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

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David Booth, Renatus Ziegler
Birkhäuser, 6 de des. 2012 - 282 pàgines
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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.

 

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Continguts

Introduction Renatus Ziegler
14
Papers of Paul Finsler
39
Formal Proofs and Decidability 1926a
51
Are there Undecidable Propositions? 1944
63
The Platonistic Standpoint in Mathematics 1956a
73
Introduction David Booth
85
Papers of Paul Finsler
103
The Existence of the Natural Numbers and
133
The Infinity of the Number Line 1954
152
On the Foundations of Set Theory Part II 1964
161
Introduction David Booth
213
Papers of Paul Finsler
241
On the Goldbach Conjecture 1965
257
Index
271
Chronology of Paul Finslers Life
277
Copyright

Concerning a Discussion on the Foundations
139

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