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