Le 30-mai-07, à 16:00, Bruno Marchal a écrit :
Le 29-mai-07, à 07:31, Russell Standish a écrit :
On Tue, May 29, 2007 at 03:05:52PM +0200, Bruno Marchal wrote:
Of course many things depends on definitions, but I thought it was
clear that I consider that any theorem prover machine,
Le 29-mai-07, à 07:31, Russell Standish a écrit :
On Tue, May 29, 2007 at 03:05:52PM +0200, Bruno Marchal wrote:
Of course many things depends on definitions, but I thought it was
clear that I consider that any theorem prover machine, for a theory
like ZF or PA, is already self-aware.
Le 26-mai-07, à 22:32, Russell Standish a écrit :
On Fri, May 25, 2007 at 04:00:40PM +0200, Bruno Marchal wrote:
Le 25-mai-07, à 04:12, Russell Standish a écrit :
I don't think anyone yet has managed a self aware formal system,
I would say all my work is about that. You can interpret
On Tue, May 29, 2007 at 03:05:52PM +0200, Bruno Marchal wrote:
Of course many things depends on definitions, but I thought it was
clear that I consider that any theorem prover machine, for a theory
like ZF or PA, is already self-aware. And of course such theorem prover
already exist
On Fri, May 25, 2007 at 04:00:40PM +0200, Bruno Marchal wrote:
Le 25-mai-07, à 04:12, Russell Standish a écrit :
I don't think anyone yet has managed a self aware formal system,
I would say all my work is about that. You can interpret Godel's
theorem, or more exactly the fact that
Hi everybody,
I need to clarify. When we build this new combined system, we would be
immune to Godelian statements for one of them not for the whole system,
whatever it might be. So Jesse's argument does not hold, and of course the
new system does not contradict the Godel's theorem, it's (was!)
Mohsen Ravanbakhsh wrote:
Hi everybody,
I need to clarify. When we build this new combined system, we would be
immune to Godelian statements for one of them not for the whole system,
whatever it might be. So Jesse's argument does not hold, and of course the
new system does not contradict the
On 5/26/07, Jesse Mazer [EMAIL PROTECTED] wrote:
Mohsen Ravanbakhsh wrote:
Hi everybody,
I need to clarify. When we build this new combined system, we would be
immune to Godelian statements for one of them not for the whole system,
whatever it might be. So Jesse's argument does not hold,
Stephen Paul King wrote:
Dear Jesse,
Hasn't Stephen Wolfram proven that it is impossible to shortcut
predictions for arbitrary behaviours of sufficienty complex systems?
http://www.stephenwolfram.com/publications/articles/physics/85-undecidability/
Stephen
The paper itself doesn't
*Russell,*
*Sounds plausible that self-aware systems can manage this. I'd like to
see this done as a formal system though, as I have a natural mistrust
of handwaving arguments! *
I like it too :).
I think the computational view would help in construction.
*Jesse,
I definitely don't think the two
Le 24-mai-07, à 19:32, Mohsen Ravanbakhsh a écrit :
Thanks for your patience! , I know that my arguments are somehow
raw and immature in your view, but I'm just at the beginning.
S1 can simulate S2, but S1 has no reason to believe whatever S2 says.
There is no problem.
Hofstadter
Mohsen Ravanbakhsh
*Jesse,
I definitely don't think the two systems could be complete, since
(handwavey
argument follows) if you have two theorem-proving algorithms A and B, it's
trivial to just create a new algorithm that prints out the theorems that
either A or B could print out, and
Bruno, et al.,
There is a CRITICAL FUNDAMENTAL ERROR in
Godel's papers and concept.
If a simpler 'less complete' system - which
-includes- its statements, attempts to make
-presumptive statements- about a 'more complete'
corresponding system ... and its relationship to
the simpler 'base of
Le 25-mai-07, à 04:12, Russell Standish a écrit :
I don't think anyone yet has managed a self aware formal system,
I would say all my work is about that. You can interpret Godel's
theorem, or more exactly the fact that machine can prove their own
provability logic, and even guess correctly
Hi Russell,
- Original Message -
From: Russell Standish [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Sent: Friday, May 25, 2007 12:14 AM
Subject: Re: Overcoming Incompleteness
On Thu, May 24, 2007 at 11:53:59PM -0400, Stephen Paul King wrote:
For me the question has always been how
Thanks for your patience! , I know that my arguments are somehow
raw and immature in your view, but I'm just at the beginning.
*S1 can simulate S2, but S1 has no reason to believe whatever S2 says.
There is no problem.
**Hofstadter strange loop are more related to arithmetical
self-reference or
Sounds plausible that self-aware systems can manage this. I'd like to
see this done as a formal system though, as I have a natural mistrust
of handwaving arguments!
On Thu, May 24, 2007 at 10:32:29AM -0700, Mohsen Ravanbakhsh wrote:
Thanks for your patience! , I know that my arguments are
to this too.
Jesse
From: Russell Standish [EMAIL PROTECTED]
Reply-To: [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Subject: Re: Overcoming Incompleteness
Date: Thu, 24 May 2007 23:59:23 +1000
Sounds plausible that self-aware systems can manage this. I'd like to
see this done as a formal system though
PROTECTED]
To: [EMAIL PROTECTED]
Subject: Re: Overcoming Incompleteness
Date: Thu, 24 May 2007 23:59:23 +1000
Sounds plausible that self-aware systems can manage this. I'd like to
see this done as a formal system though, as I have a natural mistrust
of handwaving arguments!
On Thu, May 24
Russell Standish:
You are right when it comes to the combination of two independent
systems A and B. What the original poster's idea was a
self-simulating, or self-aware system. In this case, consider the liar
type paradox:
I cannot prove this statement
Whilst I cannot prove this
Barwise's treatment of the Liar
Paradox?
http://en.wikipedia.org/wiki/Jon_Barwise
Kindest regards,
Stephen
- Original Message -
From: Russell Standish [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Sent: Thursday, May 24, 2007 10:12 PM
Subject: Re: Overcoming Incompleteness
You are right
On Thu, May 24, 2007 at 11:53:59PM -0400, Stephen Paul King wrote:
For me the question has always been how does one overcome
Incompleteness when it is impossible for a simulated system to be identical
to its simulator unless the two are one and the same.
Is it though? If the
PROTECTED]
To: [EMAIL PROTECTED]
Sent: Thursday, May 24, 2007 10:31 PM
Subject: Re: Overcoming Incompleteness
snip
The same thing would be true even if you replaced an individual in a
computer simulation with a giant simulated community of mathematicians who
could only output a given theorem
PROTECTED]
Reply-To: [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Subject: Re: Overcoming Incompleteness
Date: Thu, 24 May 2007 23:59:23 +1000
Sounds plausible that self-aware systems can manage this. I'd like to
see this done as a formal system though, as I have a natural mistrust
of handwaving
Le 22-mai-07, à 12:57, Mohsen Ravanbakhsh a écrit :
Hi everybody,
It seems Bruno's argument is a bit rich for some of us to digest, so I
decided to keep talking by posing another issue.
By Godel's argument we know that every sufficiently powerful system of
logic would be incomplete, and
Hi everybody,
It seems Bruno's argument is a bit rich for some of us to digest, so I
decided to keep talking by posing another issue.
By Godel's argument we know that every sufficiently powerful system of logic
would be incomplete, and recently there has been much argument to make human
an
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