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
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)
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