Subject: Re: returning from a function (Ex: Re: some small proposed changes to standard) From: Erik Naggum <erik@naggum.no> Date: 1999/07/27 Newsgroups: comp.lang.lisp Message-ID: <3142057178277430@naggum.no> * rpw3@rigden.engr.sgi.com (Rob Warnock) | While it is certainly possible to create an editor that guarantees | that an initially valid SGML document remains valid after every | subsequent allowed editing step, Godel's Proof suggests that there | will always be some valid SGML documents which it is impossible | to create using such an editor. in what way is a mathematical proof a _process_ that resembles editing? Gödel's Incompleteness Theorem isn't a trivial statement of a problem with all sorts of complex systems. is very carefully constrained to say something about proofs _inside_ a complex system. it is possible to prove any mathematical theorem, but you might have to add something from outside the system to accomplish it. the incompleteness theorem states, as far as I have understood it, that no system is able to prove all its true statements within itself. I find that intuitively evident, because "truth" is already a concept that is not contained fully by the system. of course, I live in a post-Gödel time and lots of stuff that was very far from intuitively evident at the time is intuitively evident today, thanks in to the trailblazing efforts of geniuses past. however, Gödel's Incompleteness theorem is perhaps the single most mis-popularized theorem from mathematics there is, probably because people still believe in the pre-Gödel idea that truth is contained by a system, such as and especially religions. the above statement from Rob Warnock sounds like New Age flirting with quantum physics to me. it sounds profound because what it flirts with is profound, while it's really just unfounded and confused opinion. in other words: I'd really like to see some evidence that there exists a valid string in a regular syntax that cannot be produced by the grammar. #:Erik -- suppose we blasted all politicians into space. would the SETI project find even one of them?