> Turing's proof of Goedel's incompleteness is easier to understand than the original 300 page paper. Suppose you have a procedure to prove for any program that it either halts or not. Then I can write a program that takes another program as input. If the input halts, then my program loops forever, otherwise it halts. Now does my program halt when given itself as input?
Yeah, that's a nice short description. > And yeah, people have argued that AI is impossible because we can know things intuitively to be true without proof Well, I'd argue that nobody is trying to make "a procedure to prove for any (!) program whether it halts". Nobody knows how to get that God-like power anyway. We do know, however, how to make increasingly intelligent thinking machines, and no actual ceiling is in sight for that, and Gödel's theorem just doesn't apply. On Fri, 22 Feb 2019 at 19:58, Matt Mahoney <[email protected]> wrote: > Turing's proof of Goedel's incompleteness is easier to understand than the > original 300 page paper. Suppose you have a procedure to prove for any > program that it either halts or not. Then I can write a program that takes > another program as input. If the input halts, then my program loops > forever, otherwise it halts. Now does my program halt when given itself as > input? > > And yeah, people have argued that AI is impossible because we can know > things intuitively to be true without proof. > > On Fri, Feb 22, 2019, 11:08 AM Stefan Reich via AGI <[email protected]> > wrote: > >> > > By "formal incompleteness" I mean Goedel's proof that "every >> sufficiently powerful formal system is either inconsistent or incomplete". >> > >> > Oh. There are a variety of completeness and incompleteness theorems. >> They always struck me as being similar to other statements about ... >> completeness, closures, compactifications, entireness. So, like Banach >> spaces are complete. Great. Very important property, when you work with >> them, but otherwise its a propos nothing at all. Some other theory will be >> different. Its just one of those properties that systems have or don't >> have. But I never really read/looked/thought hard about that so I dunno. >> Doesn't strike me as important for for AGI or anything. >> >> Completely agree here, another refreshing view on things by Linas (he has >> a few of those). >> >> What Gödel proved is much overrated. Some people even take it to mean >> that "computers can't be as smart as humans" which is obviously not what >> the theorem says it all. >> >> Stefan >> > *Artificial General Intelligence List <https://agi.topicbox.com/latest>* > / AGI / see discussions <https://agi.topicbox.com/groups/agi> + > participants <https://agi.topicbox.com/groups/agi/members> + delivery > options <https://agi.topicbox.com/groups/agi/subscription> Permalink > <https://agi.topicbox.com/groups/agi/T581199cf280badd7-Mf3c88fe25ccae4f2aa16de1d> > -- Stefan Reich BotCompany.de // Java-based operating systems ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/T581199cf280badd7-M388bf68c0ef712bd6fb5cbca Delivery options: https://agi.topicbox.com/groups/agi/subscription
