Monday, August 20, 2007

Links, or, theft 2, honest toil 0

This is not news by any means, but there are a few good entries in the Stanford Encyclopedia that are worth bringing everyone's attention to. The first is the algebra entry. It is written by Vaughan Pratt. Both Restall's Introduction to Substructural Logics and Dunn and Hardegree's Algebraic Methods in Philosophical Logic make it clear that there are important links between algebra and various areas of logic. Both books are also very well written, although Restall's has an unfortunate number of typos. There is also an entire entry on the mathematics of boolean algebra, which at first brush seems to be the least well written of the three. Finally there is an article on category theory, which I gather isn't that popular as a subject except at Carnegie Mellon and among some physicists. Eventually they will teach it again at CMU and I will take it; then I will be able to comment on the SEP article. It looks good to my untutored eye though.


Kenny said...

The article on algebra seems somewhat uneven. I took Vaughan Pratt's algebraic logic class at Stanford, so I remember seeing a lot of that stuff. But he sometimes explains very basic things, and then sometimes presupposes complicated definitions that he doesn't mention. I think he's writing the article just as a central place that mentions many of the results, but it's a bit idiosyncratic I think, given that it basically says nothing about algebraic number theory, and lots about lattices.

Shawn said...

It had been a while since I looked at the algebra entry. I agree; it is a bit idiosyncratic. I think I didn't mind it so much since the algebraic concepts I am most familiar with are the ones that get deployed in talking about logic. Lots of lattices, little number theory. (At least, as far as I can tell right now.) It is a bit weak as an overview of all of algebra, but it gives a bit of a taste of things in algebraic logic. Maybe they should rename the article "algebraic logic" and write a new algebra entry?

You took a class from Pratt on algebraic logic? That is pretty cool. I had wondered why he wrote the SEP entry. I had only heard about him in relation to his work in dynamic logic. That was in a modal logic class taught by van Benthem. He said that Pratt left the field shortly after doing his major work in it. I take it he eventually went to algebraic logic.