Brouwer's intuitionism:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
North-Holland Publ.
1990
|
| Schriftenreihe: | Studies in the history and philosophy of mathematics
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. [507] - 516 |
| Beschreibung: | XXVI, 530 S. |
| ISBN: | 0444883843 |
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Datensatz im Suchindex
| _version_ | 1804128287697403904 |
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| adam_text | Titel: Brouwer s Intuitionism
Autor: Stigt, Walter P. van
Jahr: 1990
CONTENTS Preface Acknowledgements References Chapter I. The Brouwer Bibliography 1.1 Publications 2 1.2 Unpublished Papers 16 Chapter II. Brouwer, Life and Work 2.1 Childhood and Student-years 21 2.2 Post-graduate Study 28 2.3 Life, Art and Mysticism [1905] 31 2.4 The Foundations of Mathematics 35 2.4.1 Chapter One - The Construction of Mathematics 37 2.4.2 Chapter Two - Mathematics and Experience 39 2.4.3 Korteweg’s Rejection 40 2.4.4 Chapter Three - Mathematics and Logic 43 2.5 Towards an Academic Career 45 2.5.1 The Unreliability of the Logical Principles [1908C] 46 2.5.2 The Rome Conference 1908 47 2.5.3 Topological Activity 1908-1912 49 2.5.4 The Nature of Geometry [1909A] 49 2.5.5 Zur Analysis Situs 51 2.5.6 The New Methods and the Invariance of Dimension 53 2.5.7 International Recognition 55 2.5.8 Professor L.E.J. Brouwer, 14 October 1912 57 2.6 Intuitionism and Formalism 61 2.6.1 Intuitionist Set Theory 62 2.7 The Signific Interlude 65 2.8 The Second Act of Intuitionism 71 2.8.1 The Foundations of Set Theory Part I 71 2.8.2 The Foundations of Set Theory Part II 75
CONTENTS XXII 2.8.3 The New Foundation Crisis 75 2.9 The Turbulent Years 77 2.9.1 Signific and Political Campaigns 77 2.9.2 Gottingen and Berlin Calls 80 2.9.3 The Intuitionist ‘Putsch’ 82 2.10 The Brouwer Logic 85 2.10.1 The Principle of the Excluded Middle - 1923 85 2.10.2 The Calculus of Absurdities 87 2.10.3 La Logique Brouwerienne 88 2.11 The Reconstruction of Analysis 90 2.11.1 The Continuity Arguments 91 2.12 The Unfinished Books 93 2.12.1 Reelle Funktionen 93 2.12.2 Die Berliner Gastvorlesungen 94 2.13 The Brouwer-Hilbert Controversy and the Annalen Affair 99 2.14 The Silent Years 103 2.15 Post-war Lectures and Final Years 107 Chapter III. Brouwer’s Philosophy 3.1 Introduction 111 3.2 Character and Early Background 112 3.3 Philosophy, Metaphysics and Ideology 115 3.4 Mysticism 119 3.5 God and the Moral Principle 122 3.6 Kant and the French Intuitionist Tradition 127 3.7 French Mathematical Intuitionism 132 3.8 The Self, Consciousness and Mind 135 3.9 Causal Attention, Will and Cunning Activity 141 3.10 The Phase of Social Acting and Language 144 Chapter IV. Brouwer’s Philosophy of Mathematics 4.1 The Primordial Intuition of Time 147 4.1.1 Introduction 147 4.1.2 Genesis of the Concept and Definitions 148 4.1.3 Brouwer’s Primordial Intuition of Mathematics 150 4.1.4 The Discrete and the Continuous in the Primordial Intuition 153
CONTENTS XXIII 4.2 Intuitive Thinking and Mathematics 157 4.3 The Nature of Mathematics 159 4.4 Reflection on the Nature of Mathematics 162 4.5 Constructiveness and Existence 164 4.5.1 Brouwer Construction 164 4.5.2 Classification of Constructions 165 4.5.3 Distinctive Features of Mathematical Constructive Thinking 168 4.6 The Subject and the Intersubjectivity of Mathematics 171 4.6.1 Brouwer’s Idealism 171 4.6.2 The Idealized Subject 172 4.6.3 Mathematics, the Life of the Idealized Free Subject 174 4.6.4 Objectivity and Inter-subjectivity 180 4.7 The Application of mathematics 182 4.7.1 Brouwer’s Critique of Scientific Practice 184 4.7.2 The Ideal Nature of Science 185 4.7.3 The Process of Application and its Mathematical Truth 188 Chapter V. Language and Logic 5.1 Society and Communication 193 5.2 The Purpose and Origin of Language 196 5.3 Language and Pure Thought 199 5.4 The Programme of Reform 201 5.5 Brouwerian Semantic Theory 203 5.5.1 The Privacy of Language 203 5.5.2 The Instability of Language 204 5.5.3 Words, Sentences and Truth 211 5.6 Brouwer’s Analysis of Mathematical and Linguistic Activity 213 5.6.1 The Language of Mathematics 215 5.6.2 The Language of Logical Reasoning 220 5.7 Brouwers’s Analysis of Logic 224 5.7.1 Logic, the Science of Reasoning 224 5.7.2 Pure Logic as Science and Abstraction 225 5.7.3 The Application of Logical Principles 230 5.8 Brouwer Negation 238 5.8.1 Brouwer’s Constructive Notion of Negation 239
