Bolzano's philosophy and the emergence of modern mathematics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
Rodopi
2000
|
| Schriftenreihe: | Studien zur österreichischen Philosophie
30 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 218 S. graph. Darst. |
| ISBN: | 9042015012 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804128137068412928 |
|---|---|
| adam_text | Titel: Bolzano s philosophy and the emergence of modern mathematics
Autor: Rusnock, Paul
Jahr: 2000
Contents
Acknowledgements....................... 1
Conventions........................... 2
Preface.............................. 3
Biographical sketch....................... 6
Introduction 14
The methodology of the Contributions 31
2.1 Introduction........................ 31
2.2 Motivation......................... 31
2.3 Definition and division of mathematics.......... 32
2.4 The logic of the Contributions.............. 33
2.4.1 Elements..................... 34
2.4.2 An intrinsic order................. 39
2.4.3 Indefinablesandindemonstrables: epistemolog-
ical considerations................ 41
2.5 Bolzano and Kant..................... 45
2.6 Conclusion........................ 50
Early work in real analysis 56
3.1 Introduction......................... 56
3.2 Infinite series: the binomial theorem........... 57
3.2.1 A sketch of Bolzano s proof for n not a positive
integer ...................... 64
3.3 The Purely Analytic Proof ............... 69
3.3.1 The proof..................... 73
3.4 Historical remarks: Bolzano s influence......... 84
3.5 Conclusion ........................ 86
Logic and methodology in the Theory of Science 88
4.1 Introduction........................ 88
4.1.1 Theory of Science: definition and organization . 90
4.2 Logical objects; propositions and terms ......... 93
4.2.1 Introduction .................... 93
4.2.2 Historical remarks: Aristotelian logic and some
early modern counterparts............94
4.2.3 Bolzano on logical objects............107
4.2.4 Propositions and ideas..............115
4.3 Bolzano s Logic of Variation...............127
4.3.1 Variation.....................127
4.3.2 Conceptual and logical form...........130
4.3.3 Some important relations in Bolzano s logic of
variation .....................140
4.4 Conclusion........................153
5 Later mathematical studies 158
5.1 Introduction........................158
5.2 Extracts from the Function Theory............159
5.2.1 Continuity ....................161
5.2.2 Three big theorems................163
5.2.3 Uniform continuity................166
5.2.4 Local maxima and minima; monotonicity and
continuity.....................173
5.3 The theory of measurable numbers............177
5.3.1 Equivalent number concepts...........184
5.3.2 Repairing the theory of measurable numbers . . 184
5.3.3 Bolzano s second proof of the Bolzano-Cauchy
theorem......................186
5.4 The paradoxes of the infinite...............188
5.5 Conclusion........................196
A On Kantian Intuitions 198
B The Bolzano-Cauchy Theorem 205
Selected Bibliography......................211
Index of Names.........................213
Index of Subjects........................215
|
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| discipline | Mathematik Philosophie Theologie / Religionswissenschaften |
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| indexdate | 2024-07-09T18:44:27Z |
| institution | BVB |
| isbn | 9042015012 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009112470 |
| oclc_num | 45109138 |
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| physical | 218 S. graph. Darst. |
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| series | Studien zur österreichischen Philosophie |
| series2 | Studien zur österreichischen Philosophie |
| spelling | Rusnock, Paul Verfasser aut Bolzano's philosophy and the emergence of modern mathematics Paul Rusnock Amsterdam [u.a.] Rodopi 2000 218 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Studien zur österreichischen Philosophie 30 Bolzano, Bernard <1781-1848> Bolzano, Bernard 1781-1848 (DE-588)118513117 gnd rswk-swf Filosofie gtt Wiskunde gtt Mathematik Philosophie Mathematics Philosophy Mathematik (DE-588)4037944-9 gnd rswk-swf Philosophie (DE-588)4045791-6 gnd rswk-swf Bolzano, Bernard 1781-1848 (DE-588)118513117 p Mathematik (DE-588)4037944-9 s DE-604 Philosophie (DE-588)4045791-6 s Studien zur österreichischen Philosophie 30 (DE-604)BV000003842 30 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009112470&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rusnock, Paul Bolzano's philosophy and the emergence of modern mathematics Studien zur österreichischen Philosophie Bolzano, Bernard <1781-1848> Bolzano, Bernard 1781-1848 (DE-588)118513117 gnd Filosofie gtt Wiskunde gtt Mathematik Philosophie Mathematics Philosophy Mathematik (DE-588)4037944-9 gnd Philosophie (DE-588)4045791-6 gnd |
| subject_GND | (DE-588)118513117 (DE-588)4037944-9 (DE-588)4045791-6 |
| title | Bolzano's philosophy and the emergence of modern mathematics |
| title_auth | Bolzano's philosophy and the emergence of modern mathematics |
| title_exact_search | Bolzano's philosophy and the emergence of modern mathematics |
| title_full | Bolzano's philosophy and the emergence of modern mathematics Paul Rusnock |
| title_fullStr | Bolzano's philosophy and the emergence of modern mathematics Paul Rusnock |
| title_full_unstemmed | Bolzano's philosophy and the emergence of modern mathematics Paul Rusnock |
| title_short | Bolzano's philosophy and the emergence of modern mathematics |
| title_sort | bolzano s philosophy and the emergence of modern mathematics |
| topic | Bolzano, Bernard <1781-1848> Bolzano, Bernard 1781-1848 (DE-588)118513117 gnd Filosofie gtt Wiskunde gtt Mathematik Philosophie Mathematics Philosophy Mathematik (DE-588)4037944-9 gnd Philosophie (DE-588)4045791-6 gnd |
| topic_facet | Bolzano, Bernard <1781-1848> Bolzano, Bernard 1781-1848 Filosofie Wiskunde Mathematik Philosophie Mathematics Philosophy |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009112470&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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