Should this article more properly be moved to "Gödel number", or are the numbers better known by the "phonetic" form?
Wouldn't it make more sense to have both this and Goedel number just redirect to Gödel's incompleteness theorem? -- John Owens 11:15 Apr 9, 2003 (UTC)
Note that the exact form of the Gödel number encoding is unimportant: there just needs to be a 1:1 mapping between local statements and manipulable expressions such as integers. You can do clever stuff with arithmetic, or you can just follow Chaikin and use Lisp S-expressions -- The Anome 23:48 15 Jul 2003 (UTC)
John - you may well be right. But in defense of a separate article, I thought there could be a place for a slightly less formal article on this topic. Gödel lite, as it were. I personally struggled to grasp the technical side of the argument (as expert readers can no doubt tell(!)), and I hoped that other people like me might appreciate a practical demo along these lines. Anome - A paragraph along these lines at the end could be a good idea. I guess it's worth pointing out the difference between a single instantiation like this, and the mathematician's quest for a general exposition. Wikid 06:24 16 Jul 2003 (UTC)
Another thought - we could re-name this page Gödel numbers - demonstration, and link to it from the Gödel's incompleteness theorem article, while redirecting Gödel number to the main article as John suggests. I'll leave that decision to the meta-mind. Wikid 08:33 16 Jul 2003 (UTC)
Anome is correct, there are a number (infinite?) of different mappings that are possible for use in Gödel's proof. I believe Gödel's original numbering system, however, used prime numbers taken to different powers to differentiate between variables, sentential variables and predicate variables. The mapping currently demonstrated in the article only works for encoding symbols and formulas but not sequences of formulas, a necessary characteristic for Gödel's proof. --128.253.167.158 18:13, 24 Oct 2004 (UTC)