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computers / comp.ai.philosophy / Re: Halting Problem proof refutation is a tautology thus irrefutable [ liar or incompetent ]

Re: Halting Problem proof refutation is a tautology thus irrefutable [ liar or incompetent ]

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https://www.novabbs.com/computers/article-flat.php?id=9603&group=comp.ai.philosophy#9603

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Subject: Re: Halting Problem proof refutation is a tautology thus irrefutable
[ liar or incompetent ]
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Newsgroups: comp.theory,comp.ai.philosophy,sci.logic,sci.math
References: <d8-dnTlDr8xgoTL_nZ2dnUU7_83NnZ2d@giganews.com>
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From: Rich...@Damon-Family.org (Richard Damon)
In-Reply-To: <jKednXIJIfHHCjL_nZ2dnUU7_8zNnZ2d@giganews.com>
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Date: Sun, 19 Jun 2022 17:52:21 -0400
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 by: Richard Damon - Sun, 19 Jun 2022 21:52 UTC

On 6/19/22 5:38 PM, olcott wrote:
> On 6/19/2022 4:30 PM, Richard Damon wrote:
>>
>> On 6/19/22 5:17 PM, olcott wrote:
>>> On 6/19/2022 4:00 PM, Richard Damon wrote:
>>>> On 6/19/22 4:43 PM, olcott wrote:
>>>>> On 6/19/2022 3:31 PM, Mr Flibble wrote:
>>>>>> On Sun, 19 Jun 2022 15:16:05 -0500
>>>>>> olcott <NoOne@NoWhere.com> wrote:
>>>>>>
>>>>>>> On 6/19/2022 3:08 PM, Mr Flibble wrote:
>>>>>>>> On Sun, 19 Jun 2022 15:05:11 -0500
>>>>>>>> olcott <NoOne@NoWhere.com> wrote:
>>>>>>>>> On 6/19/2022 2:59 PM, Mr Flibble wrote:
>>>>>>>>>> On Sun, 19 Jun 2022 14:17:42 -0500
>>>>>>>>>> olcott <NoOne@NoWhere.com> wrote:
>>>>>>>>>>> On 6/19/2022 1:43 PM, Richard Damon wrote:
>>>>>>>>>>>> On 6/19/22 2:30 PM, olcott wrote:
>>>>>>>>>>>>> On 6/19/2022 1:20 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 6/19/22 2:08 PM, olcott wrote:
>>>>>>>>>>>>>>> On 6/19/2022 12:40 PM, Mr Flibble wrote:
>>>>>>>>>>>>>>>> On Sun, 19 Jun 2022 12:16:05 -0500
>>>>>>>>>>>>>>>> olcott <NoOne@NoWhere.com> wrote:
>>>>>>>>>>>>>>>>> On 6/19/2022 12:01 PM, Mr Flibble wrote:
>>>>>>>>>>>>>>>>>> On Sun, 19 Jun 2022 11:23:24 -0500
>>>>>>>>>>>>>>>>>> olcott <NoOne@NoWhere.com> wrote:
>>>>>>>>>>>>>>>>>>> On 6/19/2022 11:01 AM, Mr Flibble wrote:
>>>>>>>>>>>>>>>>>>>> On Sun, 19 Jun 2022 10:39:34 -0500
>>>>>>>>>>>>>>>>>>>> olcott <NoOne@NoWhere.com> wrote:
>>>>>>>>>>>>>>>>>>>>> On 6/19/2022 10:23 AM, Mr Flibble wrote:
>>>>>>>>>>>>>>>>>>>>>> On Sun, 19 Jun 2022 10:13:00 -0500
>>>>>>>>>>>>>>>>>>>>>> olcott <NoOne@NoWhere.com> wrote:
>>>>>>>>>>>>>>>>>>>>>>> computation that halts … the Turing machine will
>>>>>>>>>>>>>>>>>>>>>>> halt
>>>>>>>>>>>>>>>>>>>>>>> whenever it enters a final state. (Linz:1990:234)
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> A halt decider must compute the mapping from its
>>>>>>>>>>>>>>>>>>>>>>> inputs to an accept or reject state on the basis of
>>>>>>>>>>>>>>>>>>>>>>> the actual behavior of these actual inputs.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> When a simulating halt decider rejects all inputs as
>>>>>>>>>>>>>>>>>>>>>>> non-halting whenever it correctly detects [in a
>>>>>>>>>>>>>>>>>>>>>>> finite number of steps] that its correct and
>>>>>>>>>>>>>>>>>>>>>>> complete
>>>>>>>>>>>>>>>>>>>>>>> simulation of its input would never reach [a] final
>>>>>>>>>>>>>>>>>>>>>>> state of this input then all [these] inputs
