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 On Wed, Oct 22, 2008 at 7:48 PM, Mark Waser <[EMAIL PROTECTED]> wrote: > Most of what I was thinking of and referring to is in Chapter 10. Gödel's > Quintessential Strange Loop (pages 125-145 in my version) but I would > suggest that you really need to read the shorter Chapter 9. Pattern and > Provability (pages 113-122) first. > > I actually had them conflated into a single chapter in my memory. > > I think that you'll enjoy them tremendously. > > ----- Original Message ----- From: "Abram Demski" <[EMAIL PROTECTED]> > To: <[email protected]> > Sent: Wednesday, October 22, 2008 4:19 PM > Subject: Re: [agi] constructivist issues > > >> Mark, >> >> Chapter number please? >> >> --Abram >> >> On Wed, Oct 22, 2008 at 1:16 PM, Mark Waser <[EMAIL PROTECTED]> wrote: >>> >>> Douglas Hofstadter's newest book I Am A Strange Loop (currently available >>> from Amazon for $7.99 - >>> http://www.amazon.com/Am-Strange-Loop-Douglas-Hofstadter/dp/B001FA23HM) >>> has >>> an excellent chapter showing Godel in syntax and semantics. I highly >>> recommend it. >>> >>> The upshot is that while it is easily possible to define a complete >>> formal >>> system of syntax, that formal system can always be used to convey >>> something >>> (some semantics) that is (are) outside/beyond the system -- OR, to >>> paraphrase -- meaning is always incomplete because it can always be added >>> to >>> even inside a formal system of syntax. >>> >>> This is why I contend that language translation ends up being >>> AGI-complete >>> (although bounded subsets clearly don't need to be -- the question is >>> whether you get a usable/useful subset more easily with or without first >>> creating a seed AGI). >>> >>> ----- Original Message ----- From: "Abram Demski" <[EMAIL PROTECTED]> >>> To: <[email protected]> >>> Sent: Wednesday, October 22, 2008 12:38 PM >>> Subject: Re: [agi] constructivist issues >>> >>> >>>> Mark, >>>> >>>> The way you invoke Godel's Theorem is strange to me... perhaps you >>>> have explained your argument more fully elsewhere, but as it stands I >>>> do not see your reasoning. >>>> >>>> --Abram >>>> >>>> On Wed, Oct 22, 2008 at 12:20 PM, Mark Waser <[EMAIL PROTECTED]> >>>> wrote: >>>>>> >>>>>> It looks like all this "disambiguation" by moving to a more formal >>>>>> language is about sweeping the problem under the rug, removing the >>>>>> need for uncertain reasoning from surface levels of syntax and >>>>>> semantics, to remember about it 10 years later, retouch the most >>>>>> annoying holes with simple statistical techniques, and continue as >>>>>> before. >>>>> >>>>> That's an excellent criticism but not the intent. >>>>> >>>>> Godel's Incompleteness Theorem means that you will be forever building >>>>> . >>>>> . . >>>>> . >>>>> >>>>> All that disambiguation does is provides a solid, commonly-agreed upon >>>>> foundation to build from. >>>>> >>>>> English and all natural languages are *HARD*. They are not optimal for >>>>> simple understanding particularly given the realms we are currently in >>>>> and >>>>> ambiguity makes things even worse. >>>>> >>>>> Languages have so many ambiguities because of the way that they (and >>>>> concepts) develop. You see something new, you grab the nearest analogy >>>>> and >>>>> word/label and then modify it to fit. That's why you then later need >>>>> the >>>>> much longer words and very specific scientific terms and names. >>>>> >>>>> Simple language is what you need to build the more specific complex >>>>> language. Having an unambiguous constructed language is simply a >>>>> template >>>>> or mold that you can use as scaffolding while you develop NLU. Children >>>>> start out very unambiguous and concrete and so should we. >>>>> >>>>> (And I don't believe in statistical techniques unless you have the >>>>> resources >>>>> of Google or AIXI) >>>>> >>>>> >>>>> >>>>> ------------------------------------------- >>>>> 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/?&; >>>>> Powered by Listbox: http://www.listbox.com >>>>> >>>> >>>> >>>> ------------------------------------------- >>>> 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/?&; >>>> Powered by Listbox: http://www.listbox.com >>>> >>> >>> >>> >>> >>> ------------------------------------------- >>> 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/?&; >>> Powered by Listbox: http://www.listbox.com >>> >> >> >> ------------------------------------------- >> 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/?&; >> Powered by Listbox: http://www.listbox.com >> > > > > > ------------------------------------------- > 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/?&; > Powered by Listbox: http://www.listbox.com > ------------------------------------------- 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
