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On 5/13/25 5:16 PM, olcott wrote:It is nuts to propose the idea of a universalOn 5/13/2025 12:06 PM, Richard Heathfield wrote:Except that we can't. And that just shows you don't understand the nature of the problem.On 13/05/2025 17:21, dbush wrote:>On 5/13/2025 12:01 PM, olcott wrote:>
<snip>
>>The actual reasoning why HHH is supposed to report>
on the behavior of the direct execution of DD()
instead of the actual behavior that the finite
string of DD specifies:
Quite simply, it's the behavior of the direct execution that we want to know about.
Why?
>
DDD doesn't do anything interesting.
>
If it were a universal halt decider we'd have a reason to care, because its very existence would overturn pretty much the whole of computability theory and enable us to clean up many of the unsolved problems of mathematics.
>
Sure and we could achieve the same thing by
simply hard-coding the actual all-knowing
mind of God into a formal system.
HHH(DDD) is correct to reject its input as non-halting>Right, but since D halts, H(D) returning 0 is just wrong.
The question is not about any universal halt
decider that must be literally all knowing.
>
It has always actually only been about things
that could prevent consistently determining
the halt status of conventional programs.
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