>>>>>>>>>>>>>>>>>>>>>>> (including pathological inputs) are decided
>>>>>>>>>>>>>>>>>>>>>>> correctly.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> void Px(u32 x)
>>>>>>>>>>>>>>>>>>>>>> {
>>>>>>>>>>>>>>>>>>>>>>           H(x, x);
>>>>>>>>>>>>>>>>>>>>>>           return;
>>>>>>>>>>>>>>>>>>>>>> }
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> int main()
>>>>>>>>>>>>>>>>>>>>>> {
>>>>>>>>>>>>>>>>>>>>>>           Output("Input_Halts = ", H((u32)Px,
>>>>>>>>>>>>>>>>>>>>>> (u32)Px)); }
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> ...[000013e8][00102357][00000000] 83c408          add
>>>>>>>>>>>>>>>>>>>>>> esp,+08 ...[000013eb][00102353][00000000] 50
>>>>>>>>>>>>>>>>>>>>>> push eax ...[000013ec][0010234f][00000427] 6827040000
>>>>>>>>>>>>>>>>>>>>>>     push 00000427 ---[000013f1][0010234f][00000427]
>>>>>>>>>>>>>>>>>>>>>> e880f0ffff      call 00000476 Input_Halts = 0
>>>>>>>>>>>>>>>>>>>>>> ...[000013f6][00102357][00000000] 83c408          add
>>>>>>>>>>>>>>>>>>>>>> esp,+08 ...[000013f9][00102357][00000000] 33c0
>>>>>>>>>>>>>>>>>>>>>> xor eax,eax ...[000013fb][0010235b][00100000] 5d
>>>>>>>>>>>>>>>>>>>>>>        pop ebp ...[000013fc][0010235f][00000004] c3
>>>>>>>>>>>>>>>>>>>>>>        ret Number of Instructions Executed(16120)
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> It gets the answer wrong, i.e. input has not been
>>>>>>>>>>>>>>>>>>>>>> decided correctly. QED.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> /Flibble
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> _P()
>>>>>>>>>>>>>>>>>>>>> [000010fa](01)  55              push ebp
>>>>>>>>>>>>>>>>>>>>> [000010fb](02)  8bec            mov ebp,esp
>>>>>>>>>>>>>>>>>>>>> [000010fd](03)  8b4508          mov eax,[ebp+08]
>>>>>>>>>>>>>>>>>>>>> [00001100](01)  50              push eax       // push
>>>>>>>>>>>>>>>>>>>>> P [00001101](03)  8b4d08          mov ecx,[ebp+08]
>>>>>>>>>>>>>>>>>>>>> [00001104](01)  51              push ecx       // push
>>>>>>>>>>>>>>>>>>>>> P [00001105](05)  e800feffff      call 00000f0a  //
>>>>>>>>>>>>>>>>>>>>> call H [0000110a](03)  83c408          add esp,+08
>>>>>>>>>>>>>>>>>>>>> [0000110d](02)  85c0            test eax,eax
>>>>>>>>>>>>>>>>>>>>> [0000110f](02)  7402            jz 00001113
>>>>>>>>>>>>>>>>>>>>> [00001111](02)  ebfe            jmp 00001111
>>>>>>>>>>>>>>>>>>>>> [00001113](01)  5d              pop ebp
>>>>>>>>>>>>>>>>>>>>> [00001114](01)  c3              ret
>>>>>>>>>>>>>>>>>>>>> Size in bytes:(0027) [00001114]
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Begin Simulation   Execution Trace Stored at:211ee2
>>>>>>>>>>>>>>>>>>>>> ...[000010da][00211ece][00211ed2] 55         push ebp
>>>>>>>>>>>>>>>>>>>>> ...[000010db][00211ece][00211ed2] 8bec       mov
>>>>>>>>>>>>>>>>>>>>> ebp,esp ...[000010dd][00211ece][00211ed2] 8b4508
>>>>>>>>>>>>>>>>>>>>> mov eax,[ebp+08] ...[000010e0][00211eca][000010da] 50
>>>>>>>>>>>>>>>>>>>>> push eax      // push P
>>>>>>>>>>>>>>>>>>>>> ...[000010e1][00211eca][000010da] 8b4d08     mov
>>>>>>>>>>>>>>>>>>>>> ecx,[ebp+08] ...[000010e4][00211ec6][000010da] 51
>>>>>>>>>>>>>>>>>>>>>     push ecx // push P
>>>>>>>>>>>>>>>>>>>>> ...[000010e5][00211ec2][000010ea] e820feffff call
>>>>>>>>>>>>>>>>>>>>> 00000f0a // call H Infinitely Recursive Simulation
>>>>>>>>>>>>>>>>>>>>> Detected Simulation Stopped
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> *All technically competent software engineers* will
