Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-25T03:08:46.119Z Has data issue: false hasContentIssue false
  • English
  • Français

American Logic in the 1920s

Published online by Cambridge University Press:  15 January 2014

Martin Davis
Martin Davis*
Affiliation:
Department of Computer Science, and Department of Mathematics, Courant Institute, New York University, New York NY 10012. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Extract

In 1934 Alonzo Church, Kurt Gödei, S. C. Kleene, and J. B. Rosser were all to be found in Princeton, New Jersey. In 1936 Church founded The Journal of Symbolic Logic. Shortly thereafter Alan Turing arrived for a two year visit. The United States had become a world center for cutting-edge research in mathematical logic. In this brief survey1 we shall examine some of the writings of American logicians during the 1920s, a period of important beginnings and remarkable insights as well as of confused gropings.

The publication of Whitehead and Russell's monumental Principia Mathematica [18] during the years 1910-1913 provided the basis for much of the research that was to follow. It also provided the basis for confusion that remained a factor during the period we are discussing. In 1908, Henri Poincaré, a famous skeptic where mathematical logic was concerned, wrote pointedly ([13]):

It is difficult to admit that the word if acquires, when written ⊃, a virtue it did not possess when written if.

Principia provided no very convincing answer to Poincaré. Indeed the fact that the authors of Principia saw fit to place their first two “primitive propositions”

*1.1: Anything implied by a true proposition is true.

*1.2: ⊢ p ⋁ p ⊃ p

under one and the same heading suggest that they had thought of what they were doing as just such a translation as Poincare had derided.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 1 , Issue 3 , June 1995 , pp. 273 - 278
Copyright
Copyright © Association for Symbolic Logic 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1] Bernays, Paul, Axiomatische Untersuchung des Aussagen-Kalküls der ‘Principia Mathematica’, Mathematische Zeitschrift, vol. 25 (1926), pp. 305–320.CrossRefGoogle Scholar
[2] Church, Alonzo, Alternatives to Zermelo's assumption, Transactions of the American Mathematical Society, vol. 29 (1926), pp. 178–208.Google Scholar
[3] Church, Alonzo, On the law of the excluded middle, Bulletin of the American Mathematical Society, vol. 34 (1928), pp. 75–78.Google Scholar
[4] Curry, Haskell, An analysis of logical substitution, American Journal of Mathematics, vol. 51 (1929), pp. 363–384.Google Scholar
[5] Davis, Martin, Why Gödel didn't have Church's Thesis, Information and Control, vol. 54 (1982), pp. 3–24.Google Scholar
[6] Davis, Martin, Emil T. Post: His life and work, In Solvability, Provability, Definability: The Collected Works of Emil L. Post [16], edited by Davis, Martin, pp. xi–xviii.Google Scholar
[7] Hilbert, D. and Ackermann, W., Grundzüge der theoretischen Logik, Julius Springer, Berlin, 1928.Google Scholar
[8] Langford, C. H., Some theorems on deducibility, Annals of Mathematics, second series, vol. 28 (1927), pp. 16–40.Google Scholar
[9] Langford, C. H., Theorems on deducibility (secondpaper ), Annals of Mathematics, second series, vol. 28 (1927), pp. 459–471.Google Scholar
[10] Langford, C. H., Concerning logical principles, Bulletin of the American Mathematical Society, vol. 34 (1928), pp. 573–582.Google Scholar
[11] Langford, C. H., Review of [7], Bulletin of the American Mathematical Society, vol. 36 (1930).Google Scholar
[12] Lewis, C.I., A survey of symbolic logic, University of California Press, Berkeley, 1918.Google Scholar
[13] Poincaré, Henri, Science and method, Dover, New York, 1952, translated by Maitland, F. from the original French edition of 1908.Google Scholar
[14] Post, Emil L., Introduction to a general theory of propositional functions, American Journal of Mathematics, vol. 43 (1921), pp. 163–185, reprinted in [17], pages 264–283 and in [16], pages 21–43.Google Scholar
[15] Post, Emil L., The two-valued iterative systems of mathematical logic, Annals of Mathematics Studies, no. 5, Princeton University Press, 1941, reprinted in [16], pages 249–374.Google Scholar
[16] Post, Emil L., Solvability, provability, definability: The collected works of Emil L. Post, Birkhäuser, Boston, 1994, edited by Davis, Martin.Google Scholar
[17] van Heijenoort, Jean (editor), From Frege to Gödel, Harvard University Press, 1967.Google Scholar
[18] Whitehead, Alfred and Russell, Bertrand, Principia mathematica, vol. 1 (1910), 2 (1912), 3 (1913), Cambridge University Press.Google Scholar