Over three months after the last instalment, here is another helping of the draft version of the second edition of my Gödel book. To keep things simple, I am posting as a single document a corrected version of what are now Chapters 1 to 8, together with five more newly revised chapters, taking us up to the presentation of Peano Arithmetic. Very many warm thanks to those who sent corrections to the previous tranche of chapters: I hope I have at least caught the typos that were pointed out to me, and I’ve adopted also some helpful suggestions for small clarifications or changes of terminology. But I still have a few more substantive suggestions to further mull over.
This has been slow work. Do you remember that exchange from the Hitchhiker’s Guide to the Galaxy?
“If you’re a researcher on this book thing and you were on Earth, you must have been gathering material on it.”
“Well, I was able to extend the original entry a bit, yes.”
“Let me see what it says in this edition, then. I’ve got to see it. … What? Harmless! Is that all it’s got to say? Harmless! One word! … Well, for God’s sake I hope you managed to recitify that a bit.”
“Oh yes, well I managed to transmit a new entry off to the editor. He had to trim it a bit, but it’s still an improvement.”
“And what does it say now?” asked Arthur.
“Mostly harmless,” admitted Ford with a slightly embarrassed cough.
That’s rather how it has been at times, working on the second edition! Three days work digging around the literature. Mmm, what I said perhaps wasn’t absolutely accurate now I come to think about it again. But the exceptions are too exotic to worry about. What to do? Instead of saying P, say mostly P. And so it goes.
Anyway, rather belatedly, here is the current draft so far. Enjoy! And as always, comments and corrections are most welcome. The previously posted version was downloaded over 450 times, and although it would be too much of a good thing if everyone commented, far fewer do than you might guess. So please don’t hesitate to add your two pennyworth, even if you have simply spotted a silly typo. (A table of contents and the biblio can be found here.)
I am delighted that your book has done well enough to justify another edition. I have a few minor but I hope constructive comments – if you have already taken care of them, apologies. If you are overwhelmed with comments, just reply ‘enough’ and I will desist, but here is the first one.
On page 28 you discuss the properties that a formal language ought to have, but I don’t think you mention ‘unique readability’. This is not quite pure pedantry -several early high level computer languages came seriously unstuck on this point. Wars have been fought for less than the correct interpretation of a dangling ‘else’ clause.