Philosophy and Foundations of Mathematics
L. E. J. Brouwer
Published on 12. May 2014
644 pages
978-1-4832-7815-5 (ISBN)
Description
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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Content
Introduction1905 Leven, Kunst en Mystiek [Life, Art and Mysticism]1907 Over de Grondslagen der Wiskunde [On the Foundations of Mathematics] Chapter 1 Chapter 2 Chapter 3 Statements, Joined to the Thesis1908 A Diemoeglichen Mächtigkeiten1908 B Over de Grondslagen der Wiskunde [On the Foundations of Mathematics]1908 C De Onbetrouwbaarheid der Logische Principes [The Unreliability of the Logical Principles]1909 Het Wezen der Meetkunde [The Nature of Geometry]1911 Review of: G. Mannoury, Methodologisches und Philosophisches zur Elementar-Mathematik (Haarlem 1909)1912 A1 Intuitionisme en Formalisme1912 A2 Intuitionism and Formalism1914 Review of: A. Schoenflies und H.
