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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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