For a number of years, when I taught a course on Gödel’s incompleteness theorems, I distributed handouts, which — as is the way of these things — grew and grew and eventually became early drafts of An Introduction to Gödel’s Theorems. But when it was eventually published, even the first edition of the book was over 350 pages long. So I then found myself writing another set of handouts for classroom use, an introduction to the Introduction, as it were! The most recent version of those handouts has been freely available here for a couple of years as Gödel Without (too many) Tears, and this has been downloaded about 4000 times.
Well, since GWT was last revised, I’ve put together a second edition of the Gödel book; so it would be useful to now update GWT (and to add some sections to correspond to the final chapters of the book as well). So here’s a plan.
Starting on Monday 15th October, I’ll be posting eight weekly instalments of a new version of Gödel Without (too many) Tears. This first tranche should take us up to the First Theorem. Then we’ll start again in the new year on Monday 20th January with another eight instalments.
The dates happen to be chosen to fit term dates here in Cambridge, but also (rather more importantly) to spread the load for me. Much better to commit to a slow delivery, than promise to rattle through faster and then not keep to schedule.
I’ll try to ensure that these freely available notes can be used as a stand-alone introduction to the incompleteness theorems as well as being an accompaniment to the second edition of the book. So this will be a sort of online course. Not an official MOOC, though, but something very much more informal. No teaching assistants grading stuff, no online tests, no accreditation — just some reader-friendly PDFs, maybe a short video or two, and intellectual fun to be had!
Still, I’ll no doubt be happy to give at least some backup and make some responses to queries. I’m still thinking a bit about how and where best to do that. I don’t particularly want to faff about e.g. setting up special discussion forum software on the logicmatters site. So one option would be to use an external service like ProBoards.com. Another option would be to keep things even simpler: invite reports of typos, thinkos, or obscurities in the appropriate comments boxes on pages here, and suggest that anyone with a substantive question which might be of more general interest ask it on math.stackexchange.com (where, with luck, I won’t be the only person answering — so you could get a helpfully different angle on some sticking point). But I’d welcome thoughts about this.
Anyway, spread the word that this sort-of-a-course is coming up!