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Between Russell and Hilbert: Behmann on the Foundations of Mathematics

Paolo Mancosu
The Bulletin of Symbolic Logic
Vol. 5, No. 3 (Sep., 1999), pp. 303-330
DOI: 10.2307/421183
Stable URL: http://www.jstor.org/stable/421183
Page Count: 28
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Between Russell and Hilbert: Behmann on the Foundations of Mathematics
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Abstract

After giving a brief overview of the renewal of interest in logic and the foundations of mathematics in Göttingen in the period 1914-1921, I give a detailed presentation of the approach to the foundations of mathematics found in Behmann's doctoral dissertation of 1918, Die Antinomie der transfiniten Zahl und ihre Auflösung durch die Theorie von Russell und Whitehead. The dissertation was written under the guidance of David Hilbert and was primarily intended to give a clear exposition of the solution to the antinomies as found in Principia Mathematica. In the process of explaining the theory of Principia, Behmann also presented an original approach to the foundations of mathematics which saw in sense perception of concrete individuals the Archimedean point for a secure foundation of mathematical knowledge. The last part of the paper points out an important numbers of connections between Behmann's work and Hilbert's foundational thought.

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