Kurt Gödel would have been 99 years old today. Happy Birthday, Kurtele! And Merry Gödelmas to everyone else.
Georges Gonthier (MS Research, Cambridge) has a paper up entitled "A computer-checked proof of the Four Colour Theorem." The original proof of the theorem by Appel and Haken relied on computer programs checking a very large number of cases, and raised some important conceptual and philosophical issues (see Tymoczko, "The four-color theorem and its philosophical … Continue reading Four Color Theorem Verified in Coq
I committed to teach a course on Logical Positivism next year, and I have to figure out which books I should order. Here's a list; if you have any comments or ideas, please let me know. Carnap, The Logical Construction of the World Ayer, Logical Positivism Ayer, Language, Truth, and Logic Friedman, Reconsidering Logical Positivism … Continue reading Course on Logical Positivism
Lillian sent me an email today about the APA Session on Logic Instruction where she asked: Was there any discussion about incorporating philosophical issues in logic @ the intro course level? I'm teaching a logic for philosophers course this semester. Most of my students haven't had any formal logic, so I'm teaching it like an … Continue reading Motivating Intro Logic for Philosophy majors (and others)
Gillian linked* to a paper by Gil Harman and Sanjeev Kulkarni, which contains this nice explanation of the distiction between inference (reasoning) and implication (what follows from what): A related problem with the traditional picture is its treatment of deductive principles like (D) as rules of inference. In fact they are rules of about what … Continue reading Inference vs. Implication
I've put up materials from the panel discussion on Logic in Philosophy Graduate Training at the 2005 ASL Spring Meeting, which featured Michael Glanzberg, Ted Sider, and Brian Weatherson, and which Andy Arana and I organized. The materials include slides for Michael's and my talks, notes for Ted's talk, and Andy's paper, as well as … Continue reading Logic Instruction and Philosophy Graduate Training
If you've read Brouwer or Heyting, you've probably seen examples involving the question if 0123456789 occurs in the decimal expansion of π. I wasn't aware that it's been known for a few years that it does: the first time at the 17,387,594,880th digit. There's also 10 consecutive 7's starting at 22,869,046,249.
I'm scheduled to teach a course on modal logic in the Fall. So I'll have to think about a textbook choice pretty soon. Last time I've used Fitting and Mendelsohn's First-order Modal Logic (Kluwer, 1999), which I quite like. It's accessible, which is important, since many of the students will be philosophy majors with little … Continue reading Modal Logic Textbooks
This year's LPAR will be held in Montego Bay, Jamaica--in early December. I missed the meetings in Havana and Reunion (Had papers and didn't go! What was I thinking?) so it's probably time to put on my computer science hat and write something.