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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: [email protected]
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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

REFERENCES

[1929] Gödel, K., Über die Vollständigkeit des Logikkalküls, doctoral dissertation, University of Vienna, 1929.Google Scholar
[1930] Gödel, K., Einige metamathematische Resultate über Entscheidungsdefinitheit und Widerspruchsfreiheit, Anzeiger der Akademie der Wissenschaften in Wien, vol. 67 (1930), pp. 214–5.Google Scholar
[1931] Gödel, K., Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatshefte für Mathematik and Physik, vol. 38 (1931), pp. 173–98.Google Scholar
[1933] Gödel, K., The present situation in the foundations of mathematics, Collected Works, vol. III, (Oxford University Press, 1995), 1933, pp. 45–53.Google Scholar
[1934] Gödel, K., On undecidable propositions of formal mathematical systems, Collected Works, vol. I, (Oxford University Press, 1986), 1934, (mimeographed lecture notes, taken by Stephen C. Kleene and J. Barkley Rosser), pp. 346–69.Google Scholar
[1930] Herbrand, J., Recherches sar la théorie de la demonstration, doctoral dissertation, University of Paris, 1930.Google Scholar
[1931] Herbrand, J., Sur la non-contradiction de l'arithmétique, Journal für die reine und ange-wandte Mathematik, vol. 166 (1931), pp. 1–8.Google Scholar
[1929] Hilbert, D., Probleme der Grundlegung der Mathematik, Atti del Congresso inter-nazionale dei matematici, Bologna 3–10 settembre 1928, vol. 1, 1929, pp. 135–41.Google Scholar
[1994] Sieg, W., Mechanical procedures and mathematical experience, Mathematics and mind (George, A., editor), Oxford University Press, 1994, pp. 71–117.Google Scholar
[1997] Sieg, W., Step by recursive step: Church's analysis of effective calculability, this Bulletin, vol. 3 (1997), pp. 154–80.Google Scholar
[1981] Wang, H., Some facts about Kurt Gödel, The Journal of Symbolic Logic, vol. 46 (1981), pp. 653–9.Google Scholar