Completeness before Post: Bernays, Hilbert, and the development of propositional logic

Bulletin of Symbolic Logic 5 (3):331-366 (1999)
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Abstract

Some of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923. The aim of this paper is to describe these results, focussing primarily on propositional logic, and to put them in their historical context. It is argued that truth-value semantics, syntactic ("Post-") and semantic completeness, decidability, and other results were first obtained by Hilbert and Bernays in 1918, and that Bernays's role in their discovery and the subsequent development of mathematical logic is much greater than has so far been acknowledged

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Richard Zach
University of Calgary

References found in this work

The Development of Logic.William Kneale & Martha Kneale - 1962 - Oxford, England: Clarendon Press. Edited by Martha Kneale.
The Development of Logic.William Kneale & Martha Kneale - 1962 - Studia Logica 15:308-310.
Principia mathematica.A. N. Whitehead & B. Russell - 1910-1913 - Revue de Métaphysique et de Morale 19 (2):19-19.
Grundzüge der theoretischen Logik.D. Hilbert & W. Ackermann - 1928 - Annalen der Philosophie Und Philosophischen Kritik 7:157-157.

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