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Sabbatical – a Real First Logic Course

July 30, 2014 pm31 12:57 pm

I took a sabbatical 2013-14, to study. I mean I did other stuff too, but studying came first. And the first class I walked into was Mathematical Logic.

I teach “Logic” – but it’s a high school course, based on the first logic course that might show up at the 100 or 200 level in a philosophy department. Hurley is my text. My content barely touches the beginnings of what we were about to study.

I was at Queens College, and this was a 600 level course – it was designed as a first real course – and it was. In college I’d only done a philosophy department logic, similar to what I teach. This was new.

I want to describe the course and the people and what I did and didn’t do, briefly. The text was Enderton “A Mathematical Introduction to Logic.” Professor showed an earnestness, an excitement about the subject. Looked vaguely like a cross between Dr. James Wilson and Lt. Reginald Barkley. There were a few complaints that he was unclear, or explained poorly – but they were off-base. The subject was very hard – the professor spoke clearly, used vocabulary carefully, introduced ideas well, offered great board notes, provided illustrative examples – but the subject was just that hard.

There was one auditor for the first two or three weeks who seemed to be a retiree – but he got bored and disappeared, leaving me probably the oldest in the room. We lost about a quarter of the class before the mid-term. Maybe more. And we were down to about half by the end.

The text for this class was divided into four chapters. We covered the first two, and part of the third.

I made it through “Sentential Logic” relatively unscathed, running an A, and while I felt shaken a bit by the level of difficulty, more or less stayed on top of everything. Professor was really good with office hours, available, and wanting to help. We used induction, but differently than I had encountered it before. It took real getting used to. The concepts were fairly familiar, or I picked them up. Or struggled through them. I had to study, which is something I did precious little of when I was younger.

The second unit, First-Order Logic tripped me up. I lost my way with “substitutability” and never fully recovered.  What’s a language? What’s a Theory? What’s a model? What does it mean to “satisfy”?  What does it mean to be “definable”?  I have answers for all of these, but I’m not 100% sure when I answer. And sometimes I know what to say, and I’m not sure what my words mean.

We touched incompleteness and undecidability at the end. I certainly did not follow all of what we were doing there.

My final exam was weaker, and I ended up with a B+. Which doesn’t sound great. In fact, I think there were only 3 or so A’s in the class; my grade’s no embarrassment. And I learned enough that I would love to do this class again (or read something, but I doubt I could do it without a smart, clear professor, like this guy). It’s a situation where I know something between half and three-quarters, and where I am well-positioned to to boost that to 90+%.

It may have untangled some vocabulary issues for my teaching, but hardly. It was good to struggle against hard material. And it was fun to study with much younger students (I worked with a teacher, two grad students, and an advanced undergrad), some of whom ran academic rings around me.

Side-note. While I was taking this class, this blog got linked by a guy who shares my initials and probably teaches the exact same class at a different campus in the same university.

 

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6 Comments leave one →
  1. July 31, 2014 pm31 10:49 pm 10:49 pm

    Try the book Godel’s Proof — it’s quite readable, as books about math go. You’ll want the one with Hofsteder as an author:
    http://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/0814758371/ref=sr_1_1?ie=UTF8&qid=1406858951&sr=8-1&keywords=godel%27s+proof

    • August 1, 2014 pm31 6:05 pm 6:05 pm

      I feel like I’m close. This is something I might be able to successfully read on my own, I take it. At $9, I tossed it in my Amazon basket… I’ll probably keep it there at my next purchase. Thanks.

      • August 2, 2014 am31 11:40 am 11:40 am

        It’s been a long time for me, so my memory of it is not sharp, but I think it is realistic to try to read it on your own.

      • August 2, 2014 am31 11:41 am 11:41 am

        (And, the ideas are both elegant and powerful, so if you’re on the cusp I think the effort would definitely be worth it.)

  2. August 11, 2014 am31 10:27 am 10:27 am

    wow. great post. DRH doesn’t appear to actually *be* an “author” of nagel-newman. his _GEB,_an_EGB_ (1980) contains (as one of its main threads) a full proof of G’s thm. i read it the year it came out. took my a little over a month, i think, at probably about an hour or two a day or so. i had a logic course much later but with a very *un*inspiring teacher (and at “senior” rather than “first-year grad” level; together with a first-year course in set-theory, these filled some “course-distribution requirement” at my uni). so i don’t know much. it seems likely that the computer-science branch has much of the best work in these realms and that “language barriers” have slowed down its dissemination into philosophy and math ed and whatnot. but, again, my active interest was always weak and is now mostly long past.

    • August 15, 2014 pm31 10:55 pm 10:55 pm

      Yes, you’re right, I mean the version edited by him.

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