Mindblown: a blog about philosophy.

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

Josh Parsons (Oxford) has written a widely discussed post on “The LaTeX cargo cult,” explaining why he discourages philosophy students from using LaTeX.  He makes some interesting points.  But what he has left out is the overarching principle that you should simply always use the best tool for the purpose at hand – and “best”…

At this year’s Vienna Summer of Logic the organizers did something I haven’t seen done before, and which I think should be emulated: over the course of the two weeks that 2,400 logicians were gathered in Vienna, they organized a Logic Lounge in seven instalments.  For an hour each, one or more conference participants engaged…

There’s a discussion going on at the Foundations of Mathematics mailing list about the purpose and value, actual and potential, for formalized proofs in mathematics.  Harvey Friedman asked Jeremy Avigad to comment; he sent this super-useful list of references, republished here with his approval. John Harrison and I recently wrote a survey on formalized mathematics,…

Just found out that Edward Nelson died last month. http://www.princeton.edu/main/news/archive/S41/11/36I14/index.xml http://en.wikipedia.org/wiki/Edward_Nelson