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Only Two Letters: The Correspondence between Herbrand and Gödel

Published online by Cambridge University Press:  15 January 2014

Wilfried Sieg
Wilfried Sieg*
Affiliation:
Carnegie Mellon University, Pittsburgh, PA 15213, USAE-mail: ws15+@andrew.cmu.edu
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Abstract

Two young logicians, whose work had a dramatic impact on the direction of logic, exchanged two letters in early 1931. Jacques Herbrand initiated the correspondence on 7 April and Kurt Gödel responded on 25 July, just two days before Herbrand died in a mountaineering accident at La Bérarde (Isère). Herbrand's letter played a significant role in the development of computability theory. Gödel asserted in his 1934 Princeton Lectures and on later occasions that it suggested to him a crucial part of the definition of a general recursive function. Understanding this role in detail is of great interest as the notion is absolutely central. The full text of the letter had not been available until recently, and its content (as reported by Gödel) was not in accord with Herbrand's contemporaneous published work. Together, the letters reflect broader intellectual currents of the time: they are intimately linked to the discussion of the incompleteness theorems and their potential impact on Hilbert's Program.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 11 , Issue 2 , June 2005 , pp. 172 - 184
Copyright
Copyright © Association for Symbolic Logic 2005

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References

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