Wednesday, December 31, 2008

A few reflections on the fall term

I'm slightly late with this, but I'll go ahead with it anyway. A few posts ago I said that I'd come up with some reflections on the term. This is more for my benefit than for the benefit of others, but someone might find it interesting. Read more

This term I took three classes: proof theory with Belnap, philosophy of math with Wilson, and truth with Gupta. They meshed well. I had hoped that I would generate a prospectus topic out of them. I have some ideas, but nothing as concrete as a prospectus topic. I also met regularly with Ken Manders to talk about prospectus ideas. This helped me come up with some promising stuff that I'll hopefully work out some over the next few weeks.

I'll start with the proof theory class. This was class number two on the topic. This time around it was with Belnap and it focused on substructural logics, particularly relevance logic. I was happy with that since I've been lately bitten by the relevance logic bug. We did some of the expected stuff and spent a while going through Gentzen's proof of cut elimination in detail. I think I got a pretty good sense of the proof. What I was rather pleased with was the forays into combinators and display logic. We did some stuff with combinators in the other proof theory class, but it was relatively unclear to me, at the time, why. This time the connection between combinators and structural rules was made clear. Display logic is, I think, quite neat. I ended up writing a short paper on some philosophical aspects of display logic.

Next up is the the philosophy of math class with Wilson. The focus of the class was on Frege's philosophy of math, particularly as it related to some of the mathematical developments of his time. I'm not sure how much it changed my view of Frege. I think it did make it clear that interpreting Frege is less straightforward than I previously thought. I'm more convinced of the importance of seeing Frege's work in logic in the context of the worries about number systems and foundations going on in the late 19th century. I suspect that the long-term upshot of this class will be what it got me to read. I was turned on to a few books on the history of math, e.g. Gray's and Grattan-Guinness's. There is a lot of material in those books on the development of concepts that is fairly digestible. I'm thinking about writing a paper on concept development in the late 19th century in something like the vein of Wandering Significance. We'll have to see how that goes. Through some of these readings I got a bit stuck on how to characterize the algebraic tradition in logic. There's something distinctive there, especially when compared to Frege's views, and I'd like to have a better sense of what is going on. It seems like it would help with interpreting the Tractatus.

Last is Gupta's truth and paradox seminar. We covered hierarchy theories of truth briefly, moved on to fixed point theories, then spent a long while on the revision theory as presented in the Revision Theory of Truth. This class was excellent. I think I got a decent handle on the basic issues in theories of truth. There was a lot of formal work and that was balanced against non-formal philosophical stuff fairly well. I'm doubtful I will write a dissertation on truth theory, but one upshot is that it has given me some good perspective on the notions of content and expressive power. These are treated well in RTT, and the discussion there has helped me generate some ideas that I'm trying to develop. The other upshot is that I got to study circular definitions. I have an interest in definitions anyway, and circular definitions, I've confirmed, are awesome. I wrote a short paper for this class on some things in the proof theory of circular definitions. I think it turned out well.

As I mentioned before, I've finished my coursework as of this term. Next term I'll be focusing primarily on working out a prospectus. I'll also be attending a few seminars: category theory with Steve Awodey, philosophy of math with Manders, and the later Wittgenstein with Ricketts. I'm not sure to what degree, if at all, these will figure in my dissertation, but they seem too good to pass up.

Blogging has been somewhat light this term, since I got a bit overburdened with regular meetings with professors, finishing some papers, and taking two logic classes. It was fairly productive though. Posting should increase some next term. (There's been a general slow down in the philosophy blogosphere, at least the parts I read, this semester that I'm a little bummed to have contributed to, but maybe things will perk up going forward, or maybe not.)

Next term should start well. The classes look good. I'm going to get to spend the next few weeks finishing up some reading and trying to formulate a few thoughts better. In late January, Greg Restall will be giving a talk at Pitt, which should be fun.

Also, this was post number 400 for my blog. Between all the announcements and links, that means I've gotten a good 200 or so vaguely philosophical posts online.

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