Sam Buss has put up an interesting paper on Edward Nelson's philosophy of mathematics and its relation to his (Nelson's) proof theoretical work.

In the last post, I pointed to some interesting work on cut-elimination and complexity of proofs. This reminded me of Richard Statman's wonderful dissertation (Structural complexity of proofs, Ph.D. thesis, Stanford University, 1974). The two most widely investigated measures of proof complexity are size (number of symbols) and length (number of steps). Statman and Orevkov's … Continue reading Complexity measures of proofs

If you've wondered what all this "cut elimination" business is about, here's a nice blog entry (on That Logic Blog) which gives a nice introduction. Jon points out that proofs with cut have (at least--depends on the logic) exponential speedup over proofs with cut. This result is due to Statman and Orevkov. Jon points to … Continue reading Eliminating cuts

Wow. CiteUlike is the best thing since Brian's OPP blog. Here's what it does: There are feeds for journals from all major publishers, plus arXiv and such. You can set up a watchlist of journal and other feeds, or other user's libraries, and then build your own library of online papers, with keywords, comments, and … Continue reading CiteULike is The Coolest Thing!

John asks if logicians should give in in the face of rising acceptance of the use of "begging the question" for "raising the question." I agree with the commenters: we should not. Also check out this delightful (and correct) use of "begs the question," posted by Sean Carroll: I once heard an astrophysics seminar with … Continue reading Begging the Question

I've been irritated for a long time that the "ö" in "Gödel" doesn't show up right on this blog. The problem was caused by the web server setting the charset in the header, thus overriding the UTF-8 charset declaration in the pages themselves. It should be fixed now, but let me know if I still … Continue reading Charset Problem Fixed

Another logic/language/philosophy of math blog started up yesterday: languageandlogic.net. It's still anonymous, but the author wrote over at consequently.org that she'll put up contact details soon. One of the first posts discusses the fact that natural deductions for ordinary propositional logic normalizes (well, at least without negation it does), but it doesn't when you add … Continue reading New Blog, Tonk, and Normalization

Jim Holt reviews two new books on Gödel and Einstein, and Yourgrau's A World Without Time. It's a nice little story about what Gödel and Einstein talked about in their daily walks to the office. The books are Rebecca Goldstein's Incompleteness (NYT review here) and John S. Rigden's Einstein 1905: The Standard of Greatness.

Philosophia Mathematica, the only (and hence, the) journal on philosophy of mathematics, is now being published/distributed by Oxford University Press (for cooperation with the Canadian Society for History and Philosophy of Mathematics/Société canadienne d'histoire et de philosophie des mathématiques. That means, in particular, that it's now (finally!) available online. The latest issue (February 2005) even … Continue reading Philosophia Mathematica now online through OUP

The "deep inference/calculus of structures" gang is organizing a workshop at ICALP (July 16-17) on "Structures and Deduction: The Quest for the Essence of Proofs." Deadline for paper submissions is April 15. Another opportunity to visit Lisbon.

Greg Restall has a new book projct: Proof and Counterexample, a text on basic proof theory (sequent calculus and natural deduction, cut elimination and normalization, and such). Knowing Greg's interests, this will cover proof theory for many non-classical logics. Greg's draft is online, and the wiki devoted to the book also has a bunch of … Continue reading Restall’s new project: Proof and Counterexample

I've been waiting for it for a while, and it has finally arrived: my copy of William Tait's collection of "essays in the philosophy of mathematics and its history," The Provenance of Pure Reason. Neither OUP nor Amazon has a table of contents for it up, so here it is: Introduction31Finitism212Remarks on finitism431Appendix to Chapters … Continue reading Bill Tait: The Provenance of Pure Reason

Proofs and Types, the classic 1989 proof theory text by Jean-Yves Girard (translated and with appendices by Paul Taylor and Yves Lafont) has been online for over a year, I just found out. Now that Troelstra/Schwichtenberg is around, perhaps no longer the first place you'd go to read up on the Curry-Howard isomorphism and normalization, … Continue reading Proofs and Types

Just got this via FOM:Logical Lyrics: From Philosophy to Poetics is available,see Amazon UK and Amazon US [and Amazon Canada]:I want to take this opportunity to thank you all for your pertinent citations and aphorisms for Logical Lyrics: From Philosophy, Vincent F. Hendricks, King's College Publications, March 2005, ISBN 1904987044, the independent follow-up to Feisty … Continue reading Logical Lyrics: From Philosophy to Poetics

Over at Metatome, Adam Potthast asks, "Does anyone have any special things they do to give formal logic more take-home value?" By which he means, "how do you motivate teaching formal logic to students who aren't math, physics or philosophy majors." And that's a good question. I've so far only tried to increase the "take-home … Continue reading Metatome on Teaching Formal Logic

I heard about this from a colleague, who played it as a kid, and then I saw it today on another colleague's shelf, who promptly gave it to me as a gift (Thanks, Jack!). It is some kind of game with wff's (in Polish notation), I haven't looked at the instructions yet. I thought something … Continue reading Wff ‘n Proof

A reader sent me email with the following interesting observations about the relative status of logic in Europe and the US (a propos Ken Taylor's remarks in the recent Jobs thread over at TAR and my post here): i'd like to offer the following observation about a difference that i see between logic in europe … Continue reading Logic in Europe and North America

Brian has already linked to this year's Berkeley/Austin Formal Epistemology workshop and the Pitt/CMU Symposium on Imprecise Probabilities. Here's a related event: CMSRA-IV will be held September 21-23 in Lisbon. The mission statement reads, in part, "The CMSRA workshops are designed to promote research of high-level cognitive reasoning that addresses both the logico-philosophical issues surrounding … Continue reading Computational Models of Scientific Reasoning & Applications IV

Jon Cohen has started That Logic Blog with a post on symmetry in propositional logic and connections to problems of automorphism of colored graphs. And I fully agree with his statement that "while many people may believe [propositional logic] to be a completely mined out and somewhat trivial area, this is not so." Especially if … Continue reading New Logic Blog

If you have a paper on cut elimination and are looking for a journal, how about Studia Logica? There's a special issue on cut elimination in preparation; call for papers here. Deadline March 31.