I now have put together a first complete [updated, now third] draft of the second edition of Gödel Without (Too Many) Tears. You can download it here.
I need to do a careful read-through for typos/thinkos. I also need to update the index, make the typography more uniform between chapters, and e.g. decide on a more consistent policy about when I cross-reference to IGT2. That sort of fun to come over the next month or so. I’ll post updates from time to time, and the link above will keep pointing to the current draft version of GWT2.
It is too late to write a very different book, and after all this is supposed to be just a revised edition of the seemingly quite well-liked GWT1! This is not the moment, then, for radical revisions. But otherwise, all suggestions, comments and corrections, including quick notes of the most trivial typos, will be most welcome! Send to the e-mail address on the first page of PDF, or comment here. (Just note the date of the version you are commenting on.)
Actually, many readers of this blog will have better things to do than spend much time with this sort of intro-level enterprise (though massive thanks are due to a handful who have already been e-mailing comments). But if you aren’t a student yourself, you could well have students who would be interested to take a look and let me know what they find too obscure, and/or give other comments and corrections. (Back in the day, I lined up a whole team of volunteers to look at a couple of chapters each of IGT2: and there turned out to be precisely zero correlation between “status”, from undergraduate to full professor, and the usefulness of comments!) So do please spread the word to any students, undergraduate or graduate, who might be — or ought to be! — interested.
It’s not much of a bribe, I know, but those impoverished students who prompt the biggest corrections/improvements will get a free paperback in due course, as well as having their name in lights in the Preface!
Added: Latest version, linked above, Thursday 12 September.
3 thoughts on “GWT2 — a first full draft”
Version of 3 September 2022:
I think more is different about this edition than the preface makes it seem. There are more chapters, for a start, and an appendix on Kripke. There are enough differences that I turned to the preface hoping for an overview of what they were; but beyond saying it “somewhat expands the material on recursive functions”, the preface mentions only correcting errors and small stylistic improvements.
I’m not thinking there should be a long discussion. A bit more would be helpful though, at least to people who have the 1st edition and are wondering whether to get the 2nd.
Chapter 18, Decidability, and the Halting Problem
p 123, “Because there is no effective way of deciding whether a recursive function g is regular” — it would be helpful to have “regular” in the index.
Chapter 21, Complications
p 137, 1st par: “prove its now consistency” — should be “own”
“This final chapter briefly explores.” — what does it explore? (I think this sentence could just be deleted.)
p 141 ” But there is more to be said (though not here).” Where, then? Seems worth a footnote
Also, “Though this time, the application of his variant Lemma …” This time … his? Was the approach in the previous paragraph also Kirpke’s? Also not clear to me quite what the contrast with the other “time” is meant to be? Did it also involve a variant Lemma?
Re O1 “We can still effectively determine (without open-ended searches) whether a given wff is an axiom – why?” I don’t know. How obvious is it meant to be?
P 142, O2 “then the only new wffs we can prove will be wffs with those constants” — I’m not sure what “with those constants” means. Wffs in which such constants appear? Wffs that correspond to such constants via the numbering scheme?
O3 “Just use the c-axioms and Leibniz’s Law” — “Leibniz”and his law aren’t in the index, btw.
p 144: “§§18.4 and 18.4” — they are the same section
p 144, last sentence: “Those first two books” — why not just “Those two books”?
Also, why a colon rather than a comma after “background”
And why “even more experienced” rather than “more experienced”?
In fact the Kripke appendix is just §13.5 of the first edition. That section was a last minute addition to GWT1, prompted by Kripke’s 2020 publication of his argument. But (i) I think the discussion is too distracting to leave where it was; while (ii) on balance I didn’t want to delete it as it was one of the few novelties in the book! Hence it is now an appendix.
I take the point about saying just a bit more about the differences between the first edition and the new one (either in the Preface, or on the associated web-page).
Thanks for the other comments/corrections!
I was wondering “how did I manage to miss §13.5?” Then I figured it out when I tried searching for “Kripke” again. I was misled by the (often annoying) way search now works in Preview. Instead of showing each occurrence, it groups them by sections (which in GWT seem to be chapters). So if I click on a “Kripke” in the sidebar, it takes me to the first on in the chapter. (To see the others, it seems I have to scroll.) I’d forgotten about that ‘feature’ and so didn’t notice I hadn’t looked at all the “Kripke”s.
Do you (or anyone else reading this) know a way to change this behaviour?