>>>>>>>>>>>>>>>>>>>>> see
>>>>>>>>>>>>>>>>>>>>> that when H bases its halt status decision on whether
>>>>>>>>>>>>>>>>>>>>> or not its complete and correct x86 emulation of its
>>>>>>>>>>>>>>>>>>>>> input would ever reach the "ret" instruction of this
>>>>>>>>>>>>>>>>>>>>> input that H is correct to reject this input.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> void Px(u32 x)
>>>>>>>>>>>>>>>>>>>> {
>>>>>>>>>>>>>>>>>>>>          H(x, x);
>>>>>>>>>>>>>>>>>>>>          return;
>>>>>>>>>>>>>>>>>>>> }
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> int main()
>>>>>>>>>>>>>>>>>>>> {
>>>>>>>>>>>>>>>>>>>>          Output("Input_Halts = ", H((u32)Px, (u32)Px));
>>>>>>>>>>>>>>>>>>>> }
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> ...[000013e8][00102357][00000000] 83c408          add
>>>>>>>>>>>>>>>>>>>> esp,+08 ...[000013eb][00102353][00000000] 50
>>>>>>>>>>>>>>>>>>>> push eax ...[000013ec][0010234f][00000427] 6827040000
>>>>>>>>>>>>>>>>>>>> push 00000427 ---[000013f1][0010234f][00000427]
>>>>>>>>>>>>>>>>>>>> e880f0ffff call 00000476 Input_Halts = 0
>>>>>>>>>>>>>>>>>>>> ...[000013f6][00102357][00000000] 83c408          add
>>>>>>>>>>>>>>>>>>>> esp,+08 ...[000013f9][00102357][00000000] 33c0
>>>>>>>>>>>>>>>>>>>> xor eax,eax ...[000013fb][0010235b][00100000] 5d
>>>>>>>>>>>>>>>>>>>>      pop ebp ...[000013fc][0010235f][00000004] c3
>>>>>>>>>>>>>>>>>>>> ret Number of Instructions Executed(16120)
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> It gets the answer wrong, i.e. input has not been
>>>>>>>>>>>>>>>>>>>> decided correctly. QED.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> /Flibble
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> *All technically competent software engineers*
>>>>>>>>>>>>>>>>>> void Px(u32 x)
>>>>>>>>>>>>>>>>>> {
>>>>>>>>>>>>>>>>>>         H(x, x);
>>>>>>>>>>>>>>>>>>         return;
>>>>>>>>>>>>>>>>>> }
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> int main()
>>>>>>>>>>>>>>>>>> {
>>>>>>>>>>>>>>>>>>         Output("Input_Halts = ", H((u32)Px, (u32)Px));
>>>>>>>>>>>>>>>>>> }
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> ...[000013e8][00102357][00000000] 83c408          add
>>>>>>>>>>>>>>>>>> esp,+08 ...[000013eb][00102353][00000000] 50
>>>>>>>>>>>>>>>>>> push eax ...[000013ec][0010234f][00000427] 6827040000
>>>>>>>>>>>>>>>>>> push 00000427 ---[000013f1][0010234f][00000427]
>>>>>>>>>>>>>>>>>> e880f0ffff
>>>>>>>>>>>>>>>>>> call 00000476 Input_Halts = 0
>>>>>>>>>>>>>>>>>> ...[000013f6][00102357][00000000] 83c408          add
>>>>>>>>>>>>>>>>>> esp,+08 ...[000013f9][00102357][00000000] 33c0
>>>>>>>>>>>>>>>>>> xor eax,eax ...[000013fb][0010235b][00100000] 5d
>>>>>>>>>>>>>>>>>>     pop ebp ...[000013fc][0010235f][00000004] c3
>>>>>>>>>>>>>>>>>> ret Number of Instructions Executed(16120)
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> It gets the answer wrong, i.e. input has not been decided
>>>>>>>>>>>>>>>>>> correctly. QED.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> /Flibble
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Because it is an easily verified fact that the correct and
>>>>>>>>>>>>>>>>> complete x86 emulation of the input to H(P,P) by H would
>>>>>>>>>>>>>>>>> never reach the "ret" instruction of P and this is the
>>>>>>>>>>>>>>>>> criterion measure for H to reject its input how do you
>>>>>>>>>>>>>>>>> figure that H gets the wrong answer?
