I'm saying Godelian completeness/incompleteness can't be easily
defined in the context of natural language, so it shouldn't be applied
there without providing justification for that application
(specifically, unambiguous definitions of "provably true" and
"semantically true" for natural language). Does that make sense, or am
I still confusing?
It makes sense but I'm arguing that you're making my point for me . . . .
agree with. Godel's incompleteness theorem tells us important
limitations of the logical approach to AI (and, indeed, any approach
that can be implemented on normal computers). It *has* however been
overused and abused throughout the years... which is one reason I
jumped on Mark...
Godel's incompleteness theorem tells us important limitations of all formal
*and complete* approaches and systems (like logic). It clearly means that
any approach to AI is going to have to be open-ended (Godellian-incomplete?
;-)
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.
The later argument is similar to saying that because an inductive
mathematical proof always operates only on just the next number, it will
never successfully prove anything about infinity. I'm a firm believe in
inductive proofs and the fact that general intelligences can be implemented
on the computers that we have today.
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, 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 . . . . ).
----- Original Message -----
From: "Abram Demski" <[EMAIL PROTECTED]>
To: <agi@v2.listbox.com>
Sent: Thursday, October 23, 2008 11:42 PM
Subject: Re: [agi] constructivist issues
Mark,
I'm saying Godelian completeness/incompleteness can't be easily
defined in the context of natural language, so it shouldn't be applied
there without providing justification for that application
(specifically, unambiguous definitions of "provably true" and
"semantically true" for natural language). Does that make sense, or am
I still confusing?
Matthias,
I agree with your point in this context, but I think you also mean to
imply that Godel's incompleteness theorem isn't of any importance for
artificial intelligence, which (probably pretty obviously) I wouldn't
agree with. Godel's incompleteness theorem tells us important
limitations of the logical approach to AI (and, indeed, any approach
that can be implemented on normal computers). It *has* however been
overused and abused throughout the years... which is one reason I
jumped on Mark...
--Abram
On Thu, Oct 23, 2008 at 4:07 PM, Mark Waser <[EMAIL PROTECTED]> wrote:
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.
OK. Personally, I think that you did a good job of defining Godelian
Incompleteness this time but arguably you did it by reference and by
building a new semantic structure as you went along.
On the other hand, you now seem to be arguing that my thinking that
linguistic vagueness comes from Godelian incompleteness is wrong because
Godelian incompleteness can't be defined . . . .
I'm sort of at a loss as to how to proceed from here. If Godelian
Incompleteness can't be defined, then by definition I can't prove
anything
but you can't disprove anything.
This is nicely Escheresque and very Hofstadterian but . . . .
----- Original Message ----- From: "Abram Demski" <[EMAIL PROTECTED]>
To: <agi@v2.listbox.com>
Sent: Thursday, October 23, 2008 11:54 AM
Subject: Re: [agi] constructivist issues
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