The Continuum: A Critical Examination of the Foundation of AnalysisCourier Corporation, 01.01.1994 - 130 Seiten "The hard won power ... to assess correctly the continuum of the natural numbers grew out of titanic struggles in the realm of mathematical logic in which Hermann Weyl took a leading part." — John Archibald Wheeler Hermann Weyl (1885–1955) ranks among the most important mathematicians and physicists of this century. Though Weyl was not primarily a philosopher, his wide-ranging philosophical reflections on the formal and empirical sciences remain extremely valuable. Besides indicating clearly which results of classical analysis are invalidated by an important family of "non-circular" (predicative) theories, The Continuum wrestles with the problem of applying constructive mathematical models to cases of concrete physical and perceptual continuity. This new English edition features a personal reminiscence of Weyl written by John Archibald Wheeler. Originally published in German in 1918, the book consists of two chapters. Chapter One, entitled Set and Function, deals with property, relation and existence, the principles of the combination of judgments, logical inference, natural numbers, iteration of the mathematical process, and other topics. The main ideas are developed in this chapter in such a way that it forms a self-contained whole. In Chapter Two, The Concept of Numbers & The Continuum, Weyl systematically begins the construction of analysis and carries through its initial stages, taking up such matters as natural numbers and cardinalities, fractions and rational numbers, real numbers, continuous functions, curves and surfaces, and more. Written with Weyl's characteristic passion, lucidity, and wisdom, this advanced-level volume is a mathematical and philosophical landmark that will be welcomed by mathematicians, physicists, philosophers, and anyone interested in foundational analysis. |
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The Continuum: A Critical Examination of the Foundation of Analysis Hermann Weyl Keine Leseprobe verfügbar - 1994 |
Häufige Begriffe und Wortgruppen
1st level algebraic apply arguments arises arithmetic axioms basic categories binary domain binary relation cardinal number category natural number category of object Chapter coincide concept of set consists construction continuous functions continuum David Hilbert Dedekind defined delimited domain of rational Élie Cartan example existence express extensionally extensionally determinate extensionally equivalent finite follows formulation foundation fractions functional connection functors geometry given Hermann Weyl holds hyperanalysis immediately individual constant intuition judgment scheme k-property least n elements least upper bound logical mathematical process means number belonging number n numbers corresponding one-dimensional sets pair precisely principle of substitution principles of definition properties and relations proposition pure number theory rational numbers real number rela relation symbol relations-in-extension sense sentence matrix sequence set and function set of natural set of real set theory spans sphere of operation subject-ordered surface-points system of elements time-points tion U(xy unit interval variables vector version of analysis Weyl's