Lakatos' philosophy of mathematics: a historical approach
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
North-Holland
1991
|
| Schriftenreihe: | Studies in the history and philosophy of mathematics
3 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. [295] - 308 |
| Beschreibung: | XI, 312 S. graph. Darst. |
| ISBN: | 0444889442 |
Internformat
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| 245 | 1 | 0 | |a Lakatos' philosophy of mathematics |b a historical approach |c Teun Koetsier |
| 264 | 1 | |a Amsterdam [u.a.] |b North-Holland |c 1991 | |
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| 490 | 1 | |a Studies in the history and philosophy of mathematics |v 3 | |
| 500 | |a Literaturverz. S. [295] - 308 | ||
| 600 | 1 | 4 | |a Lakatos, Imre <1922-1974> |
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| 650 | 4 | |a Mathématiques - Philosophie | |
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| 650 | 4 | |a Geschichte | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Philosophie | |
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| 650 | 4 | |a Mathematics |x Philosophy | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Introduction 1
Chapter I On two Lakatosian reconstructions of
developments in mathematics
1.1 Introductory remarks: fallibility and rationality 9
1.1.1 Lakatos s f allibilist philosophy of mathematics 9
1.1.2 Rational (reconstructions: some definitions 11
1.1.3 A remark on Lakatos s view of methodology 16
1.2 An example of a rational reconstruction 17
1.2.1 Pythagoras theorem 17
1.2.2 Some further remarks on Rules 1,2 and 3 20
1.3 Lakatos s reconstruction of the history of Euler s formula
for polyhedra 22
1.3.1 The methodology of proofs and refutations 22
1.3.2 A summary of Lakatos s reconstruction 24
1.3.3 The real history 30
1.3.4 Evaluation in terms of the rationality thesis 42
1.3.5 Strong fallibility or weak fallibility? 45
1.4 Uniform convergence: a second Lakatosian reconstruction
on the basis of the methodology of proofs and refutations 50
1.4.1 A survey of the relevant events 50
1.4.2 Lakatos s reconstruction 53
1.4.3 A different interpretation of the events 55
1.4.4 Conclusion 56
Chapter II The Methodology of Scientific Research
Programmes
n.l Mathematics as quasi empirical science 59
n.2 Some problems 62
n.3 The Methodology of Scientific Research Programmes 64
n.4 The applicability of the MSRP to mathematics 66
n.5 The fallibility thesis and the rationality thesis 70
viii Koetsier
Chapter III Cauchy and the continuum
ELI Introduction 73
m.2 Lakatos s views on Cauchy s mathematics 74
m.3 Interpreting Cauchy 77
m.3.1 Cauchy s 1821 text 77
III.3.2 Lakatos s non standard interpretation of the 1821 proof
versus a standard interpretation 81
m.3.3 Cauchy s 1853 text 82
111.3.4 A standard interpretation of the 1853 text 84
111.3.5 A non standard interpretation of the 1853 text 87
in.3.6 An argument in favour of a standard interpretation 87
m.4 Concluding remarks 92
Chapter IV A meta methodological intermezzo
IV.l Spalt s Vom Mythos der Mathematischen Vernunft 93
IV.2 The first circularity problem: concerning the identification of
competing units 95
IV.3 The second circularity problem: concerning criteria
of acceptance or rejection 99
IV.4 Objections to the solution 102
IV.5 My proposal 105
IV.6 Conclusion 107
Chapter V Two reconstructions of developments in
mathematics by means of the Methodology of
Scientific Research Programmes
V.I Introduction 109
V.2 The development of Archimedes s work 110
V.2.1 Archimedes s method of mechanical theorems 113
V.2.2 The lever principle 111
V.2.3 The Method 113
V.2.4 The mechanical proof in The Quadrature of the Parabola 115
V.2.5 The geometrical proof in The Quadrature of the Parabola 117
V.2.6 The importance of The Method 119
V.3 Giorello s views of Archimedes s work 122
Contents ix
V.3.1 Archimedes s research programme 122
V.3.2 The need to modify Lakatos s MSRP 124
V.4 Riemann 126
V.4.1 Introduction 126
V.4.2 The problem of how to deal globally with a particular function
the input from physics 127
V.4.3 Conformal mappings 129
V.4.4 Potential theory 130
V.4.5 Riemann surfaces and cross cuts 132
V.4.6 Klein s hypothesis 136
V.4.7 The hypothesis of Brill and Noether 141
V.5 Giorello s views of Riemann 143
V.5.1 Three heuristic principles 143
V.5.2 A critique of Giorello s reconstruction 145
V.6 Concluding remarks 147
Chapter VI Outline of a Methodology of Mathematical
Research Traditions
VI. 1 Research traditions 151
VI.2 Examples of traditions 153
VI.3 Research projects 154
VI.4 Progress and rationality in mathematics 155
VI.5 Some problems 161
VI.6 About the next two chapters 173
Chapter VII Two research traditions in Greek mathematics
VII.1 A thesis of Lakatos 175
VII.2 Lakatos s thesis is to a large extent correct 176
VII.3 Two phases in Greek pre Euclidean mathematics 180
VII.4 Van Hide s levels of thinking 182
VII.5 Two traditions in Greek mathematics 184
Vn.6 The transition in terms of the methodology of mathematical
research traditions 191
Vn.7 Conclusion 197
x Koetsier
Chapter VIII Two research traditions in analysis
Vm.1 Introduction 199
Vni.1.1 Eighteenth century analysis versus nineteenth
century analysis 199
VIII. 1.2 A Kuhnian proposal and its dismissal 200
Vm.2 The Formalist Tradition 203
