Peli Grietzer shared a blog post by David Auerbach on Twitter yesterday containing the following lovely quote about Smullyan and Carnap: I particularly delighted in playing tricks on the philosopher Rudolf Carnap; he was the perfect audience! (Most scientists and mathematicians are; they are so honest themselves 'that they have great difficulty in seeing through … Continue reading Proof by legerdemain

Yesterday, @gravbeast asked on Twitter, Does anyone know why we traditionally use Greek phi and psi for metasyntactic variables representing arbitrary logic formulas? Is it just because 'formula' begins with an 'f' sound? And chi was being used for other things? Although Whitehead and Russell already used φ and ψ for propositional functions, the convention … Continue reading Why φ?

The European Summer Meeting of the Association of Symbolic Logic will be in Udine, just north of Venice, July 23-28. Abstracts for contributed talks are due on April 27. Student members of the ASL are eligible for travel grants! lc18.uniud.it  

If you wanted to explain how philosophy has been important to mathematics, and why it can and should continue to be, it would be hard to do it better than Jeremy Avigad. In this beautiful plea for a mathematically relevant philosophy of mathematics disguised as a book review he writes: Throughout the centuries, there has … Continue reading The Significance of Philosophy to Mathematics

Working on the chapters on counterfactual conditionals for the Open Logic Project, I needed some illustrations for David Lewis's sphere models, which he jokingly called "Ptolemaic astronomy." Since Franz Berto joked that this should just require \usepackage{ptolemaicastronomy}, I wrote some LaTeX macros to make this easier using TikZ. You can download ptolemaicastronomy.sty (it should work … Continue reading Ptolemaic Astronomy

Lots of new stuff in the Open Logic repository! I’m teaching modal logic this term, and my ambitious goal is to have, by the end of term or soon thereafter, another nicely organized and typeset open textbook on modal logic. The working title is Boxes and Diamonds, and you can check out what’s there so far on the builds site. This project of course required new material on modal logic.  So far this consists in revised and expanded notes by our dear late colleague Aldo Antonelli. These now live in content/normal-modal-logic and cover relational models for normal modal logics, frame correspondence, derivations, canonical models, and filtrations. So that’s one big exciting addition. Since the OLP didn’t cover propositional logic separately, I just now added that part as well so I can include it as review chapters. There’s a short chapter on truth-value semantics in propositional-logic/syntax-and-semantics. However, all the proof systems and completeness for them are covered as well. I didn’t write anything new for those, but rather made the respective sections for first-order logic flexible. OLP now has an FOL “tag”: if FOL is set to true, and you compile the chapter on the sequent calculus, say, you get the full first-order version with soundness proved relative to first-order structures. If FOL is set to false, the rules for the quantifiers and identity are omitted, and soundness is proved relative to propositional valuations. The same goes for the completeness theorem: with FOL set to false, it leaves out the Henkin construction and constructs a valuation from a complete consistent set rather than a term model from a saturated complete consistent set. This works fine if you need only one or the other; if you want both, you’ll currently get a lot of repetition. I hope to add code so that you can first compile without FOL then with, and the second pass will refer to the text produced by the first pass rather than do everything from scratch. You can compare the two versions in the complete PDF. Proofs systems for modal logics are tricky; and many systems don’t have nice, say, natural deduction systems. The tableau method, however, works very nicely and uniformly. The OLP didn’t have a chapter on tableaux, so this motivated me to add that as well. Tableaux are also often covered in intro logic courses (often called “truth trees”), so having them as a proof system included has the added advantage of tying in better with introductory logic material. I opted for prefixed tableaux (true and false are explicitly labelled, rather than implicit in negated and unnegated formulas), since that lends itself more easily to a comparison with the sequent calculus, but also because it extends directly to many-valued logics. The material on tableaux lives in first-order-logic/tableaux. Thanks to Clea Rees for the the prooftrees package, which made it much easier to typeset the tableaux, and to Alex Kocurek for his tips on doing modal diagrams in Tikz.

As I reported last year, we've been running surveys in our classes that use open logic textbooks. We now have another year of data, and I've figured out R well enough to plot the results. Perhaps someone else is in a similar situation, so I've written down all the steps. Results aren't perfect yet. All the … Continue reading Graphing Survey Responses

I drank the Koolaid and set up my CV so it's generated automatically from a YAML file with a Pandoc template. The basic functionality is copied from bmschmidt/CV-pandoc-healy. My version generates the bibliography from a BibTeX file however, using biblatex.  The biblatex code is tweaked to include links to PhilPapers and Google Scholar citation counts. … Continue reading Citations in your CV

Jonathan Greig (LMU Munich) posted the picture above to Twitter the other day, crediting Laura Castelli with finding it. It's from a 14th Century illuminated manuscript by Thomas Le Myésier, Breviculum ex artibus Raimundi Lulli electum, and depicts Aristotle, Averroes, and Ramon Llull leading an army charging the Tower of Falsehood. I put a full … Continue reading Illuminated Manuscript of Aristotle, Averroes, and Ramon Llull Charging the Tower of Falsehood

Aldo Antonelli's last paper, "Completeness and Decidability of General First-Order Logic (with a Detour Through the Guarded Fragment)" is now out in the most recent issue of the Journal of Philosophical Logic. This paper investigates the “general” semantics for first-order logic introduced to Antonelli (Review of Symbolic Logic 6(4), 637–58, 2013): a sound and complete … Continue reading Aldo Antonelli’s last paper

I made a textbook on incompleteness for my Logic III course. See it/read about it over at the Open Logic Project.

From the Group in Logic and the Methodology of Science: It is with great sadness that we announce that Professor Jack Howard Silver died on Thursday, December 22, 2016. Professor Silver was born April 23, 1942 in Missoula, Montana. After earning his A.B. at Montana State University (now the University of Montana) in 1961, he … Continue reading Jack Howard Silver, 1942-2016