« logicnazi moves out | Main | On the BBC »
June 10, 2005
Kripke's Incompleteness Proof
Michael De, over at Lumpy Pea Coat, was wondering whether there is any literature on Kripke's version of Gödel's incompleteness proof. As he puts it:
Kripke gave a proof of the incompleteness theorem through ventriloquism in a lecture at Beijing University in 1984 using a very different (algebraic) approach, but I cannot find it anywhere. Does it exist? Has the lecture been transcribed? Anyone?
Richard Zach came through with the most important source, Putnam's "Nonstandard Models and Kripke's Proof of the Gödel Theorem" Notre Dame J. Formal Logic 41, no. 1 (2000), 53–58.
But I could also remember a talk that David Lewis gave at the University of Melbourne on Kripke and a version of the incompleteness proof, and Allen Hazen, who was in attendance, had turned out to have some rare notes that were relevant to the topic. Unfortunately it's not a lost Kripke manuscript, or even notes on a Kripke lecture, but, as Allen writes:
Notes Graham Solomon (Philosophy Dept, Wilfried Laurier University, deceased) sent me, coming from Bill Demopoulos (Philosophy Department, U of W Ontario), of -- not Kripke's original lecture, but -- a lecture by ... you guessed it ... Hilary Putnam.
Allen went on, in subsequent email:
Kripke, when he actually does write, gives marvelously followable expositions, and the proof is interestingly different from G's. More different than is George Boolos's proof, which I assume you are familiar with (ch. 26 of "Logic, Logic and Logic").
(In my opinion, it's worth listening when Allen says "I assume you are familiar with..." All through my Australian breaks from grad school he completed that sentence with the names of brilliant and wonderful things I'd never come across.)
He has also kindly given me permission to make the Putnam/Kripke/Solomon/Demopoulos notes available here, for anyone who's interested:
- First File (28kb pdf)
- Second file (28kb pdf)
Posted by logican at June 10, 2005 01:43 AM
Trackback Pings
The trackback address for this entry is:
http://www.logicandlanguage.net/trakbak.cgi/78
Comments
Isn't that Boolos proof the one that uses words of only one syllable? Or four letters or less? Or something like that? Too bad my copy is away in the office. And that I haven't (yet) read farther than the table of contents.
Posted by: Kenny Easwaran at June 10, 2005 04:40 AM
You're 4 chapters ahead of us! Chapter 30 is "Goedel's second incompleteness theorem explained in worlds of one syllable." This one contains harder words like "language", ""numbers" and "statement."
Posted by: Gillian Russell at June 10, 2005 09:56 AM
IIRC chapter 30 is only an explanation of the theorem, not a proof. Still cooler than ice cream, though, with bonus Byron quote.
Posted by: Matt Weiner ![[TypeKey Profile Page]](http://www.logicandlanguage.net/nav-commenters.gif)
at June 13, 2005 01:00 PM