On Friday, November 23, 2012 11:54:57 AM UTC-5, Bruno Marchal wrote:
>
>
> On 22 Nov 2012, at 18:38, Stephen P. King wrote:
>
>  
>
>
>     How exactly does the comparison occur? 
>
>
>  By comparing the logic of the observable inferred from observation (the 
> quantum logic based on the algebra of the observable/linear positive 
> operators) and the logic obtained from the arithmetical quantization, which 
> exists already. 
>
>   
>
>     How does the comparison occur? I will not ask what or who is involved, 
> only how. What means exists to compare and contrast a pair of logics?
>
>
>
> The logic exists, because, by UDA, when translated in arithmetic, makes a 
> relative physical certainty into a true Sigma_1 sentence, which has to be 
> provable, and consistent. So the observability with measure one is given by 
> []p = Bp & Dt & p, with p arithmetical sigma_1 (this is coherent with the 
> way the physical reality has to be redefined through UDA). Then the quantum 
> logic is given by the quantization []<>p, thanks to the law p -> []<>p, and 
> this makes possible to reverse the Goldblatt modal translation of quantum 
> logic into arithmetic. 
> Comparison is used in the everyday sense. Just look if we get the quantum 
> propositions, new one, different one, etc.
>


The question is straightforward to me - what makes logical comparison 
happen? Let me try to tease out what you answer is here, because it is not 
obvious. 

The logic exists, because, 

so far so good. 

by UDA, 

Isn't UDA a logical construct already? Is your answer to 'what makes logic 
happen?' rooted in the presumption of logic? That's ok with me, but you 
don't need any smoke or mirrors after that, you are pretty much committed 
to 'because maths' as the alpha and omega answer to all possible questions. 

when translated in arithmetic, makes a relative physical certainty into a 
true Sigma_1 sentence, which has to be provable, and consistent. 

Proof and consistency, again, are already features of logic. What makes 
things true? How does it actually happen?

So the observability with measure one is given by []p = Bp & Dt & p, with p 
arithmetical sigma_1 (this is coherent with the way the physical reality 
has to be redefined through UDA). Then the quantum logic is given by the 
quantization []<>p, thanks to the law p -> []<>p, and this makes possible 
to reverse the Goldblatt modal translation of quantum logic into 
arithmetic. 


Way over my head, but it sounds like logic proving logic again. 

Comparison is used in the everyday sense.

Yes! Now that I understand. What's wrong with the 'everyday sense' being 
the reality and the specialized logic being one category of specialized 
mechanisms within that?
 
Craig

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