David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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 Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923.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
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Mirja Helena Hartimo (2007). Towards Completeness: Husserl on Theories of Manifolds 1890–1901. Synthese 156 (2):281 - 310.
Ivahn Smadja (2012). Local Axioms in Disguise: Hilbert on Minkowski Diagrams. Synthese 186 (1):315-370.
Similar books and articles
Solomon Feferman (2008). Lieber Herr Bernays!, Lieber Herr Gödel! Gödel on Finitism, Constructivity and Hilbert's Program. Dialectica 62 (2: Table of Contents"/> Select):179–203.
Gregory H. Moore (1997). Hilbert and the Emergence of Modern Mathematical Logic. Theoria 12 (1):65-90.
Wilfried Sieg (1999). Hilbert's Programs: 1917-1922. Bulletin of Symbolic Logic 5 (1):1-44.
Graham Priest (1997). On a Paradox of Hilbert and Bernays. Journal of Philosophical Logic 26 (1):45-56.
Richard Zach (2003). The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program. Synthese 137 (1-2):211 - 259.
Enrico Moriconi (2003). On the Meaning of Hilbert's Consistency Problem (Paris, 1900). Synthese 137 (1-2):129 - 139.
Richard Zach (2004). Hilbert's 'Verunglückter Beweis', the First Epsilon Theorem, and Consistency Proofs. History and Philosophy of Logic 25 (2):79-94.
Matthias Schirn & Karl-Georg Niebergall (2001). Extensions of the Finitist Point of View. History and Philosophy of Logic 22 (3):135-161.
Paolo Mancosu (ed.) (1998). From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s. Oxford University Press.
Miriam Franchella (2006). Paul Bernays' Philosophical Way. Grazer Philosophische Studien 70 (1):47-66.
Added to index2009-01-28
Total downloads15 ( #107,679 of 1,100,932 )
Recent downloads (6 months)3 ( #115,721 of 1,100,932 )
How can I increase my downloads?