*To*: soft_skinned_space <empyre@lists.cofa.unsw.edu.au>*Subject*: RE: [-empyre-] replying to several posts*From*: Jim Andrews <jim@vispo.com>*Date*: Sun, 04 May 2003 15:48:13 -0700*Delivered-to*: empyre@bebop.cofa.unsw.edu.au*Importance*: Normal*In-reply-to*: <BADBE4D3.AAA1%simon@littlepig.org.uk>*Reply-to*: soft_skinned_space <empyre@lists.cofa.unsw.edu.au>

> > The 'undecidable proposition' was theorized and used by Godel. > ----- > Sorry to be pedantic. Incompleteness Theorem, the formal refutation of > Whitehead and Russell's theories. This secondarily led to the development of > the symbolic logics that made Turing's work possible. Yes, that is the larger picture, isn't it, as described at http://www.miskatonic.org/godel.html or, slightly more rigorously, http://www.myrkul.org/recent/godel.htm (I just did a search for 'Godel' and 'incompleteness' and there are scads of pages). The Incompleteness Theorem establishes that in a system/language of formal logic at least as powerful as one capable of supporting arithmetic, there will always be 'undecidable propositions'. That is, one cannot form a system of formal logic in which all well-formed propositions are either false or provably true. There are *always* truths that cannot be proved within the system (whatever the system). By the way, I think the argument on http://www.miskatonic.org/godel.html "that a computer can never be as smart as a human being because the extent of its knowledge is limited by a fixed set of axioms, whereas people can discover unexpected truths" is mistaken: Godel's proof says that even any formal system used by humans is incomplete. So the only question is whether the 'human system' is necessarily more comprehensive or flexible than a computer's system and it doesn't seem likely to me. I wonder whether, given any particular undecidable proposition, there exists an axiom that one could introduce into the system that would render the undecidable proposition a theorem? Of course, even if there does exist such an axiom for each undecidable proposition, even then, with infinitely many axioms, one could still apply the argument to show that that system also was incomplete. We are profoundly certain that we will never know all there is to know. We are profoundly certain that the range of thought and accessible truth can always be expanded via new language, and that no language will ever have all the answers. We see that the margins are attached to the foundations. How does this relate to digital poetry and programming? In any number of ways... 1. we see the intensity of its engagement with language--here we have Godel inquiring into the possibility of the 'completeness' of knowledge, expressable in language. And he finds that any conceivable language can never attain completeness. And this (drop-dead gorgeous) work that sees into the necessary incompleteness of (human and non-human) knowledge thereby provides some important groundwork for the invention of machines capable of expanding human knowledge in the way that the computer has and will--but will never be complete. 2. The soaring aspiration of this work--and yet its 'humbling' conclusions--seem to me to be way poetical. 3. Here we have work concerning the formal properties of language that is sooooooo far beyond pedantry and grammar rules that it has rocked the world with the full force of knowledge we associate with the fierce chemistry of the sun and knowledge of it. There is knowledge of atoms and the material world, physics. Then there is knowledge of the formal properties of language and thereby some knowledge of the incompleteness of any and all epistemologies. Yet with that knowledge goes the ability to extend knowledge into the digital age. And the promise of much more to come. 4. Poetry and programming... ja x . . . . . . x . . . . . . x . . . . . . . . . . . .

**Follow-Ups**:**Re: [-empyre-] replying to several posts***From:*Simon Biggs <simon@littlepig.org.uk>

**References**:**Re: [-empyre-] replying to several posts***From:*Simon Biggs <simon@littlepig.org.uk>

- Previous by Date: Re: [-empyre-] re machine interfaces
- Next by Date: Re: [-empyre-] Welcome Jim Andrews re: Electronic Poetry
- Previous by Thread: Re: [-empyre-] replying to several posts
- Next by Thread: Re: [-empyre-] replying to several posts
- empyre May 2003 archives indexes sorted by: [ thread ] [ subject ] [ author ] [ date ]
- empyre list archive Table of Contents
- More information about the empyre mailing list