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|Additional Physical Format:||Print version:
Brouwer, L.E.J. (Luitzen Egbertus Jan), 1881-1966.
Amsterdam : North-Holland Pub. Co. ; New York : American Elsevier Pub. Co., 1975-1976
|Material Type:||Document, Internet resource|
|Document Type:||Internet Resource, Computer File|
|All Authors / Contributors:||
L E J Brouwer; A Heyting
|ISBN:||9781483278155 1483278158 0720420768 9780720420760|
|Description:||1 online resource (645 pages)|
|Contents:||Front Cover; Philosophy and Foundations of Mathematics; Copyright Page; Table of Contents; BIBLIOGRAPHY; INTRODUCTION; 1905. LIFE, ART AND MYSTICISM; THE SAD WORLD; TURNING INTO THE SELF; MAN'S FALL CAUSED BY THE INTELLECT; RECONCILIATION; LANGUAGE; IMMANENT TRUTH; TRANSCENDENT TRUTH; LIBERATED LIFE; ECONOMY; OVER DE GRONDSLAGEN DER WISKUNDE; 1907. ON THE FOUNDATIONS OF MATHEMATICS; CHAPTER I. THE CONSTRUCTION OF MATHEMATICS; Arithmetic of inteqers; Negative numbers; Rational numbers; Irrational numbers; The continuum; The measurable continuum. Definition of addition on the continuum in terms of a groupDefinition ofmultiplication on the continuum in terms of a group; Taking the inverse. The projective group; Projective geometry; Cartesian geometry; Euclidean geometry; The similarity group; The group of complex operations; Group of complex projective transformations; Characterization oj' the projective group; The non-Euclidean groups; Deduction of the differential of the arc for the Euclidean and the non-Euclidean groups; Characterization of the Euclidean and non-Euclidean groups by HELMHOLTZ. Correction of HELMHOLTZ' characterization by LIECharacterization of the linear system of the Cartesian or Euclidean and of the hyperbolic space; Variational problems leading to linear systems; Thus he looks for minimal curves of the integral; The possible pointsets; Solution of the continuum problem; Non-Archimedean uniform groups on the one-dimensional continuum; Non-Archimedean and non-Pascalian geometries; Semi-congruent groups in non-Archimedean geometry; CHAPTER II. MATHEMATICS AND EXPERIENCE; The intellect and the jump from the end to the means. Mathematical systems, containing more than given realityExtension of applicability of mathematics by actual intervention; Extension by induction from the real to the possible; Continuity of functions in physics; Differentiability of physical functions; Principles of mechanics; Mechanical interpretations of nature; Value of the 'explanation' of phenomena; Problems of space and time; Objectivity; Apriority; Russell's point of view; Summary of the relation between mathematics and experience; CHAPTER III. MATHEMATICS AND LOGIC; Mathematics is independent of logic; Logic depends upon mathematics. The denumerably unfinished setsThe continuum problem; The well-orderinq of an arbitrary set; The transfinite exponentiation; The contradiction; The logic of relations; Infinite numbers; Conclusions on logistics; Consistency proofs for formal systems, independent of their interpretation; Attempt to make these proofs independent of intuition; Enumeration of the stages which are confused in the logical treatment of mathematics; STATEMENTS; 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.|
|Responsibility:||L.E.J. Brouwer ; edited by A. Heyting.|