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Finsler Set Theory: Platonism and Circularity

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

  • David Booth
  • Renatus Ziegler

Table of contents

  1. Front Matter
    Pages i-ix
  2. Philosophical Part

    1. Front Matter
      Pages 1-1
    2. David Booth, Renatus Ziegler
      Pages 3-13
    3. David Booth, Renatus Ziegler
      Pages 14-38
    4. David Booth, Renatus Ziegler
      Pages 39-49
    5. David Booth, Renatus Ziegler
      Pages 50-55
    6. David Booth, Renatus Ziegler
      Pages 56-62
    7. David Booth, Renatus Ziegler
      Pages 63-72
    8. David Booth, Renatus Ziegler
      Pages 73-77
    9. David Booth, Renatus Ziegler
      Pages 78-81
  3. Foundational Part

    1. Front Matter
      Pages 83-83
    2. David Booth, Renatus Ziegler
      Pages 85-102
    3. David Booth, Renatus Ziegler
      Pages 103-132
    4. David Booth, Renatus Ziegler
      Pages 133-138
    5. David Booth, Renatus Ziegler
      Pages 139-151
    6. David Booth, Renatus Ziegler
      Pages 152-160
    7. David Booth, Renatus Ziegler
      Pages 161-210
  4. Combinatorial Part

    1. Front Matter
      Pages 211-211
    2. David Booth, Renatus Ziegler
      Pages 213-214
    3. David Booth, Renatus Ziegler
      Pages 215-240
    4. David Booth, Renatus Ziegler
      Pages 241-256
    5. David Booth, Renatus Ziegler
      Pages 257-259
  5. Erratum

    1. David Booth, Renatus Ziegler
      Pages 279-279
  6. Back Matter
    Pages 261-278

About this book

Introduction

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.

Keywords

Mathematica Volume arithmetic class eXist field form group identity mathematics proposition set set theory sets time

Editors and affiliations

  • David Booth
    • 1
  • Renatus Ziegler
    • 2
  1. 1.Three Fold Foundation 307New YorkUSA
  2. 2.Mathematisch-Astronomische Sektion am GeotheanumDornachSwitzerland

Bibliographic information