XXIV CONTENTS 5.8.2 Absurdity as Impossibility of‘Fitting-in’ 240 5.8.3 Constructed Impossibility 242 5.8.4 Mathematical Absurdity and Other Notions of Negation 244 5.9 The Refutation of the PEM 247 5.9.1 The Unreliability of the PEM, 1908 248 5.9.2 Mathematics Without the PEM, 1917 250 5.9.3 Brouwer’s Counterexamples 252 5.9.4 The Contradictority of the PEM 255 5.10 Logical Negation and the‘Brouwer Logic’ 257 5.10.1 The Calculus of Absurdities 257 5.10.2 Logical Necessity and Truth 260 5.10.3 Logical Absurdity 262 5.10.4 Non-contradictority and Absurdity-of-absurdity 265 5.11 The Crisis in Brouwer’s Intuitionism 270 5.11.1 The Use of Language and Logic in Brouwer’s Reconstruction of Mathematics 271 5.11.2 The Pragmatism of Post-Brouwer Intuitionism 274 5.12 The Formalization of Mathematics 279 5.12.1 The ‘Formalist’ Schools and Formal Axiomatic Theory 279 5.12.2 The Formalization of Intuitionist Mathematics 285 5.12.3 Heyting’s Formalization of Intuitionist Logic 288 Selected Contributions to the Formalization of Intuitionist Logic and Mathematics 293 Chapter VI. Brouwer’s Intuitionist Mathenlatics 6.1 Introduction 295 6.2 Brouwerian Separable Mathematics 300 6.2.1 The Primordial Intuition as Set-construction 301 6.2.2 The Fundamental Sequence 305 6.2.2.1 The Order-type n 306 6.2.2.2 The Order-type to 309 6.2.2.3 Brouwer’s Generalization of the Concept Sequence 309 6.2.3 Cardinality 312 6.2.4 Systems and Operations of Separable Mathematics 314 6.2.4.1 The Operations on Ordinal Numbers 314 6.2.4.2 The Integers 315
CONTENTS XXV 6.2.4.3 Rationals and the Order-type q 316 6.3 The Brouwer Mathematical Continuum 318 6.3.1 Introduction 318 6.3.2 The Genesis and Nature of the Intuitive Continuum 323 6.3.2.1 The Construction of Intervals 325 63.22 Relations and Ordering of Intervals 326 6.3.3 Point-sets on the Continuum and the ‘Made-measurable Continuum’ (pre-1917) 328 6.3.3.1 The‘Made-measurable Continuum’ 328 6.3.3.2 Point on the Continuum 330 6.3.3.3 Sets of Constructed Points 332 6.3.3.4 Denumerably-unfinished Systems and Definable Points 333 6.3.4 The New Set-theory 1917 334 6.3.5 Mathematical Species 335 6.3.6 The Genesis of Species 337 6.3.7 The Hierarchy of Species 340 6.3.8 The Theory of Species 345 6.3.8.1 Union and Intersection of Species 346 6.3.8.2 The Empty Species 347 6.3.8.3 Relations between Species 347 6.3.8.4 Difference, Deviation and Apartness 348 6.3.8.5 Congruence and Agreement 351 6.3.9 The Complementarity of Species 352 6.3.10 Spreads and Choice-sequences 357 6.3.11 Real Elements of the Continuum 361 6.3.11.1 Interval 362 6.3.11.2 Real Point or Real Number 362 6.3.11.3 Law and Choice 363 6.3.11.4 Species of Coincident Points or Point-cores 364 6.3.11.5 Point-set or Point-spread 366 6.3.11.6 Fundamental Sequences of Intervals and Finite Point-spreads 369 6.3.12 The General Spread Concept 370 6.3.13 Continuity and Uniform Continuity of Spread Functions 378 6.3.13.1 Finite Spreads 378 6.3.13.2 The Brouwer Continuity Hypothesis or the Fundamental Hypothesis for Real Functions 379
XXVI CONTENTS 6.3.13.3 The Fundamental Theorem of Finite Spreads 381 6.3.13.4 The Uniform-Continuity Theorem 384 Appendices 1 Profession of Faith of L.E.J. Brouwer [BMS 1 A] (Dutch original and English translation) 387 2 Student Notebook [BMS IB] (Dutch original and English translation) 394 3 The Rejected Parts of Brouwer’s Dissertation [BMS 3B] 405 4 Intuitive Signifies [BMS 22B] (Dutch original and English translation) 416 5 Will, Knowledge and Speech (English translation of BR[ 1933]) 418 6 Short Retrospective Notes on the Course “Intuitionist Mathematicsâ€
