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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Who here understands that the last paragraph is Necessarily true?
Date: Fri, 19 Jul 2024 09:46:19 -0500
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On 7/19/2024 4:07 AM, Mikko wrote:
> On 2024-07-17 13:30:07 +0000, olcott said:
>
>> On 7/17/2024 2:49 AM, Mikko wrote:
>>> 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.
>>>
>>
>> <MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
>> If simulating halt decider H correctly simulates its input D
>> until H correctly determines that its simulated D would never
>> stop running unless aborted then
>>
>> H can abort its simulation of D and correctly report that D
>> specifies a non-halting sequence of configurations.
>> </MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
>>
>> _DDD()
>> [00002163] 55 push ebp ; housekeeping
>> [00002164] 8bec mov ebp,esp ; housekeeping
>> [00002166] 6863210000 push 00002163 ; push DDD
>> [0000216b] e853f4ffff call 000015c3 ; call HHH(DDD)
>> [00002170] 83c404 add esp,+04
>> [00002173] 5d pop ebp
>> [00002174] c3 ret
>> Size in bytes:(0018) [00002174]
>>
>> DDD emulated by HHH according to the semantic meaning of
>> its x86 instructions never stops running unless aborted.
>
> That Professor Sipser does not express any agreement with anything
> about the syntax of facts is not relevant to our (or any) discussion
> about syntax of facts.
>
void DDD()
{
HHH(DDD);
}
int main()
{
DDD();
}
<MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
If simulating halt decider H correctly simulates its input D
until H correctly determines that its simulated D would never
stop running unless aborted then
H can abort its simulation of D and correctly report that D
specifies a non-halting sequence of configurations.
</MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
int main { DDD(); } calls HHH(DDD) that must abort the
emulation of its input or HHH, emulated DDD and executed DDD
never stop running.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer