Completeness before Post: Bernays, Hilbert, and the Development of Propositional Logic Export

@article{citeulike:130240, 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 Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923.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.}, author = {Zach, Richard}, citeulike-article-id = {130240}, citeulike-linkout-0 = {http://www.jstor.org/stable/421184}, journal = {The Bulletin of Symbolic Logic}, keywords = {bernays, hilbert, history, history\_of\_logic, logic, post}, number = {3}, pages = {331--366}, posted-at = {2005-03-16 18:07:57}, priority = {0}, title = {Completeness before Post: Bernays, Hilbert, and the Development of Propositional Logic}, url = {http://www.jstor.org/stable/421184}, volume = {5}, year = {1999} }

TY - JOUR ID - citeulike:130240 L3 - citeulike-article-id:130240 N2 - 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 Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923.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. IS - 3 JF - The Bulletin of Symbolic Logic EP - 366 TI - Completeness before Post: Bernays, Hilbert, and the Development of Propositional Logic VL - 5 SP - 331 KW - bernays KW - hilbert KW - history KW - history_of_logic KW - logic KW - post AU - Zach, Richard PY - 1999/// UR - http://www.jstor.org/stable/421184 ER -