Ticking over quietly …

My short joint review of Volker Halbach’s and Leon Horsten’s not-now-so-recent books on truth (surprisingly published as a ‘Critical Notice’), which I’d already posted excerpts from here on the blog, is now online.

Things have been ticking over quietly since I sent off the book-I-promised-not-to-mention-again-until-the-dratted-thing-is-actually-published. But I have made a start in getting a page with sets of exercises under way. I envisage almost as many sets of exercises as there are chapters, which is a lot. And it is very slow work. For example, the very next set to be done, corresponding to the new Ch. 3 on the idea of effectively computable functions and effectively decidable sets, is planned to be almost a guided-teach-yourself-tour-through-the-very-basics-of-computability-theory: and doing this sort of thing well is not easy. So I certainly don’t promise a full set of exercises by publication day. But — at least when interspersed with other things — it should be fun to slowly put them together.

I was in two minds about whether do include sets of answers alongside the question sets. But in fact, the time consuming part of all this is deciding what to put in the exercises: writing up answers is just a quick check that all is well [nerdy aside: exam.sty is a nice LaTeX package for keeping everything in one document]. And the utilitarian calculation is that there will be more students who will be pleased to have answers than there are instructors who will be displeased to have to think up a few more exercises of their own if/when they want class tests! So I will be providing answers.

In other news, just before Christmas Joseph Jedwab very kindly sent me a depressingly long list of corrections for the reprinted, supposedly corrected, version of Intro to Formal Logic. Sigh. You can download a list from the link on the book’s page here. (I hope the corrections can be made in physical copies when the book is next reprinted.)

What else? I’ve been distracted a little (one of the better things about being retired is that you have time for this sort of distraction) by reading one of those Great Books which has been on my shelves for years, but never properly read — on this occasion, it’s Saunders Mac Lane’s Mathematics: Form and Function. It’s a remarkable achievement. It’s not always easy to follow, so there was a bit of skipping. But there was the pleasure of being re-acquainted with some bits of maths that I last met doing tripos aeons ago. And more seriously, there was the pleasure and instruction of being reminded (or getting to see) How It All Hangs Together. If you think, as that Sellars quote has it, that philosophy is in the business of “seeing how things … hang together”, then this is a philosophical exploration (quite apart from Mac Lane’s occasional tanglings with explicitly philosophical claims about mathematics). I guess it should be compulsory reading for any philosopher interested in mathematics, and I’m rather regretting only having dipped in it before.

A suitable accompaniment to reading Mac Lane? My Christmas present to myself. Yes, yes, I agree: no one needs quite so many discs of that composer! Yet they are endlessly enjoyable if undemanding listening. Warmly recommended!

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