My main logical resolution for 2015 is to get to know quite a bit more category theory. Well, it’s fun, I find it aesthetically very appealing, there are some super-smart category theory people here in Cambridge — and there seem to be enough lurking conceptual issues to engage the philosophical bits of my brain, though I want to know (a lot) more category theory before sounding off about them.

I’ve therefore now started a new section of Logic Matters on categories where I’ll be posting various stuff — starting with my slowly-expanding *Notes on Category Theory*, and eventually some book notes, links to on-line resources on Category Theory, and so on. Enjoy!

(Other New Year’s resolutions? One is to stop wasting time and endangering my blood pressure reading the comments on various Well Known Philosophy Blogs, comments which seem too often to be getting increasingly bonkers, unpleasant and — let’s hope — unrepresentative. Feeling better already …)

Rowsety MoidI’m of two minds about learning more category theory. It’s long been on my list of things to do, I’ve accumulated some books that I ought to read, and your notes look like an interesting road into the subject. However …

There seem to be two ‘sides’ to category theory. One is like an extra high level branch of algebra (Leinster’s “bird’s eye view”). That’s potentially interesting, but I’ve never been all that keen on algebra, and I often get a “so what?” feeling when bits of category theory appear in other contexts. Still, I think I may have finally reached the point of thinking I have make a more serious attempt to try it, to see if it becomes interesting or not. However …

The other side seems to be as a foundation for mathematics, an alternative to set theory. I would normally find that more interesting, but there are two problems. One is that it looks like you have to learn an awful lot of category theory before you can understand how it works as a foundation, and then it looks like you have to learn a bunch of other stuff too (such as homotopy type theory); and it all seems so

complicatedcompared to first-order logic + set theory. (In a way I’m glad I learned mathematical logic, set theory, and computing before type theoretic approaches gained so much ground. I’m not sure my interests in those subjects would have survived if I hadn’t.)The other problem is that there’s an ‘ideological’ element that I find quite off-putting. I’m reminded at times of what happened in AI when logic programming came along and many things started to be described as “___ done right” when they were done in Prolog.

Peter HancockI heartily endorse your first paragraph. I hope we’re both still alive when you are ready to start sounding off, or can gasp something intelligible to each other between our screams of torment. It is (mostly) a very beautiful, enlightening, yet exasperating subject.

To get in a position to sound off, or even to appreciate category theory, sadly, one actually needs to *do* it. Evisceration of category theorists sounding off about philosophy is (sometimes) a bit easier.

Peter SmithWell, I hope we can avoid actual torment, if not occasional exasperation.

David Auerbachyes, I implemented my version of your resolution even before the new year. Dispiriting but there is evidence for unrepresentative.