The main item in the present volume was published in 1930 under the
title Das Unendliche in der Mathematik und seine Ausschaltung. It
was at that time the fullest systematic account from the standpoint
of Husserl's phenomenology of what is known as 'finitism' (also as
'intuitionism' and 'constructivism') in mathematics. Since then,
important changes have been required in philosophies of
mathematics, in part because of Kurt Godel's epoch-making paper of
1931 which established the essential in completeness of arithmetic.
In the light of that finding, a number of the claims made in the
book (and in the accompanying articles) are demon strably mistaken.
Nevertheless, as a whole it retains much of its original interest
and value. It presents the issues in the foundations of mathematics
that were under debate when it was written (and in some cases still
are);, and it offers one alternative to the currently dominant
set-theoretical definitions of the cardinal numbers and other
arithmetical concepts. While still a student at the University of
Vienna, Felix Kaufmann was greatly impressed by the early
philosophical writings (especially by the Logische Untersuchungen)
of Edmund Husser ' He was never an uncritical disciple of Husserl,
and he integrated into his mature philosophy ideas from a wide
assortment of intellectual sources. But he thought of himself as a
phenomenologist, and made frequent use in all his major
publications of many of Husserl's logical and epistemological
theses."
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