On Wednesday, November 7, 2012 6:50:03 PM UTC-5, Stephen Paul King wrote:
>
>  On 11/7/2012 10:24 AM, Craig Weinberg wrote:
>  
>
>
> On Wednesday, November 7, 2012 8:19:03 AM UTC-5, Stephen Paul King wrote: 
>>
>> On 11/7/2012 7:42 AM, Craig Weinberg wrote: 
>> > Can anyone explain why geometry/topology would exist in a comp 
>> universe? 
>> > -- 
>> Hi Craig, 
>>
>>      So far it seems that there is only a singular set of countable 
>> recursive functions (or equivalent) and thus a single Boolean algebra 
>> for the Universal Machine. If the BA (of the Universal number or 
>> Machine) has an infinite number of propositions, how could it be divided 
>> up into finite Boolean subalgebras BA_i, where each of them has a 
>> mutually consistent set of propositions? 
>>      Additionally, how is 'time' defined by comp such that 
>> transformations of topologies can be considered. 
>>
>>  
> It occurs to me that computation can only occur where topological position 
> is borrowed from the physical, spacetime presence of persistent bodies. 
> Sense and static realism must exist a priori to computation.
>
> Craig
>  
> Hi Craig,
>
>     Yes, the set of equivalent computations (equivalent in the sense of 
> all are capable of generating the 1p content) can only occur if there is a 
> topological position. This position is "borrowed" from the space-time that 
> a set of persistent logics have in common. Remember, one Boolean algebra 
> has many different but equivalent Stone spaces as its dual and each Stone 
> space has as it dual many equivalent Boolean algebras. I am using the 
> concept of an equivalence class. A space-time is a Stone space that has 
> some evolution, so it is a sequence of Stone spaces. A computation is the 
> evolution of a Boolean algebra or, equivalently, a sequence of Boolean 
> algebras. S3nse is the 1p content/static realism of every Boolean 
> algebra/Stone space pair - like a snapshot of an experience. 
>     What must be understood is that there is an (at least) uncountable 
> infinity of these dual pairs and only a finite number of them can have a 
> Boolean algebra (equivalence class) between then, so this gives the 
> illusion of a finite universe of physical stuff for almost any finite 
> subset of dual pairs.
>
> -- 
>
>
As far as falsifying comp though, is there any reason for Boolean algebra 
in and of itself to present itself as a Stone dual? Why have any new 
ontological presentation of equivalence at all from a pure arithmetic 
motive?

Craig
 

> Onward!
>
> Stephen
>
>  

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