Finsler Set Theory: Platonism and Circularity: Translation of Paul Finsler’s papers on set theory with introductory comments - Hardcover

David Booth

Hardcover

ISBN 10: 3764354003 ISBN 13: 9783764354008

Publisher: Birkhauser, 1996

Synopsis

Finsler's papers on set theory are presented, here for the first time in English translation, in three parts, and each is preceded by an introduction to the field written by the editors. In the philosophical part of his work Finsler develops his approach to the paradoxes, his attitude toward formalized theories and his defense of Platonism in mathematics. He insisted on the existence of a conceptual realm within mathematics that transcends formal systems. From the foundational point of view, Finsler's set theory contains a strengthened criterion for set identity and a coinductive specification of the universe of sets. The notion of the class of circle free sets introduced by Finsler is potentially a very fertile one although not very widespread today. Combinatorially, Finsler considers sets as generalized numbers to which one may apply arithmetical techniques. The introduction to this third section of the book extends Finsler's theory to non-well-founded sets. The present volume makes Finsler's papers on set theory accessible at long last to a wider group of mathematicians, philosophers and historians of science. A technical background is not necessary to appreciate the satisfying interplay of philosophical and mathematical ideas that characterizes this work.

About this title

Language Notes

Text: English (translation)
Original Language: German

Edition details

• Publisher: Birkhauser
• Publication date: 1996
• ISBN 10: 3764354003
• ISBN 13: 9783764354008
• Binding: Hardcover
• Language: English