David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
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Bulletin of Symbolic Logic 5 (3):331-366 (1999)
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 Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923.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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Citations of this work BETA
Steve Awodey & Erich H. Reck (2002). Completeness and Categoricity. Part I: Nineteenth-Century Axiomatics to Twentieth-Century Metalogic. History and Philosophy of Logic 23 (1):1-30.
Kosta Došen (2003). Identity of Proofs Based on Normalization and Generality. Bulletin of Symbolic Logic 9 (4):477-503.
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Ivahn Smadja (2012). Local Axioms in Disguise: Hilbert on Minkowski Diagrams. Synthese 186 (1):315-370.
Corey Edward Mulvihill (2015). Existence Assumptions and Logical Principles: Choice Operators in Intuitionistic Logic. Dissertation, University of Waterloo
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