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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Is Richard a Liar?
Date: Sat, 11 May 2024 11:26:30 -0500
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On 5/11/2024 3:27 AM, Mikko wrote:
> On 2024-05-11 02:21:10 +0000, olcott said:
> 
>> On 5/10/2024 9:17 PM, Richard Damon wrote:
>>> On 5/10/24 7:39 PM, olcott wrote:
>>>> On 5/10/2024 5:39 PM, Richard Damon wrote:
>>>>> On 5/10/24 6:28 PM, olcott wrote:
>>>>>> On 5/10/2024 4:59 PM, Richard Damon wrote:
>>>>>>> On 5/10/24 5:43 PM, olcott wrote:
>>>>>>>> On 5/10/2024 4:19 PM, Richard Damon wrote:
>>>>>>>>> On 5/10/24 5:11 PM, olcott wrote:
>>>>>>>>>> On 5/10/2024 3:50 PM, Richard Damon wrote:
>>>>>>>>>>> On 5/10/24 4:27 PM, olcott wrote:
>>>>>>>>>>>> On 5/10/2024 3:09 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 5/10/24 1:49 PM, olcott wrote:
>>>>>>>>>>>>>> On 5/10/2024 11:12 AM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 5/10/24 11:50 AM, olcott wrote:
>>>>>>>>>>>>>>>> On 5/10/2024 9:18 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>> On 5/9/24 11:10 PM, olcott wrote:
>>>>>>>>>>>>>>>>>> On 5/9/2024 9:31 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>> On 5/9/24 11:38 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>> On 5/8/2024 8:38 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>> On 8/05/24 21:05, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>> On 5/8/2024 10:13 AM, Mike Terry wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 08/05/2024 14:01, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 5/8/2024 3:59 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 2024-05-07 19:05:54 +0000, olcott said:
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> On 5/7/2024 1:54 PM, Fred. Zwarts wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>> Op 07.mei.2024 om 17:40 schreef olcott:
>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 5/7/2024 6:18 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 5/7/24 3:30 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2024-05-06 18:28:37 +0000, olcott said:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 5/6/2024 11:19 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2024-05-05 17:02:25 +0000, olcott said:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The x86utm operating system: 
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> https://github.com/plolcott/x86utm enables
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> one C function to execute another C 
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> function in debug step mode.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Simulating Termination analyzer H 
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulates the x86 machine code of its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input (using libx86emu) in debug step 
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mode until it correctly matches a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> correct non-halting behavior pattern 
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proving that its input will never
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> stop running unless aborted.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Can D correctly simulated by H 
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> terminate normally?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 00 int H(ptr x, ptr x)  // ptr is 
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> pointer to int function
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 01 int D(ptr x)
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 02 {
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 03   int Halt_Status = H(x, x);
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 04   if (Halt_Status)
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 05     HERE: goto HERE;
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 06   return Halt_Status;
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 07 }
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 08
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 09 int main()
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 10 {
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 11   H(D,D);
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 12 }
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> *Execution Trace*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Line 11: main() invokes H(D,D);
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> *keeps repeating* (unless aborted)
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Line 03: simulated D(D) invokes 
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulated H(D,D) that simulates D(D)
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> *Simulation invariant*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> D correctly simulated by H cannot 
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> possibly reach past its own line 03.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The above execution trace proves that 
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (for every H/D pair of the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> infinite set of H/D pairs) each D(D) 
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulated by the H that this D(D)
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calls cannot possibly reach past its 
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> own line 03.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When you say "every H/D pair" you should 
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specify which set of pairs
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you are talking about. As you don't, 
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> your words don't mean anything.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Every H/D pair in the universe where D(D) 
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is simulated by the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> same H(D,D) that D(D) calls. This 
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> involves 1 to ∞ steps of D
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and also includes zero to ∞ recursive 
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulations where H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H simulates itself simulating D(D).
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "In the universe" is not a set. In typical 
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set theories like ZFC there
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is no universal set.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> This template defines an infinite set of 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> finite string H/D pairs where each D(D) that 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> is simulated by H(D,D) also calls this same 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> H(D,D).
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> These H/D pairs can be enumerated by the one 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> to ∞ simulated steps of D and involve zero 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> to ∞ recursive simulations of H simulating 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> itself simulating D(D). Every time Lines 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1,2,3 are simulated again defines
>>>>>>>>>>>>>>>>>>>>>>>>>>>> one more level of recursive simulation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1st element of H/D pairs 1 step  of D  is 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulated by H
>>>>>>>>>>>>>>>>>>>>>>>>>>>> 2nd element of H/D pairs 2 steps of D are 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulated by H
>>>>>>>>>>>>>>>>>>>>>>>>>>>> 3rd element of H/D pairs 3 steps of D are 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulated by H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> 4th element of H/D pairs 4 steps of D are 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulated by H
>>>>>>>>>>>>>>>>>>>>>>>>>>>> this begins the first recursive simulation 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> at line 01
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> 5th element of H/D pairs 5 steps of D are 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulated by
>>>>>>>>>>>>>>>>>>>>>>>>>>>> next step of the first recursive simulation 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> at line 02
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> 6th element of H/D pairs 6 steps of D are 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulated by
>>>>>>>>>>>>>>>>>>>>>>>>>>>> last step of the first recursive simulation 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> at line 03
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> 7th element of H/D pairs 7 steps of D are 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulated by H
>>>>>>>>>>>>>>>>>>>>>>>>>>>> this begins the second recursive simulation 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> at line 01
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> Is this the definition of the infinite set of 
>>>>>>>>>>>>>>>>>>>>>>>>>>> H? We can think of many more simulations that 
>>>>>>>>>>>>>>>>>>>>>>>>>>> only these.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> This template defines an infinite set of 
>>>>>>>>>>>>>>>>>>>>>>>>>> finite string H/D pairs where
>>>>>>>>>>>>>>>>>>>>>>>>>> each D(D) that is simulated by H(D,D) also 
>>>>>>>>>>>>>>>>>>>>>>>>>> calls this same H(D,D).
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> No-one can possibly show one element of this 
>>>>>>>>>>>>>>>>>>>>>>>>>> set where D(D) reaches
>>>>>>>>>>>>>>>>>>>>>>>>>> past its own line 03.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> If H is a decider of any kind then the D build 
>>>>>>>>>>>>>>>>>>>>>>>>> from it reaches its line
>>>>>>>>>>>>>>>>>>>>>>>>> 4 as numberd above. Whether the simulation of D 
>>>>>>>>>>>>>>>>>>>>>>>>> by H reaches that line
>>>>>>>>>>>>>>>>>>>>>>>>> is another question.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> *My fully operational code proves otherwise*
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