The Infinite in Mathematics

The Infinite in Mathematics

Author: Felix Kaufmann

Publisher: Springer Science & Business Media

ISBN: 9789400997950

Category: Science

Page: 237

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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 in completeness of arithmetic. In the light of that finding, a number of the claims made in the book (and in the accompanying articles) are demon 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.
The Infinite in Mathematics
Language: en
Pages: 237
Authors: Felix Kaufmann
Categories: Science
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

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.
To Infinity and Beyond
Language: en
Pages: 304
Authors: Eli Maor
Categories: Mathematics
Type: BOOK - Published: 2017-11-21 - Publisher: Princeton University Press

Eli Maor examines the role of infinity in mathematics and geometry and its cultural impact on the arts and sciences. He evokes the profound intellectual impact the infinite has exercised on the human mind, from the "horror infiniti" of the Greeks to the works of M.C. Escher; from the ornamental
In Search of Infinity
Language: en
Pages: 146
Authors: N.Ya. Vilenkin
Categories: Mathematics
Type: BOOK - Published: 2013-06-29 - Publisher: Springer Science & Business Media

The concept of infinity is one of the most important, and at the same time, one of the most mysterious concepts of science. Already in antiquity many philosophers and mathematicians pondered over its contradictory nature. In mathematics, the contradictions connected with infinity intensified after the creation, at the end of
Georg Cantor
Language: en
Pages: 424
Authors: Joseph Warren Dauben
Categories: Science
Type: BOOK - Published: 2020-06-16 - Publisher: Princeton University Press

One of the greatest revolutions in mathematics occurred when Georg Cantor (1845-1918) promulgated his theory of transfinite sets. This revolution is the subject of Joseph Dauben's important studythe most thorough yet writtenof the philosopher and mathematician who was once called a "corrupter of youth" for an innovation that is now
How To Measure The Infinite: Mathematics With Infinite And Infinitesimal Numbers
Language: en
Pages: 348
Authors: Mauro Di Nasso, Vieri Benci
Categories: Mathematics
Type: BOOK - Published: 2019-02-19 - Publisher: World Scientific

'This text shows that the study of the almost-forgotten, non-Archimedean mathematics deserves to be utilized more intently in a variety of fields within the larger domain of applied mathematics.'CHOICEThis book contains an original introduction to the use of infinitesimal and infinite numbers, namely, the Alpha-Theory, which can be considered as