I apologize but it seems that none of us has time to explain other people's
ideas to each other or to read their papers for ourselves.

On Fri, Sep 16, 2016 at 11:27 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:

>
> On 16 Sep 2016, at 03:27, Stephen Paul King wrote:
>
> The idea is to think of computations as discrete, they do one thing:
> process one algorithm and halt.
>
>
> or not halt. You limit yourself to halting computation.
>
> If each halting computation is simpler than arbitrary computations, it
> happens that the notion of halting computations is more complex than the
> notion of arbitrary computations.
>
> For example, there is no universal halting machine, and there is no UD
> computting all and only all halting computations.
>
> The only way to generate all halting computations necessitate the
> generations of all computations, the halting one and the non halting. There
> is no algorithmic means to separate the halting machine from the non
> halting one.
>
> yet, the halting computations, when you get them all, is what structure
> the "measure space", and that is exploited to get the measure one case by
> the intensional ("material") variant of the self-reference logic,
> restricted to the "halting computations", modeled by the true sigma_1
> sentences.
>
>
>
> Obviously I am not talking about Turing machines...
>
>
> ?
>
> We seem to miss a precise idea of what you are talking about, I'm afraid.
>
> Bruno
>
>
>
>
>
> On Thu, Sep 15, 2016 at 9:03 PM, Brent Meeker <meeke...@verizon.net>
> wrote:
>
>>
>>
>> On 9/15/2016 4:29 PM, Stephen Paul King wrote:
>>
>>
>>
>> On Thu, Sep 15, 2016 at 6:47 PM, Brent Meeker <meeke...@verizon.net>
>> wrote:
>>
>>>
>>>
>>> On 9/15/2016 11:03 AM, Stephen Paul King wrote:
>>>
>>> I get that and buy it too, Brent. Platonia is the "flat" Complete
>>> version, I am looking for the infinite tower of incomplete yet consistent
>>> theories
>>>
>>>
>>> I don't understand what you mean by that.  I assume "theories" refers to
>>> axiomatic systems.  If I take one such system, like arithmetic, I can keep
>>> adding the unprovable Godel sentences as axioms and so create an unbounded
>>> "tower" of systems.  Is that what you mean?
>>>
>>
>> ​Yes, sorta.​
>>
>>
>>
>>>
>>>
>>> and trying to make sense of computational languages that could use those
>>> theories. Remember that computers do not need to be Turing Complete if they
>>> only need to compute one algorithm efficiently and correctly.
>>>
>>>
>>> That's the view of an algorithm as computing a function; so given an
>>> input there is a certain correct output.  But the UD doesn't have any input.
>>>
>>
>> ​It has itself as an input. :-P​
>>
>>
>> I suppose you can think of it as a null input.  But it also has not
>> output.  It doesn't halt.  So I'm not sure what you mean by computing one
>> algorithm efficiently and correctly.
>>
>> Brent
>>
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>
>
>
> --
>
> Kindest Regards,
>
> Stephen Paul King
>
> Senior Researcher
>
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>
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-- 

Kindest Regards,

Stephen Paul King

Senior Researcher

Mobile: (864) 567-3099

stephe...@provensecure.com

 http://www.provensecure.us/

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