### Re: Overcoming Incompleteness

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,

### Re: Overcoming Incompleteness

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.

### Re: Overcoming Incompleteness

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

### Re: Overcoming Incompleteness

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

### Re: Overcoming Incompleteness

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

### Re: Overcoming Incompleteness

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!)

### Re: Overcoming Incompleteness

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

### Re: Overcoming Incompleteness

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,

### Re: Overcoming Incompleteness

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

### Re: Overcoming Incompleteness

*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

### Re: Overcoming Incompleteness

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

### Re: Overcoming Incompleteness

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

### Re: Overcoming Incompleteness

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

### Re: Overcoming Incompleteness

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

### Re: Overcoming Incompleteness

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

### Re: Overcoming Incompleteness

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

### Re: Overcoming Incompleteness

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

### Re: Overcoming Incompleteness

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

### Re: Overcoming Incompleteness

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

### Re: Overcoming Incompleteness

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

### Re: Overcoming Incompleteness

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

### 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 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

### Re: Overcoming Incompleteness

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

### Re: Overcoming Incompleteness

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

### Re: Overcoming Incompleteness

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