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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Who here understands that the last paragraph is Necessarily true?
Date: Wed, 17 Jul 2024 10:49:48 +0300
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On 2024-07-16 14:20:09 +0000, olcott said:

> On 7/16/2024 3:32 AM, Mikko wrote:
>> On 2024-07-15 13:26:22 +0000, olcott said:
>> 
>>> On 7/15/2024 3:23 AM, Mikko wrote:
>>>> On 2024-07-14 14:38:31 +0000, olcott said:
>>>> 
>>>>> 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.
>>>> 
>>>> That the input is aborted does not mean that the input must be aborted.
>>> 
>>> Weasel words. This is an axiom:
>>> Input XXX must be aborted to prevent the non-termination of HHH.
>> 
>> That is not an acceptable axiom. That you are unable to prove that
>> either XXX is aborted or HHH does not terminate is insufficient
>> reason to call it an axiom.
>> 
> 
> *Premise* (assumed to be true)
> Any input that must be aborted to prevent
> the non termination of HHH
> 
> *Logically entailed by the above premise*
> necessarily specifies non-halting behavior or
> it would never need to be aborted.

No, it is not. Both "need to be" and "must be" are different from "is".
The correct asxiom is "If the program can be executed to its halting in
a finite time then the program specifies a halting behaviour."

>>> From the fact that XXX must be aborted we can conclude that XXX must be 
>>> aborted.
>> 
>> Nothing that contains the word "must" is a fact.
>> 
> 
> When simulated input X stops running {if and only if}
> the simulation of this input X has been aborted this
> necessitates that input X specifies non-halting behavior.

Nothing that contains the word "necessitates" is a fact, either.
Perhaps you should learn some philosophy.

-- 
Mikko