...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 … Continue reading One person’s modus ponens…

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 … Continue reading Kennedy’s Interpreting Gödel Out Now

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 … Continue reading Two New(ish) Surveys on Gödel’s Incompleteness Theorems

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 … Continue reading Possible Postdoc on Genesis of Mathematical Knowledge

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 … Continue reading Kalmár’s Compleness Proof

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 … Continue reading Dana Scott’s Favorite Completeness Proof

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" … Continue reading The Real Reasons Why Philosophers Shouldn’t Use LaTeX

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 … Continue reading Bringing Logic (and Philosophy, CS) to the Masses

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, … Continue reading Proof Formalization in Mathematics: Guest Post by Jeremy Avigad

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

Steve Awodey's talk in the Calgary Mathematics & Philosophy lecture series ("Univalence as a New Principle of Logic" aka "HoTT for Philosophers") is now up on mathtube.org.

I've fixed a bug in bpextra.The new version can be downloaded from github. See also this issue for how to define your own deduction styles.

The second installment of SotFom (Symposium on the Foundations of Math) is asking for papers by Halloween: http://sotfom.wordpress.com/2014/10/14/final-cfp-and-extended-deadline-sotfom-ii-competing-foundations-12-13-january-2015-london/ FINAL CFP and *EXTENDED DEADLINE*: SoTFoM II `Competing Foundations?’, 12-13 January 2015, London. The focus of this conference is on different approaches to the foundations of mathematics. The interaction between set-theoretic and category-theoretic foundations has had significant … Continue reading SotFoM II: Competing Foundations

Did you know? The Moritz Schlick Gesamtausgabe is available for free at the Moritz-Schlick-Forschungsstelle! Just click on the cover image to download the PDF (instead of the "order online" link).  Alas, it's only in German.

If you're in that part of the world (or will be in January), you might be interested to know that registration for the 8th Annual Cambridge Graduate Conference on the Philosophy of Mathematics and Logic (17-18 January 2015) is now open: The conference will be held in St. John's College, Cambridge. There will be two … Continue reading Cambridge Graduate Conference on the Philosophy of Mathematics and Logic

Hilary Putnam is writing on Tarski's theory of truth (and Field's analysis of it) at Sardonic Comment. First two blog posts are up: http://putnamphil.blogspot.ca/2014/09/first-of-series-of-posts-on-tarski-i-am.html http://putnamphil.blogspot.ca/2014/09/a-second-post-on-tarski-this-post.html

I'm very excited that Steve Awodey is on his way here to deliver the first Calgary Mathematics & Philosophy Lecture tomorrow! He's speaking on "Univalence as a New Principle of Logic." If you're in Calgary, you should come.  It'll be exciting. Thursday, 3:30 pm, in Engineering Building A aka ENA 101 on the UofC campus. … Continue reading Steve Awodey gives inaugural Calgary Mathematics & Philosophy Lecture

I've been having a conversation with Alex Douglas and Eric Schliesser on their posts (Alex's, Eric's) about Milton Friedman's footnote about observer-dependence and Gödel's incompleteness theorem.