Finsler Set Theory: Platonism and Circularity; Translations of Paul Finsler's Papers on Set Theory with Introductory Comments

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Springer Science & Business Media, May 1, 1996 - Mathematics - 278 pages
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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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Contents

Introduction
3
Intrinsic Analysis of Antinomies and SelfReference
14
Are There Contradictions in Mathematics? 1925
37
Formal Proofs and Decidibility 1926a
48
On the Solution of Paradoxes 1927b
54
Are There Undecidable Propositions? 1944
61
The Platonistic Standpoint in Mathematics 1956a
71
Platonism After All 1956
76
The Existence of the Number Numbers and the Continuum 1933
131
Concerning a Discussion On the Foundations of Mathematics 1954
137
The Infinity of the Number Line 1954
150
On the Foundations of Set Theory Part II 1964
159
Combinatorial Part
209
Introduction
211
The Combinatorics of Nonwellfounded Sets
213
Totally Finite Sets 1965
237

Foundational Part
81
Introduction
83
On the Foundations of Set Theory Part I 1926b
101
On the Goldbach Conjecture 1965
251
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About the author (1996)

David Booth grew up in Norfolk, Virginia area where he became a Christian, was called into ministry, and started his family with his wife Christy. The Booths moved to Fort Worth, Texas where David earned a Master of Divinity degree at Southwestern Baptist Theological Seminary. David has had the honor of serving in Virginia, Georgia, and Texas church for 15 years, primarily as Student Minister. He is currently completing his Ph.D. residency in Educational Ministries at Southwestern, with a focus on family ministry in the local church. David lives in Winnsboro, Texas with his wife Christy and their three children, where he serves First Baptist Church as Minister of Education and Family Discipleship. David's passion is building God's Kingdom by leading Sunday School small group participants to live on-mission in their homes, in their community, and around the world.

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