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Between Russell and Hilbert: Behmann on the Foundations of Mathematics

  • Paolo Mancosu (a1)

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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[4] Heinrich Behmann , Beiträge zur Algebra der Logik, insbesondere zum Entscheidungsproblem, Mathematische Annalen, vol. 86 (1922), pp. 163229.

[11] Paul Bernays , Erwiderung auf die Note von Herrn Aloys Müller: Über Zahlen als Zeichen, Mathematische Annalen, vol. 90 (1923), pp. 159–63, English translation in [24], pp. 223226.

[13] Paul Bernays and Moses Schönfinkel , Zum Entscheidungsproblem der mathematischen Logik, Mathematische Annalen, vol. 99 (1928), pp. 342372.

[29] Moses Schönfinkel , Über die Bausteine der mathematischen Logik, Mathematische Annalen, vol. 92 (1924), pp. 305–316, English translation in [32], pp. 355366.

[33] Hermann Weyl , Randbemerkungen zu Hauptproblemen der Mathematik, Mathematische Zeitschrift, vol. 20 (1924), pp. 131–50, Reprinted in: [35], pp. 433–52.

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Bulletin of Symbolic Logic
  • ISSN: 1079-8986
  • EISSN: 1943-5894
  • URL: /core/journals/bulletin-of-symbolic-logic
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