Delayed by distractions of one sort and another, I’ve now finished the first draft of a new chapter for the Beginning Mathematical Logic Study Guide. Earlier in the month, I posted a draft version of Part I of the revised Guide (i.e. Chapters 1 to 9). And now — drum roll and fanfare — here at last is
A draft of the first chapter of Part II, Chapter 10 on Modal Logics.
As always, comments are extremely welcome. If you want to know how this new chapter fits into the overall shape of the Guide, and hence its intended purpose, take a quick look at the short §§1.2–1.4 in Part I.
So, as they say, enjoy! I certainly much enjoyed rereading Boolos when writing about provability logic in particular.
Afterthought: This Chapter 10 is quite long. On reflection, I’m now rather inclined to divide it into a chapter on modal logics and a chapter on provability logic.
A further afterthought: To my considerable surprise, I find that the earlier Boolos book is not available at the Usual PDF Repositories … so (for many readers) it won’t be at all helpful to have it as the main recommendation on provability logic. So I will revise accordingly.
In your “Beklemishev’s worm” post, you wrote that you “found Boolos’s The Logic of Provability rather less easy going than (you’d) remembered it”. That book has always seemed quite hard going to me, and I’m surprised when I see comments from reviewers saying it has a “gentle, friendly style” or is “remarkably easy to read.” So I was intrigued, and then pleased, to see his earlier The Unprovability of Consistency as the main recommendation instead, because it seems considerably friendlier, even where the two books are discussing essentially the same thing.
What you say in the current post seems very different: you “much enjoyed rereading Boolos when writing about provability logic in particular.” However, it’s not clear which book(s) that’s about. Was finding The Logic of Provability less easy going than you’d remembered a temporary phenomenon, now past? And if so, is there anything you could say, and perhaps put in the Guide, that might help other readers get past the point of finding it rather impenetrable?
No, I did mean I much enjoyed revisiting the earlier Boolos book. I still prefer it. My added afterthought was prompted by the fact that the earlier version is not available in the now usual way, so I’ll need to revise the entry somehow to take account of that (I imagine that readers of the Guide aren’t rushing to physical libraries these days!). But I think I’ll still make my current preference order clear.
In my teaching I’ve moved from Girle to Priest (and then to self-made lecture notes) because the Girle book is so full of errors. I wouldn’t call Humberstone’s book a survey, or recommend it as such. It’s really only useful after you’ve already read a few introductory texts on the covered topics.
Your comments on Cresswell’s intro to modal logic?
There are a few comments on one book of Cresswell’s at the top of p. 129. Did you have something else in mind?