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| series | Studies in the history and philosophy of mathematics |
| series2 | Studies in the history and philosophy of mathematics |
| spelling | Stigt, Walter P. van Verfasser aut Brouwer's intuitionism Walter P. van Stigt Amsterdam [u.a.] North-Holland Publ. 1990 XXVI, 530 S. txt rdacontent n rdamedia nc rdacarrier Studies in the history and philosophy of mathematics 2 Literaturverz. S. [507] - 516 Brouwer, L. E. J - (Luitzen Egbertus Jan) Brouwer, L. E. J <1881-1966> - (Luitzen Egbertus Jan) Brouwer, L. E. J <1881-1966> (Luitzen Egbertus Jan) Brouwer, Luitzen E. J. 1881-1966 (DE-588)118988131 gnd rswk-swf Intuïtionisme gtt Mathématiciens - Pays-Bas - Biographies Mathématiques - Philosophie Mathematik Philosophie Intuitionistic mathematics Mathematicians Netherlands Biography Mathematics Philosophy Mathematik (DE-588)4037944-9 gnd rswk-swf Philosophie (DE-588)4045791-6 gnd rswk-swf Intuitionistische Mathematik (DE-588)4162200-5 gnd rswk-swf Niederlande (DE-588)4006432-3 Bibliografie gnd-content (DE-588)4006804-3 Biografie gnd-content Mathematik (DE-588)4037944-9 s Philosophie (DE-588)4045791-6 s DE-604 Brouwer, Luitzen E. J. 1881-1966 (DE-588)118988131 p Intuitionistische Mathematik (DE-588)4162200-5 s DE-188 Studies in the history and philosophy of mathematics 2 (DE-604)BV004415113 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009212627&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stigt, Walter P. van Brouwer's intuitionism Studies in the history and philosophy of mathematics Brouwer, L. E. J - (Luitzen Egbertus Jan) Brouwer, L. E. J <1881-1966> - (Luitzen Egbertus Jan) Brouwer, L. E. J <1881-1966> (Luitzen Egbertus Jan) Brouwer, Luitzen E. J. 1881-1966 (DE-588)118988131 gnd Intuïtionisme gtt Mathématiciens - Pays-Bas - Biographies Mathématiques - Philosophie Mathematik Philosophie Intuitionistic mathematics Mathematicians Netherlands Biography Mathematics Philosophy Mathematik (DE-588)4037944-9 gnd Philosophie (DE-588)4045791-6 gnd Intuitionistische Mathematik (DE-588)4162200-5 gnd |
| subject_GND | (DE-588)118988131 (DE-588)4037944-9 (DE-588)4045791-6 (DE-588)4162200-5 (DE-588)4006432-3 (DE-588)4006804-3 |
| title | Brouwer's intuitionism |
| title_auth | Brouwer's intuitionism |
| title_exact_search | Brouwer's intuitionism |
| title_full | Brouwer's intuitionism Walter P. van Stigt |
| title_fullStr | Brouwer's intuitionism Walter P. van Stigt |
| title_full_unstemmed | Brouwer's intuitionism Walter P. van Stigt |
| title_short | Brouwer's intuitionism |
| title_sort | brouwer s intuitionism |
| topic | Brouwer, L. E. J - (Luitzen Egbertus Jan) Brouwer, L. E. J <1881-1966> - (Luitzen Egbertus Jan) Brouwer, L. E. J <1881-1966> (Luitzen Egbertus Jan) Brouwer, Luitzen E. J. 1881-1966 (DE-588)118988131 gnd Intuïtionisme gtt Mathématiciens - Pays-Bas - Biographies Mathématiques - Philosophie Mathematik Philosophie Intuitionistic mathematics Mathematicians Netherlands Biography Mathematics Philosophy Mathematik (DE-588)4037944-9 gnd Philosophie (DE-588)4045791-6 gnd Intuitionistische Mathematik (DE-588)4162200-5 gnd |
| topic_facet | Brouwer, L. E. J - (Luitzen Egbertus Jan) Brouwer, L. E. J <1881-1966> - (Luitzen Egbertus Jan) Brouwer, L. E. J <1881-1966> (Luitzen Egbertus Jan) Brouwer, Luitzen E. J. 1881-1966 Intuïtionisme Mathématiciens - Pays-Bas - Biographies Mathématiques - Philosophie Mathematik Philosophie Intuitionistic mathematics Mathematicians Netherlands Biography Mathematics Philosophy Intuitionistische Mathematik Niederlande Bibliografie Biografie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009212627&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004415113 |
| work_keys_str_mv | AT stigtwalterpvan brouwersintuitionism |