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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: davism@cs.nyu.edu
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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

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References

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