Mike, "Personally, I always have trouble separating out Godel and Tarski as they are obviously both facets of the same underlying principles."
This is essentially what I'm complaining about. If you had used Tarski's theorem to begin with, I wouldn't be bugging you :). --Abram On Fri, Oct 24, 2008 at 12:58 PM, Mark Waser <[EMAIL PROTECTED]> wrote: >> I'm making the point "natural language is incompletely defined" for >> you, but *not* the point "natural language suffers from Godelian >> incompleteness", unless you specify what concept of "proof" applies to >> natural language. > > I'm back to being lost I think. You agree that natural language is > incompletely defined. Cool. My saying that natural language suffers from > Godelian incompleteness merely adds that it *can't* be defined. Do you mean > to say that natural languages *can* be completely defined? Or are you > arguing that I can't *prove* that they can't be defined? If it is the last, > then that's like saying that Godel's theorem can't prove itself -- which is > exactly the point to what Godel's theorem says . . . . > >> Have you heard of Tarski's undefinability theorem? It is relevant to >> this discussion. >> http://en.wikipedia.org/wiki/Indefinability_theory_of_truth > > Yes. In fact, the restatement of Tarski's theory as "No sufficiently > powerful language is strongly-semantically-self-representational" also > fundamentally says that I can't prove in natural language what you're asking > me to prove about natural language. > > Personally, I always have trouble separating out Godel and Tarski as they > are obviously both facets of the same underlying principles. > > I'm still not sure of what you're getting at. If it's a "proof", then Godel > says I can't give it to you. If it's something else, then I'm not getting > it. > > > ----- Original Message ----- From: "Abram Demski" <[EMAIL PROTECTED]> > To: <[email protected]> > Sent: Friday, October 24, 2008 11:31 AM > Subject: Re: [agi] constructivist issues > > >> Mark, >> >> "It makes sense but I'm arguing that you're making my point for me . . . >> ." >> >> I'm making the point "natural language is incompletely defined" for >> you, but *not* the point "natural language suffers from Godelian >> incompleteness", unless you specify what concept of "proof" applies to >> natural language. >> >> "It emphatically does *not* tell us anything about "any approach that >> can be implemented on normal computers" and this is where all the >> people who insist that "because computers operate algorithmically, >> they will never achieve true general intelligence" are going wrong." >> >> It tells us that any approach that is implementable on a normal >> computer will not always be able to come up with correct answers to >> all halting-problem questions (along with other problems that suffer >> from incompleteness). >> >> "You are correct in saying that Godel's theory has been improperly >> overused and abused over the years but my point was merely that AGI is >> Godellian Incomplete, natural language is Godellian Incomplete, " >> >> Specify "truth" and "proof" in these domains before applying the >> theorem, please. For "agi" I am OK, since "X is provable" would mean >> "the AGI will come to believe X", and "X is true" would mean something >> close to what it intuitively means. But for natural language? "Natural >> language will come to believe X" makes no sense, so it can't be our >> definition of proof... >> >> Really, it is a small objection, and I'm only making it because I >> don't want the theorem abused. You could fix your statement just by >> saying "any proof system we might want to provide" will be incomplete >> for "any well-defined subset of natural language semantics that is >> large enough to talk fully about numbers". Doing this just seems >> pointless, because the real point you are trying to make is that the >> semantics is ill-defined in general, *not* that some hypothetical >> proof system is incomplete. >> >> "and effectively AGI-Complete most probably pretty much exactly means >> Godellian-Incomplete. (Yes, that is a radically new phrasing and not >> necessarily quite what I mean/meant but . . . . )." >> >> I used to agree that Godelian incompleteness was enough to show that >> the semantics of a knowledge representation was strong enough for AGI. >> But, that alone doesn't seem to guarantee that a knowledge >> representation can faithfully reflect concepts like "continuous >> differentiable function" (which gets back to the whole discussion with >> Ben). >> >> Have you heard of Tarski's undefinability theorem? It is relevant to >> this discussion. >> http://en.wikipedia.org/wiki/Indefinability_theory_of_truth >> >> --Abram >> ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
