On Thu, Aug 06, 2009 at 12:37:38PM +1000, Colin Hales wrote:
> 
> (b) is not a claim of truth or falsehood. It is a claim that the very 
> idea of <Sa> ever proposing COMP (= doubting that COMP is true) is 
> impossible. This is because it is a formal system trying, with a fixed, 
> formal set of rules (even self modifying according to yet more rules) to 
> construct statements that are the product of an informal system (a human 
> scientist). The very idea of this is a contradiction in terms. The 
> formal system is 100% deterministic, unable to violate rules. When it 
> encounters a liar it will be unable to resolve what falsehood is being 
> presented. It requires all falsehoods to be a-priori known. Impossible. 
> How can a formal system encounter a world in which COMP is actually 
> false? If it could, COMP would be FALSE! If COMP is true then it can't. 
> Humans are informal....ergo we have some part of the natural world 
> capable of behaving informally....=> GOTCHA!
> 
> This argument is has very 'Godellian' structure. That was accidental.
> 

I think all you have established with this is that the robotic
scientist can never know it is a robot. Therefore it can doubt
COMP. But this result is already a known theorem - which is why Bruno
says we can only bet on COMP.

-- 

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Prof Russell Standish                  Phone 0425 253119 (mobile)
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