Mark, My type 1 & 2 are probably the source of your confusion, since I phrased them so that (as you said) they depend on "intention". Logicians codify the intension using semantics, so it is actually well defined, even though it sounds messy. But, since that explanation did not work well, let me try to put it a completely different way rather than trying to better explain the difference between 1 and 2.
Godel's incompleteness theorem says that any logic with a sufficiently strong semantics will be syntactically incomplete; there will be theorems that are true according to the semantics, but based on allowed proofs, they will be neither true nor false. So Godel's theorem is about an essential lack of match-up between proof and truth, or as is often said, syntax and semantics. To apply the theorem to natural language, we've got to identify the syntax and semantics: the notions of "proof" and "truth" that apply. But in attempting to define these, we will run into some serious problems: proof and truth in natural language is only partially defined. Furthermore, those "serious problems" are (it seems to me) precisely what you are referring to. So to sum up, while you think linguistic vagueness comes from Godelian incompleteness, I think Godelian incompleteness can't even be defined in this context, due to linguistic vagueness. --Abram On Thu, Oct 23, 2008 at 9:54 AM, Mark Waser <[EMAIL PROTECTED]> wrote: >>> But, I still do not agree with the way you are using the incompleteness >>> theorem. > > Um. OK. Could you point to a specific example where you disagree? I'm a > little at a loss here . . . . > >>> It is important to distinguish between two different types of >>> incompleteness. >>> 1. Normal Incompleteness-- a logical theory fails to completely specify >>> something. >>> 2. Godelian Incompleteness-- a logical theory fails to completely specify >>> something, even though we want it to. > > I'm also not getting this. If I read the words, it looks like the > difference between Normal and Godelian incompleteness is based upon our > desires. I think I'm having a complete disconnect with your intended > meaning. > >>> However, it seems like all you need is type 1 completeness for what > > you are saying. >>> >>> So, Godel's theorem is way overkill here in my opinion. > > Um. OK. So I used a bazooka on a fly? If it was a really pesky fly and I > didn't destroy anything else, is that wrong? :-) > > It seems as if you're not arguing with my conclusion but saying that my > arguments were way better than they needed to be (like I'm being > over-efficient?) . . . . > > = = = = = > > Seriously though, I having a complete disconnect here. Maybe I'm just > having a bad morning but . . . huh? :-) > If I read the words, all I'm getting is that you disagree with the way that > I am using the theory because the theory is overkill for what is necessary. > > ----- Original Message ----- From: "Abram Demski" <[EMAIL PROTECTED]> > To: <[email protected]> > Sent: Wednesday, October 22, 2008 9:05 PM > Subject: Re: [agi] constructivist issues > > > Mark, > > I own and have read the book-- but my first introduction to Godel's > Theorem was Douglas Hofstadter's earlier work, Godel Escher Bach. > Since I had already been guided through the details of the proof (and > grappled with the consequences), to be honest chapter 10 you refer to > was a little boring :). > > But, I still do not agree with the way you are using the incompleteness > theorem. > > It is important to distinguish between two different types of > incompleteness. > > 1. Normal Incompleteness-- a logical theory fails to completely > specify something. > 2. Godelian Incompleteness-- a logical theory fails to completely > specify something, even though we want it to. > > Logicians always mean type 2 incompleteness when they use the term. To > formalize the difference between the two, the measuring stick of > "semantics" is used. If a logic's provably-true statements don't match > up to its semantically-true statements, it is incomplete. > > However, it seems like all you need is type 1 completeness for what > you are saying. Nobody claims that there is a complete, well-defined > semantics for natural language against which we could measure the > "provably-true" (whatever THAT would mean). > > So, Godel's theorem is way overkill here in my opinion. > > --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
