice sequences |
| title_exact_search_txtP | Brouwer meets Husserl on the phenomenology of choice sequences |
| title_full | Brouwer meets Husserl on the phenomenology of choice sequences by Mark van Atten |
| title_fullStr | Brouwer meets Husserl on the phenomenology of choice sequences by Mark van Atten |
| title_full_unstemmed | Brouwer meets Husserl on the phenomenology of choice sequences by Mark van Atten |
| title_short | Brouwer meets Husserl |
| title_sort | brouwer meets husserl on the phenomenology of choice sequences |
| title_sub | on the phenomenology of choice sequences |
| topic | Brouwer, L. E. J <1881-1966> (Luitzen Egbertus Jan) Husserl, Edmund <1859-1938> Brouwer, Luitzen E. J. 1881-1966 (DE-588)118988131 gnd Husserl, Edmund 1859-1938 (DE-588)118555006 gnd Phänomenologie - Wahlfolge Intuitionistic mathematics Phenomenology Sequences (Mathematics) Phänomenologie (DE-588)4045660-2 gnd Ontologie (DE-588)4075660-9 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Brouwer, L. E. J <1881-1966> (Luitzen Egbertus Jan) Husserl, Edmund <1859-1938> Brouwer, Luitzen E. J. 1881-1966 Husserl, Edmund 1859-1938 Phänomenologie - Wahlfolge Intuitionistic mathematics Phenomenology Sequences (Mathematics) Phänomenologie Ontologie Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014865978&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT attenmarkvan brouwermeetshusserlonthephenomenologyofchoicesequences |