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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Who here understands that the last paragraph is Necessarily true?
Date: Sun, 14 Jul 2024 17:41:43 -0400
Organization: i2pn2 (i2pn.org)
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On 7/14/24 10:38 AM, olcott wrote:
> On 7/14/2024 3:09 AM, Mikko wrote:
>> On 2024-07-13 20:15:56 +0000, olcott said:
>>
>>> typedef void (*ptr)();
>>> int HHH(ptr P);
>>>
>>> void Infinite_Loop()
>>> {
>>>    HERE: goto HERE;
>>> }
>>>
>>> void Infinite_Recursion()
>>> {
>>>    Infinite_Recursion();
>>> }
>>>
>>> void DDD()
>>> {
>>>    HHH(DDD);
>>> }
>>>
>>> int main()
>>> {
>>>    HHH(Infinite_Loop);
>>>    HHH(Infinite_Recursion);
>>>    HHH(DDD);
>>> }
>>>
>>> Any input that must be aborted to prevent the non
>>> termination of HHH necessarily specifies non-halting
>>> behavior or it would never need to be aborted.
>>
>> Everyone understands that DDD specifies a halting behaviour if 
>> HHH(DDD) does,
> 
> 
> *You can comprehend this is a truism or fail to*
> *comprehend it disagreement is necessarily incorrect*
> Any input that must be aborted to prevent the non
> termination of HHH necessarily specifies non-halting
> behavior or it would never need to be aborted.
> 
> Disagreeing with the above is analogous to disagreeing
> with arithmetic.
> 

But if HHH does abort and return 0, then the full correct simulaton of 
the input DDD (which need to include that HHH that aborted at the 
address) will halt, HHH did not "need" to abort.

The fact that the HHH the doesn't abort when given the DDD paired with 
it doesn't count, as that DDD is a DIFFERENT DDD, as it includes the HHH 
that it called, which is different.

Trying to exclude the HHH from the definiton of DDD just means that DDD 
is now  NOT a program, and thus isn't a valid input for a Halt Decider. 
(The act of the input accessing something outside what it has been 
defined to have makes it invalid, and if you include that code, it is 
part of the input, even if not shown explicitily, as part of the 
conversion of the subjective question to an objective question which 
deciders are defined to handle).