Philosophy and Foundations of Mathematics

L. E. J. Brouwer

A. Heyting

• Publisher: North Holland
• Year: 2014
• Print ISBN:
  9780720420760
• eBook ISBN:
  9781483278155
• Topic: Mathematics
• Subtopic: Logic in Mathematics
• Index: Mathematics

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.

Table of contents

• Front Cover
• Philosophy and Foundations of Mathematics
• Copyright Page
• Table of Contents
• BIBLIOGRAPHY
• INTRODUCTION
• 1905. LIFE, ART AND MYSTICISM
• OVER DE GRONDSLAGEN DER WISKUNDE
• 1907. ON THE FOUNDATIONS OF MATHEMATICS
• 1908 A. DIE MOE GLIO HEN MAEORTIGKEITEN
• 1908 B. ON THE FOUNDATIONS OF MATHEMATICS
• 1908 C. THE UNRELIABILITY OF THE LOGICAL PRINCIPLES
• 1909. THE NATURE OF GEOMETRY
• 1911. FROM THE REVIEW OF: G. MANNOURY, METHODOLOGISCHES UND PHILOSOPHISCHES ZUR ELEMENTARMATHEMATIK (HAARLEM 1909)
• 1912 A. INTUITIONISM AND FORMALISM
• 1913. INTUITIONISM AND FORMALISM
• 1914. A. Schoenflies und H. Hahn, Die Entwickelung der M:engenlehre und ihrer Anwendungen
• 1917. ADDENDA AND CORRIGENDA TO 'ON THE FOUNDATIONS OF MATHEMATICS'1)
• 1918 B. Begrfmdung der Mengenlehre unabhangig vom logischen Satz vom ausgeschlosseneu Dritten
• 1919 A. Beg'rundllng del' Mengenlehre unabhangig vom logischen Satz vorn ausgeschlossenen Dritten
• 1919 C. SIGNIFISCHE SPRACHFORSCHUNG
• 1919 D. Mathematic's
• 1921. Mathematics
• 1923 A. BEGRÜNDUNG DER FUNKTIONENLEHRE UNABHÄNGIG YOM LOGISCHEN SATZ VOM AUSGESCHLOSSENEN DRITTEN
• 1923 B Über die Bedeutung des Satzes vom ausgeschlossenen Dritten in der Mathematik, insbesondere in der Funktionentheorie 1)
• 1923 C. Intuitionistische Zerlegung mathematischer Gmndbegrifle.1)
• 1924 A. Mathematics — ,,Ueber die Zulassunq unendllcher Werte für (len Funktionsbeqriff:"
• 1924 B. Mathematics — "Perfect sets of points with positively-irrational distances"
• 1924 C. Mathematics — "Intuitionistisclier Beuieis lies Fundamentaisatses der Algebra"
• 1924 D. Mathematics — "Beioeis, dass jede volle Funktiou qleicluntissiq stetig ist",
• 1924 E. Mathematics — "Lntultionistische Ergänzunq des Fundomentalsatzes der Alqebra"
• 1924 F. Zur intnitionistischen Zerlegnng mathematischer Grundbegriffe.1)
• 1924 G. Mathematics
• 1925 A. Zur Begrtlndung der intnitionistischen Mathematik1)
• 1925 B. Mathematics
• 1926 A. Zur Begriindung der intnitionistischen Mathematik. II
• 1926 B. Mathematics
• 1926 C. Mathematics
• 1927 A. Znr Begriindnng der intnitionistischen Mathematik. III
• 1927 B. Über Definitionsbereiche von Funktionen
• 1927 C. Virtuelle Ordnung und unerweiterbare Ordnung
• 1928 A. Mathematics
• 1928 B. Mathematics
• 1929. Mathematik, Wissenschaft und Sprache
• 1930 A. Die Struktur des Kontinuums.
• 1930 B. A. Fraenkel, Zehn Vorlesungen tiber die Grundlegung der Mengenlehre
• 1933. VOLITION, KNOWLEDGE, LANGUAGE
• 1937. SIGNIFIC DIALOGUES
• 1939. Mathematics — Zum Triangulationsproblem
• 1942 A. Mathematics. - Zum freien Werden von Mengen und Funktionen
• 1942 B. Mathematics — Die reptiisentierende Menge det stetigen Funktionen des Einheitskontinuums
• 1942 C. Mathematics.— Betoeis dass det Begriff der Menge höherer Ordnung nicht als Grundbegriff det intuitionistischen Mathematik in Betracht kommt
• 1946 A. Synopsis of the signific movement in the Netherlands. Prospects of the signific movement
• 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
• 1947 GUIDELINES OF INTUITIONISTIC MATHEMATICS
• 1948 A. ESSENTIALLY NEGATIVE PROPERTIES
• 1948 C. CONSCIOUSNESS, PHILOSOPHY, AND MATHEMATICS
• 1949 A. THE NON-EQUIVALENCE OF THE CONSTRUCTIVE AND THE NEGATIVE ORDER RELATION ON THE CONTINUUM
• 1949 B. CONTRADICTORITY OF ELEMENTARY GEOMETRY
• 1950 A. LOGIQUE MATHEMATIQUE.— Remarques sur la notion d'ordre
• 1950 B. LOGIQUE MATHEM1\TIQUE.— Sur la possibilite d'ordonner le continu
• 1950 C. Discours final de M. BROUWER
• 1951. ON ORDER IN THE CONTINUUM, AND THE RELATION OF TRUTH TO NON-CONTRADICTORITY
• 1952 A. An intuitionist correction of the fixed-point* theorem on the sphere
• 1952 B. HISTORICAL BACKGROUND, PRINCIPLES AND METHODS OF INTUITIONISM
• 1952 C. ON ACCUMULATION CORES OF INFINITE CORE SPECIES
• 1952 D. FIXED CORES WHICH CANNOT BE FOUN'D, THOUGH THEY ARE CLAIMED TO EXIST BY CLASSICAL THEOREMS
• 1954 A. POINTS AND SPACES
• 1954 B. ADDENDA AND CORRIGENDA ON THE ROLE OF THE PRINCIPIUM TERTII EXCLUSI IN MATHEMATICS
• 1954 C. FURTHER ADDENDA AND CORRIGENDA ON THE ROLE OF THE PRINCIPIUM TERTII EXCLUSI IN MATHEMATICS
• 1954 D. ORDNUNGSWECHSEL IN BEZUG AUF EINE COUPIERBARE GESCHLOSSENE STETIGE KURVE
• 1954 E. INTUITIONISTIC DIFFERENTIABILITY
• 1954 F. AN EXAMPLE OF CONTRADICTORITY IN CLASSICAL THEORY OF FUNCTIONS
• 1955. THE EFFECT OF INTUTIONISM ON CLASSICAL AGEBRA OF LOGIC
• I. ON THE EXTENSION OF THE DOMAIN OF A FUNCTION I
• II. DISCONTINUOUS INTUITIONISTIC FUNCTIONS OF A REAL VARIABLE
• III. SYLLABUS OF A POSTHUMOUS MANUSCRIPT BASED ON THE LECTURES WHICH BROUWER GAVE AT CAMBRIDGE, ENGLAND, IN 1946
• NOTES
• LITERATURE
• SACHVERZEICHNIS
• INDEX OF SUBJECTS