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I’m working on a paper that features Moses Schönfinkel, so I was reading through a manuscript of his where he rattles off a long list of important logicians.  In addition to the usual suspects, it features the names “Schatunowski, Sleschinski, Kahan, Poretski.”  I spent the better part of a day trying to figure out to…

Shawn Standefer has done us all a great service by starting and populating a Wiki of PhD programs in Philosophical Logic! This wiki provides an unranked list of PhD (and (eventually) terminal M.A.) programs that have strengths in philosophical logic. Links are provided to the websites, CVs, and PhilPapers profiles of the relevant faculty at…

…is another’s modus tollens. [W]hen I was nine years old, I came down with scarlet fever. […] During that year there was nothing in the world which I wanted so much as a bicycle. My father assured me that when I got well I would get one but, childlike, I interpreted this as meaning that…

Interpreting Gödel: Critical Essays, edited by Juliette Kennedy, was just published by Cambridge. It looks extremely interesting, with an all-star cast of contributors: Introduction: Gödel and analytic philosophy: how did we get here? Juliette Kennedy Part I. Gödel on Intuition:2. Intuitions of three kinds in Gödel’s views on the continuum, John Burgess 3. Gödel on…

Gödel’s incompleteness theorems have many variants: semantic vs. syntactic versions, which specific theory is taken as basic, what model of computability is used, which logical system is assumed to underlie the provability relation, how syntax is arithmetized, what hypotheses the theorem itself uses (soundness, consistency, $latex \omega$-consistency, etc.). These result in trade-offs regarding simplicity of…

Via the APMP list: Expressions of interest are invited for a postdoc grant (financed by Junta de Andalucia) associated with the following research project:  “THE GENESIS OF MATHEMATICAL KNOWLEDGE: COGNITION, HISTORY, PRACTICES” (P12-HUM-1216). IP: Jose Ferreiros Contact: josef@us.es The grant consists in a 2-year research contract to be held at the University of Sevilla. Salary…

Dana Scott’s proof reminded commenter “fbou” of Kalmár’s 1935 completeness proof. (Original paper in German on the Hungarian Kalmár site.) Mendelsohn’s Introduction to Mathematical Logic also uses this to prove completeness of propositional logic. Here it is (slightly corrected): We need the following lemma: Let $latex v$ be a truth-value assignment to the propositional variables…

Last week I gave my decision problem talk at Berkeley. I briefly mentioned the 1917/18 Hilbert/Bernays completeness proof for propositional logic. It (as well as Post’s 1921 completeness proof) made essential use of provable equivalence of a formula with its conjunctive normal form. Dana Scott asked who first gave (something like) the following simple completeness…

Back in 2009, I taught a short course on the epsilon calculus at the Vienna University of Technology.  I wrote up some of the material, intending to turn them into something longer.  I haven’t had time to do that, but someone might find what I did helpful. So I put it up on arXiv: http://arxiv.org/abs/1411.3629