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!
3 thoughts on “Back to Gödel Without Tears — but not a MOOC”
I hope that this doesn’t mean the end of the TYL serie
By happy(?) coincidence, this spring term I’ll be teaching my bi-annual version of Advanced Logic, which here means not so advanced. I’ll be using B&J 3rd, but it would be both fun and useful to interleave GW(tm)T. I would, of course, undertake to collect feedback and pass it on.
I assume that the objective is to collect comments that can then be used to improve the notes, so that once each comment has affected the notes, it can be discarded. If this is a mistaken assumption, and the objective is to create a standing resources of comments, which users of the notes can read, and to which they can add, year after year, an external forum is probably the right thing to use.
If the objective is what I assume it to be, then the advantage of an external forum is that it allows you to have several discussion threads, with highly descriptive titles, so that all comments on the same point (apart from the few accidentally posted in the wrong threads) get collected together. If you anticipate dozens of comments in response to each blogpost, that might be helpful. But if there are likely to be only a modest number of responses, or if each blogpost is tightly focused on one topic, the effort that people would have to make to go to another forum, and presumably to log into it, and the risk of losing commentators simply on account of that effort, might outweigh any advantage from having comments sorted by topic.
You might try to get the best of both worlds by inviting comments on the blog, but asking people to include highly descriptive headings at the starts of their comments, so that you and other readers can quickly pick out which comments go with which other comments.
If you can think of the likely topics in advance, would it be worth your starting the comments by inserting several comments, each simply naming a topic? Then others could put their comments under the relevant headings, by using the option of replying to the appropriate initial comment. Anyone who thought of a new topic could do the same thing: start with a comment that gave the topic’s title, then reply to that comment. This would reproduce the effect of several threads on a forum.
Finally, it may be worth reminding your readers, at the end of each post, how to open, and how to close, the math environment. Commentators are quite likely to need to use it.