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

Bulletin of Symbolic Logic 5 (3):331-366 (1999)
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 Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923.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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DOI 10.2307/421184
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References found in this work BETA
Categoricity.John Corcoran - 1980 - History and Philosophy of Logic 1 (1):187-207.
Husserl and Hilbert on Completeness.Ulrich Majer - 1997 - Synthese 110 (1):37-56.
From Categoricity to Completeness.J. Corcoran - 1981 - History and Philosophy of Logic 2:113.
Hilberts Logik. Von der Axiomatik zur Beweistheorie.Volker Peckhaus - 1995 - NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin 3 (1):65-86.
Paul Bernays (1888–1977).Henri Lauener - 1978 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 9 (1):13-20.

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Citations of this work BETA
Identity of Proofs Based on Normalization and Generality.Kosta Došen - 2003 - Bulletin of Symbolic Logic 9 (4):477-503.

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