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From: olcott <polcott2@gmail.com>
Newsgroups: sci.logic,comp.theory
Subject: Re: ZFC solution to incorrect questions: reject them --discourse
 context --
Date: Mon, 18 Mar 2024 18:54:51 -0500
Organization: A noiseless patient Spider
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On 3/18/2024 6:35 PM, immibis wrote:
> On 19/03/24 00:10, olcott wrote:
>> On 3/18/2024 11:19 AM, immibis wrote:
>>> On 18/03/24 06:32, olcott wrote:
>>>> On 3/17/2024 11:49 PM, immibis wrote:
>>>>> On 18/03/24 05:40, olcott wrote:
>>>>>> When H1 says YES it is right.
>>>>>> When H says YES it is wrong.
>>>>>
>>>>> Any halt decider is right to say YES on the input (D,D) if and only 
>>>>> if D(D) halts.
>>>>>
>>>> *When H(D,D) says YES D gets stuck at line 05*
>>>>
>>>> Can D correctly simulated by H terminate normally?
>>>> 01 int D(ptr x)  // ptr is pointer to int function
>>>> 02 {
>>>> 03   int Halt_Status = H(x, x);
>>>> 04   if (Halt_Status)
>>>> 05     HERE: goto HERE;
>>>> 06   return Halt_Status;
>>>> 07 }
>>>> 08
>>>> 09 void main()
>>>> 10 {
>>>> 11   D(D);
>>>> 12 }
>>>>
>>>>
>>>
>>> That would be a different D. The facts that Hah(Dah,Dah) returns TRUE 
>>> and Dah gets stuck at line 05 do not prove that Han(Dan,Dan) returns 
>>> TRUE and Dan gets stuck at line 05.
>>
>> *D is always the exact same finite string of machine code bytes*
>>
> 
> The argument to a halting decider must be a self-contained program and 
> the input to that program. The same finite string must always have the 
> same behaviour.

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn   // Ĥ applied to ⟨Ĥ⟩ does not halt

is self-contained yet still refers to an infinite set of encoding of H
such that the answer Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ is always contradicted.

Every yes/no question: Does Ĥ ⟨Ĥ⟩ halt?
such that YES is a correct answer from one entity
and YES is an incorrect answer from another entity
is an incorrect question when posed to this second entity.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer