> On 22 Apr 2018, at 19:28, John Clark <johnkcl...@gmail.com> wrote:
> 
> On Sun, Apr 22, 2018 at 12:21 AM, Russell Standish <li...@hpcoders.com.au 
> <mailto:li...@hpcoders.com.au>> wrote:
> 
> >> How can I determine if that particular Turing Machine is doing something 
> >> fundamentally different from what every other Turing Machine is doing?
> 
> > I would say that it is a machine that proves Loeb's theorem.
> A machine that could show that Loeb’s theorem was consistent with 
> Zermelo–Fraenkel set theory plus the axiom of choice and its negation was not 
> but could do nothing else would display no more general intelligence than a 
> chess program or a checkers program or even a tic tac toe program. 
> 
> 

?

Löb’s theorem is a scheme of theorem of arithmetic, or ZF. That has to be as 
consistent than arithmetic or set theory.


> > Not all Turing machines are capable of that, even universal machines absent 
> > the right software.
> Without the right software a universal machine is not capable of doing 
> anything,
> 

?

A universal machine is the right software able to do any computation. But of 
course not all proof. It need the scheme of induction formulas. RA and PA are 
Turing universal, but only PA is Löbian (it can prove its own universality and 
the consequences of it).


> with the right software it can calculate anything that can be calculated 
> including loeb’s theorem.
> 
> 


That does not make sense. Usual confusion compute/prove.

Bruno

> 
>  >​>​ There is no way I can ever know if Hod Lipson 's robots are self aware, 
> I don't even know if Hod Lipson is self aware, all I know for sure is that 
> both behave intelligently. 
>  
> > His argument is that his robot is self-aware, for some operational 
> > definition of self-aware.
> If his definition is operational it must involve intelligent behavior, I 
> don’t see how it could be otherwise.
> 
> 
> ​ ​John K Clark
> 
> 
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