Philosophy and Foundations of Mathematics
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Philosophy and Foundations of Mathematics

L. E. J. Brouwer

  1. 644 pages
  2. English
  3. PDF
  4. Only available on web
eBook - PDF

Philosophy and Foundations of Mathematics

L. E. J. Brouwer

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About This Book

L.E.J. Brouwer: Collected Works, Volume 1: Philosophy and Foundations of Mathematics focuses on the principles, operations, and approaches promoted by Brouwer in studying the philosophy and foundations of mathematics. The publication first ponders on the construction of mathematics. Topics include arithmetic of integers, negative numbers, measurable continuum, irrational numbers, Cartesian geometry, similarity group, characterization of the linear system of the Cartesian or Euclidean and hyperbolic space, and non-Archimedean uniform groups on the one-dimensional continuum. The book then examines mathematics and experience and mathematics and logic. Topics include denumerably unfinished sets, continuum problem, logic of relations, consistency proofs for formal systems independent of their interpretation, infinite numbers, and problems of space and time. The text is a valuable reference for students, mathematicians, and researchers interested in the contributions of Brouwer in the studies on the philosophy and foundations of mathematics.

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Information

Publisher
North Holland
Year
2014
ISBN
9781483278155
Topic
Mathematics
Subtopic
Logic in Mathematics
Index
Mathematics