V1II.2.1 The object of eighteenth century analysis 203
Vm.2.2 The inductive character of eighteenth century analysis 204
VIII.2.3 The principle of the generality of algebra 206
VIII.3 Problems that vexed the eighteenth century tradition 210
Vm.4 The 19th century Conceptual Tradition in analysis 214
VIII.4.1 The object of nineteenth century analysis 214
VHI.4.2 The methods of nineteeth century analysis 216
Vin.4.3 Cauchy and continuity 218
Vin.5 The transition from the Formalist Tradition
to the Conceptual Tradition 219
Vin.5.1 Cauchy s rejection of the generality of algebra 219
VIIL5.2 The competition between the two research traditions 222
VIII.6 Conclusion 226
Chapter IX The history of the interchangeability
theorem for partial differentiation from
Nicolaus I. Bernoulli to Schwarz
IX. 1 Introduction 227
DC.2 The interchangeability theorem in the eighteenth century 228
IX.2.1 Nicolaus I Bernoulli 228
IX.2.2 Euler and the transition to the Formalist Transition 231
IX.2.3 Fontaine s fluxio differential calculus 234
IX.2.4 Fontaine s formalist calculus 239
IX.2.5 Clairaut on the interchangeability theorem 242
IX.2.6 Lagrange 244
IX.2.7 Concluding remarks on the eighteenth century
versions of the theorem 248
K.3 The nineteenth century Conceptual Tradition in analysis 250
IX.3.1 Cauchy 250
DC.3.2 Blanchet fills the gap in Cauchy s proof 255
Contents xi
DC.3.3 Two other nineteenth century French proofs of the theorem 257
K.3.4 Schlomilch und Lindelof 260
IX.3.5 Schwarz: The conditions become subject of investigation 268
IX.4 Conclusion 272
Chapter X Some concluding remarks
X. 1 The rationality of mathematics 275
X.2 Fallibility and continuity 277
X.2.1 The fallibility of mathematics in general 277
X.2.2 The fallibility of twentieth century mathematics 280
X.3 The tradition independent subject matter of mathematics 283
X.3.1 Mathematical facts 283
X.3.2 Mathematics is not a natural science 286
X.3.3 A tentative global characterization of mathematics 288
Bibliography 295
Index 309
|
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| discipline | Mathematik Philosophie |
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| indexdate | 2024-07-09T16:16:46Z |
| institution | BVB |
| isbn | 0444889442 |
| language | English |
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| series2 | Studies in the history and philosophy of mathematics |
| spelling | Koetsier, Teun 1946- Verfasser (DE-588)139037896 aut Lakatos' philosophy of mathematics a historical approach Teun Koetsier Amsterdam [u.a.] North-Holland 1991 XI, 312 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Studies in the history and philosophy of mathematics 3 Literaturverz. S. [295] - 308 Lakatos, Imre <1922-1974> Lakatos, Imre Lakatos, Imre 1922-1974 (DE-588)118568817 gnd rswk-swf Filosofie van de wiskunde gtt Mathématiques - Histoire Mathématiques - Histoire ram Mathématiques - Philosophie Mathématiques - Philosophie ram Geschichte Mathematik Philosophie Mathematics History Mathematics Philosophy Mathematik (DE-588)4037944-9 gnd rswk-swf Philosophie (DE-588)4045791-6 gnd rswk-swf Lakatos, Imre 1922-1974 (DE-588)118568817 p Mathematik (DE-588)4037944-9 s Philosophie (DE-588)4045791-6 s DE-604 Studies in the history and philosophy of mathematics 3 (DE-604)BV004415113 3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002906606&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Koetsier, Teun 1946- Lakatos' philosophy of mathematics a historical approach Studies in the history and philosophy of mathematics Lakatos, Imre <1922-1974> Lakatos, Imre Lakatos, Imre 1922-1974 (DE-588)118568817 gnd Filosofie van de wiskunde gtt Mathématiques - Histoire Mathématiques - Histoire ram Mathématiques - Philosophie Mathématiques - Philosophie ram Geschichte Mathematik Philosophie Mathematics History Mathematics Philosophy Mathematik (DE-588)4037944-9 gnd Philosophie (DE-588)4045791-6 gnd |
| subject_GND | (DE-588)118568817 (DE-588)4037944-9 (DE-588)4045791-6 |
| title | Lakatos' philosophy of mathematics a historical approach |
| title_auth | Lakatos' philosophy of mathematics a historical approach |
| title_exact_search | Lakatos' philosophy of mathematics a historical approach |
| title_full | Lakatos' philosophy of mathematics a historical approach Teun Koetsier |
| title_fullStr | Lakatos' philosophy of mathematics a historical approach Teun Koetsier |
| title_full_unstemmed | Lakatos' philosophy of mathematics a historical approach Teun Koetsier |
| title_short | Lakatos' philosophy of mathematics |
| title_sort | lakatos philosophy of mathematics a historical approach |
| title_sub | a historical approach |
| topic | Lakatos, Imre <1922-1974> Lakatos, Imre Lakatos, Imre 1922-1974 (DE-588)118568817 gnd Filosofie van de wiskunde gtt Mathématiques - Histoire Mathématiques - Histoire ram Mathématiques - Philosophie Mathématiques - Philosophie ram Geschichte Mathematik Philosophie Mathematics History Mathematics Philosophy Mathematik (DE-588)4037944-9 gnd Philosophie (DE-588)4045791-6 gnd |
| topic_facet | Lakatos, Imre <1922-1974> Lakatos, Imre Lakatos, Imre 1922-1974 Filosofie van de wiskunde Mathématiques - Histoire Mathématiques - Philosophie Geschichte Mathematik Philosophie Mathematics History Mathematics Philosophy |
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