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From: olcott <polcott333@gmail.com>
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Date: Wed, 21 May 2025 17:34:39 -0500
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On 5/21/2025 4:21 PM, Richard Heathfield wrote:
> On 21/05/2025 21:28, olcott wrote:
>> On 5/21/2025 3:13 PM, Richard Heathfield wrote:
>>> On 21/05/2025 20:28, olcott wrote:
> 
> <snip>
> 
>>>> I have only been talking about the ACTUAL
>>>> conventional proof of the halting problem.
>>>
>>> The ACTUAL conventional proof of the Halting Problem goes something 
>>> like this:
>>>
>>> 1) assume that it is possible to devise an algorithm that can 
>>> determine in finitely many steps ascertain whether an arbitrary 
>>> program applied to arbitrary data does or does not stop.
>>>
>>> 2) given such an algorithm, imagine incorporating it into a program 
>>> that ascertains whether a supplied program with supplied data halts, 
>>> loops if it does, and halts if it doesn't.
>>>
>>
>> This step is impossible.
> 
> Correct. We have derived an impossible consequence of our assumption, 
> thus proving that the assumption is false.
> 
>> It only seemed possible
> 
> No. It never seemed possible. It always seemed like the impossible 
> contradiction that it is.
> 
>> because no one ever
>> tried to completely encode every detail.
> 
> Why would they? One would have to be pretty stupid to try.
> 
>> This screwy mistake came about
> 
> It's not screwy, and it's not a mistake. It's a proof that there is at 
> least one thing which we'd like a computer to be able to do but which it 
> will never be able to do.
> 
> Like you said, it's impossible. QED.
> 
> 
>> because fools thought
>> that a halt decider H is supposed to report on the behavior
>> of the program that itself is contained within rather
>> than the behavior that its actual input actually specifies.
> 
> What your halt decider reports on is entirely up to you, but thanks to 
> Turing we know that it will not be able to act as a /universal/ 
> termination analyser that always gets the answer right regardless of the 
> input.
> 
> Sometimes? Sure. bool decide(whatever){return true;} will get it right 
> sometimes. But for some inputs your decider will get it wrong.
> 
>> int main()
>> {
>>    DDD(); // No HHH can report on the behavior of its caller.
>> }
> 

Show an actual input to HHH that actually does
the opposite of whatever value that HHH returns.



-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer