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Finsler Set Theory: Platonism and Circularity

Translation of Paul Finsler’s papers on set theory with introductory comments

  • Book
  • © 1996

Overview

Editors:
  1. David Booth

    1. Three Fold Foundation 307, New York, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Renatus Ziegler

    1. Mathematisch-Astronomische Sektion am Geotheanum, Dornach, Switzerland

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-ix
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  2. Philosophical Part

    1. Front Matter

      Pages 1-1
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    2. Introduction

      • David Booth, Renatus Ziegler
      Pages 3-13

    3. Intrinsic Analysis of Antinomies and Self-Reference

      • David Booth, Renatus Ziegler
      Pages 14-38

    4. Are There Contradictions in Mathematics?

      • David Booth, Renatus Ziegler
      Pages 39-49

    5. Formal Proofs and Decidibility

      • David Booth, Renatus Ziegler
      Pages 50-55

    6. On the Solution of Paradoxes

      • David Booth, Renatus Ziegler
      Pages 56-62

    7. Are There Undecidable Propositions?

      • David Booth, Renatus Ziegler
      Pages 63-72

    8. The Platonistic Standpoint in Mathematics

      • David Booth, Renatus Ziegler
      Pages 73-77

    9. Platonism After All

      • David Booth, Renatus Ziegler
      Pages 78-81

  3. Foundational Part

    1. Front Matter

      Pages 83-83
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    2. Introduction

      • David Booth, Renatus Ziegler
      Pages 85-102

    3. On the Foundations of Set Theory

      • David Booth, Renatus Ziegler
      Pages 103-132

    4. The Existence of the Number Numbers and the Continuum

      • David Booth, Renatus Ziegler
      Pages 133-138

    5. Concerning a Discussion On the Foundations of Mathematics

      • David Booth, Renatus Ziegler
      Pages 139-151

    6. The Infinity of the Number Line

      • David Booth, Renatus Ziegler
      Pages 152-160

    7. On the Foundations of Set Theory

      • David Booth, Renatus Ziegler
      Pages 161-210

  4. Combinatorial Part

    1. Front Matter

      Pages 211-211
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    2. Introduction

      • David Booth, Renatus Ziegler
      Pages 213-214

    3. The Combinatorics of Non-well-founded Sets

      • David Booth, Renatus Ziegler
      Pages 215-240
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Keywords

About this book

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.

Editors and Affiliations

  • Three Fold Foundation 307, New York, USA

    David Booth

  • Mathematisch-Astronomische Sektion am Geotheanum, Dornach, Switzerland

    Renatus Ziegler

Bibliographic Information

  • Book Title: Finsler Set Theory: Platonism and Circularity

  • Book Subtitle: Translation of Paul Finsler’s papers on set theory with introductory comments

  • Editors: David Booth, Renatus Ziegler

  • DOI: https://doi.org/10.1007/978-3-0348-9031-1

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag 1996

  • Softcover ISBN: 978-3-0348-9876-8Published: 04 October 2011

  • eBook ISBN: 978-3-0348-9031-1Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: IX, 282

  • Topics: History of Mathematical Sciences

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