Table of contents

  1. Front Cover
  2. Philosophy and Foundations of Mathematics
  3. Copyright Page
  4. Table of Contents
  5. BIBLIOGRAPHY
  6. INTRODUCTION
  7. 1905. LIFE, ART AND MYSTICISM
  8. OVER DE GRONDSLAGEN DER WISKUNDE
  9. 1907. ON THE FOUNDATIONS OF MATHEMATICS
  10. 1908 A. DIE MOE GLIO HEN MAEORTIGKEITEN
  11. 1908 B. ON THE FOUNDATIONS OF MATHEMATICS
  12. 1908 C. THE UNRELIABILITY OF THE LOGICAL PRINCIPLES
  13. 1909. THE NATURE OF GEOMETRY
  14. 1911. FROM THE REVIEW OF: G. MANNOURY, METHODOLOGISCHES UND PHILOSOPHISCHES ZUR ELEMENTARMATHEMATIK (HAARLEM 1909)
  15. 1912 A. INTUITIONISM AND FORMALISM
  16. 1913. INTUITIONISM AND FORMALISM
  17. 1914. A. Schoenflies und H. Hahn, Die Entwickelung der M:engenlehre und ihrer Anwendungen
  18. 1917. ADDENDA AND CORRIGENDA TO 'ON THE FOUNDATIONS OF MATHEMATICS'1)
  19. 1918 B. Begrfmdung der Mengenlehre unabhangig vom logischen Satz vom ausgeschlosseneu Dritten
  20. 1919 A. Beg'rundllng del' Mengenlehre unabhangig vom logischen Satz vorn ausgeschlossenen Dritten
  21. 1919 C. SIGNIFISCHE SPRACHFORSCHUNG
  22. 1919 D. Mathematic's
  23. 1921. Mathematics
  24. 1923 A. BEGRÜNDUNG DER FUNKTIONENLEHRE UNABHÄNGIG YOM LOGISCHEN SATZ VOM AUSGESCHLOSSENEN DRITTEN
  25. 1923 B Über die Bedeutung des Satzes vom ausgeschlossenen Dritten in der Mathematik, insbesondere in der Funktionentheorie 1)
  26. 1923 C. Intuitionistische Zerlegung mathematischer Gmndbegrifle.1)
  27. 1924 A. Mathematics — ,,Ueber die Zulassunq unendllcher Werte fĂŒr (len Funktionsbeqriff:"
  28. 1924 B. Mathematics — "Perfect sets of points with positively-irrational distances"
  29. 1924 C. Mathematics — "Intuitionistisclier Beuieis lies Fundamentaisatses der Algebra"
  30. 1924 D. Mathematics — "Beioeis, dass jede volle Funktiou qleicluntissiq stetig ist",
  31. 1924 E. Mathematics — "Lntultionistische ErgĂ€nzunq des Fundomentalsatzes der Alqebra"
  32. 1924 F. Zur intnitionistischen Zerlegnng mathematischer Grundbegriffe.1)
  33. 1924 G. Mathematics
  34. 1925 A. Zur Begrtlndung der intnitionistischen Mathematik1)
  35. 1925 B. Mathematics
  36. 1926 A. Zur Begriindung der intnitionistischen Mathematik. II
  37. 1926 B. Mathematics
  38. 1926 C. Mathematics
  39. 1927 A. Znr Begriindnng der intnitionistischen Mathematik. III
  40. 1927 B. Über Definitionsbereiche von Funktionen
  41. 1927 C. Virtuelle Ordnung und unerweiterbare Ordnung
  42. 1928 A. Mathematics
  43. 1928 B. Mathematics
  44. 1929. Mathematik, Wissenschaft und Sprache
  45. 1930 A. Die Struktur des Kontinuums.
  46. 1930 B. A. Fraenkel, Zehn Vorlesungen tiber die Grundlegung der Mengenlehre
  47. 1933. VOLITION, KNOWLEDGE, LANGUAGE
  48. 1937. SIGNIFIC DIALOGUES
  49. 1939. Mathematics — Zum Triangulationsproblem
  50. 1942 A. Mathematics. - Zum freien Werden von Mengen und Funktionen
  51. 1942 B. Mathematics — Die reptiisentierende Menge det stetigen Funktionen des Einheitskontinuums
  52. 1942 C. Mathematics.— Betoeis dass det Begriff der Menge höherer Ordnung nicht als Grundbegriff det intuitionistischen Mathematik in Betracht kommt
  53. 1946 A. Synopsis of the signific movement in the Netherlands. Prospects of the signific movement
  54. 1946 B. Address delivered on September 16th, 1946, at the University of Amsterdam by Professor L. E. J. Brouwer on the conferment upon Professor G. Mannoury of the honorary degree of Doctor of Science
  55. 1947 GUIDELINES OF INTUITIONISTIC MATHEMATICS
  56. 1948 A. ESSENTIALLY NEGATIVE PROPERTIES
  57. 1948 C. CONSCIOUSNESS, PHILOSOPHY, AND MATHEMATICS
  58. 1949 A. THE NON-EQUIVALENCE OF THE CONSTRUCTIVE AND THE NEGATIVE ORDER RELATION ON THE CONTINUUM
  59. 1949 B. CONTRADICTORITY OF ELEMENTARY GEOMETRY
  60. 1950 A. LOGIQUE MATHEMATIQUE.— Remarques sur la notion d'ordre
  61. 1950 B. LOGIQUE MATHEM1\TIQUE.— Sur la possibilite d'ordonner le continu
  62. 1950 C. Discours final de M. BROUWER
  63. 1951. ON ORDER IN THE CONTINUUM, AND THE RELATION OF TRUTH TO NON-CONTRADICTORITY
  64. 1952 A. An intuitionist correction of the fixed-point* theorem on the sphere
  65. 1952 B. HISTORICAL BACKGROUND, PRINCIPLES AND METHODS OF INTUITIONISM
  66. 1952 C. ON ACCUMULATION CORES OF INFINITE CORE SPECIES
  67. 1952 D. FIXED CORES WHICH CANNOT BE FOUN'D, THOUGH THEY ARE CLAIMED TO EXIST BY CLASSICAL THEOREMS
  68. 1954 A. POINTS AND SPACES
  69. 1954 B. ADDENDA AND CORRIGENDA ON THE ROLE OF THE PRINCIPIUM TERTII EXCLUSI IN MATHEMATICS
  70. 1954 C. FURTHER ADDENDA AND CORRIGENDA ON THE ROLE OF THE PRINCIPIUM TERTII EXCLUSI IN MATHEMATICS
  71. 1954 D. ORDNUNGSWECHSEL IN BEZUG AUF EINE COUPIERBARE GESCHLOSSENE STETIGE KURVE
  72. 1954 E. INTUITIONISTIC DIFFERENTIABILITY
  73. 1954 F. AN EXAMPLE OF CONTRADICTORITY IN CLASSICAL THEORY OF FUNCTIONS
  74. 1955. THE EFFECT OF INTUTIONISM ON CLASSICAL AGEBRA OF LOGIC
  75. I. ON THE EXTENSION OF THE DOMAIN OF A FUNCTION I
  76. II. DISCONTINUOUS INTUITIONISTIC FUNCTIONS OF A REAL VARIABLE
  77. III. SYLLABUS OF A POSTHUMOUS MANUSCRIPT BASED ON THE LECTURES WHICH BROUWER GAVE AT CAMBRIDGE, ENGLAND, IN 1946
  78. NOTES
  79. LITERATURE
  80. SACHVERZEICHNIS
  81. INDEX OF SUBJECTS