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AuthorKaufmann, Felix. author
TitleThe Infinite in Mathematics [electronic resource] : Logico-mathematical writings / by Felix Kaufmann ; edited by Brian McGuinness
ImprintDordrecht : Springer Netherlands, 1978
Connect tohttp://dx.doi.org/10.1007/978-94-009-9795-0
Descript XVII, 237 p. online resource

SUMMARY

The main item in the present volume was published in 1930 under the title Das Unendliche in der Mathematik und seine Ausschaltung. It was at that time the fullest systematic account from the standpoint of Husserl's phenomenology of what is known as 'finitism' (also as 'intuitionism' and 'constructivism') in mathematics. Since then, important changes have been required in philosophies of mathematics, in part because of Kurt Godel's epoch-making paper of 1931 which established the essential inยญ completeness of arithmetic. In the light of that finding, a number of the claims made in the book (and in the accompanying articles) are demonยญ strably mistaken. Nevertheless, as a whole it retains much of its original interest and value. It presents the issues in the foundations of mathematics that were under debate when it was written (and in some cases still are); , and it offers one alternative to the currently dominant set-theoretical definitions of the cardinal numbers and other arithmetical concepts. While still a student at the University of Vienna, Felix Kaufmann was greatly impressed by the early philosophical writings (especially by the Logische Untersuchungen) of Edmund Husser!' He was never an uncritical disciple of Husserl, and he integrated into his mature philosophy ideas from a wide assortment of intellectual sources. But he thought of himself as a phenomenologist, and made frequent use in all his major publications of many of Husserl's logical and epistemological theses


CONTENT

The Infinite in Mathematics and its Elimination (1930) -- Preface -- Analytic Table of Contents -- 1. Basic Facts of Cognition -- II. Symbolism and Axiomatics -- III. Natural Number and Set -- IV. Negative Numbers, Fractions and Irrational Numbers -- V. Set Theory -- VI. The Problem of Complete Decidability of Arithmetical Questions -- VII. The Antinomies -- Remarks on the Controversy about the Foundations of Logic and Mathematics (1931) -- Questions of Logical Principle in the Investigation of the Foundations of Mathematics (ca. 1931) -- Bibliography of the Published Writings of Felix Kaufman -- Bibliography of Works cited in the Present Volume -- Index of Names


Philosophy Philosophy and science Mathematical logic Philosophy Philosophy of Science Mathematical Logic and Foundations



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