>> Well, if you are a computable system, and if by "think" you mean "represent
>> accurately and internally" then you can only think that odd thought via
>> being logically inconsistent... ;-)
True -- but why are we assuming *internally*? Drop that assumption as Charles
clearly did and there is no problem.
It's like infrastructure . . . . I don't have to know all the details of
something to use it under normal circumstances though I frequently need to know
the details is I'm doing something odd with it or looking for extreme
performance and I definitely need to know the details if I'm
diagnosing/fixing/debugging it -- but I can always learn them as I go . . . .
----- Original Message -----
From: Ben Goertzel
To: agi@v2.listbox.com
Sent: Tuesday, October 21, 2008 11:26 PM
Subject: Re: [agi] constructivist issues
Well, if you are a computable system, and if by "think" you mean "represent
accurately and internally" then you can only think that odd thought via being
logically inconsistent... ;-)
On Tue, Oct 21, 2008 at 11:23 PM, charles griffiths <[EMAIL PROTECTED]> wrote:
I disagree, and believe that I can think X: "This is a thought (T)
that is way too complex for me to ever have."
Obviously, I can't think T and then think X, but I might represent T
as a combination of myself plus a notebook or some other external media. Even
if I only observe part of T at once, I might appreciate that it is one thought
and believe (perhaps in error) that I could never think it.
I might even observe T in action, if T is the result of billions of
measurements, comparisons and calculations in a computer program.
Isn't it just like thinking "This is an image that is way too
detailed for me to ever see"?
Charles Griffiths
--- On Tue, 10/21/08, Ben Goertzel <[EMAIL PROTECTED]> wrote:
From: Ben Goertzel <[EMAIL PROTECTED]>
Subject: Re: [agi] constructivist issues
To: agi@v2.listbox.com
Date: Tuesday, October 21, 2008, 7:56 PM
I am a Peircean pragmatist ...
I have no objection to using infinities in mathematics ... they can
certainly be quite useful. I'd rather use differential calculus to do
calculations, than do everything using finite differences.
It's just that, from a science perspective, these mathematical
infinities have to be considered finite formal constructs ... they don't existP
except in this way ...
I'm not going to claim the pragmatist perspective is the only
subjectively meaningful one. But so far as I can tell it's the only useful one
for science and engineering...
To take a totally different angle, consider the thought X = "This
is a thought that is way too complex for me to ever have"
Can I actually think X?
Well, I can understand the *idea* of X. I can manipulate it
symbolically and formally. I can reason about it and empathize with it by
analogy to "A thought that is way too complex for my three-year-old past-self
to have ever had" , and so forth.
But it seems I can't ever really think X, except by being logically
inconsistent within that same thought ... this is the Godel limitation applied
to my own mind...
I don't want to diss the personal value of logically inconsistent
thoughts. But I doubt their scientific and engineering value.
-- Ben G
On Tue, Oct 21, 2008 at 10:43 PM, Abram Demski <[EMAIL PROTECTED]>
wrote:
Ben,
How accurate would it be to describe you as a finitist or
ultrafinitist? I ask because your view about restricting
quantifiers
seems to reject even the infinities normally allowed by
constructivists.
--Abram
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Ben Goertzel, PhD
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Director of Research, SIAI
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"Nothing will ever be attempted if all possible objections must be
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Ben Goertzel, PhD
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[EMAIL PROTECTED]
"Nothing will ever be attempted if all possible objections must be first
overcome " - Dr Samuel Johnson
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