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> What I am saying is a logical tautology the same as
>>>>>>>>>>>>>>>>> when we
>>>>>>>>>>>>>>>>> know that X is a black cat then we know that X is a cat.
>>>>>>>>>>>>>>>> We are talking about Px, not P. We are talking about your H
>>>>>>>>>>>>>>>> not analysing what its input actually does and instead
>>>>>>>>>>>>>>>> assuming that an input that calls H is always pathological.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> void Px(u32 x)
>>>>>>>>>>>>>>>> {
>>>>>>>>>>>>>>>>        H(x, x);
>>>>>>>>>>>>>>>>        return;
>>>>>>>>>>>>>>>> }
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> int main()
>>>>>>>>>>>>>>>> {
>>>>>>>>>>>>>>>>        Output("Input_Halts = ", H((u32)Px, (u32)Px));
>>>>>>>>>>>>>>>> }
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> ...[000013e8][00102357][00000000] 83c408          add
>>>>>>>>>>>>>>>> esp,+08 ...[000013eb][00102353][00000000] 50
>>>>>>>>>>>>>>>> push eax ...[000013ec][0010234f][00000427] 6827040000
>>>>>>>>>>>>>>>> push 00000427 ---[000013f1][0010234f][00000427] e880f0ffff
>>>>>>>>>>>>>>>> call 00000476 Input_Halts = 0
>>>>>>>>>>>>>>>> ...[000013f6][00102357][00000000] 83c408          add
>>>>>>>>>>>>>>>> esp,+08 ...[000013f9][00102357][00000000] 33c0
>>>>>>>>>>>>>>>> xor eax,eax ...[000013fb][0010235b][00100000] 5d
>>>>>>>>>>>>>>>>    pop ebp ...[000013fc][0010235f][00000004] c3
>>>>>>>>>>>>>>>> ret Number of Instructions Executed(16120)
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> It gets the answer wrong, i.e. input has not been decided
>>>>>>>>>>>>>>>> correctly. QED.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> /Flibble
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> DO YOU AGREE WITH THIS?
>>>>>>>>>>>>>>> H(Px,Px) does correctly determine that the complete and
>>>>>>>>>>>>>>> correct x86 emulation of its input would never reach the
>>>>>>>>>>>>>>> "ret" instruction of Px.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> That is only true if H never returns ANY answer (and thus
>>>>>>>>>>>>>> fails to be a decider).
>>>>>>>>>>>>> Competent software engineers will understand that when the
>>>>>>>>>>>>> behavior of Px matches this pattern that correct and complete
>>>>>>>>>>>>> x86 emulation of the input to H(Px,Px) by H would never reach
>>>>>>>>>>>>> the "ret" instruction of Px:
>>>>>>>>>>>>>
>>>>>>>>>>>>> H knows its own machine address and on this basis:
>>>>>>>>>>>>> (a) H recognizes that Px is calling H with the same arguments
>>>>>>>>>>>>> that H was called with.
>>>>>>>>>>>>> (b) There are no instructions in Px that could possibly escape
>>>>>>>>>>>>> this infinitely recursive emulation.
>>>>>>>>>>>>> (c) H aborts its emulation of Px before Px its call to H is
>>>>>>>>>>>>> invoked.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Only if H never aborts. If H does abort, then Px(Px), whose
>>>>>>>>>>>> behavior exactly matches the CORRECT emulation of the input to
>>>>>>>>>>>> H(Px,Px) BY DEFINITION shows this.
>>>>>>>>>>>
>>>>>>>>>>> The question is: Would (future tense) the complete and correct
>>>>>>>>>>> x86 emulation of the input to H(Px,Px) by H ever reach the "ret"
>>>>>>>>>>> instruction of Px.
>>>>>>>>>>>
>>>>>>>>>>> You always change this question to a different question:
>>>>>>>>>>>
>>>>>>>>>>> Does (present tense) the complete and correct x86 emulation of
>>>>>>>>>>> the input to H(Px,Px) by H ever reach the "ret" instruction of
>>>>>>>>>>> Px.
>>>>>>>>>>
>>>>>>>>>> The complete and correct x86 emulation of the input to H(Px, Px)
>>>>>>>>>> should be to allow Px to halt, which is what Px is defined to do:
>>>>>>>>>
>>>>>>>>> You are doing the same thing Richard is doing, getting at least
>>>>>>>>> one
>>>>>>>>> word of what I am saying incorrectly and then rebutting the
>>>>>>>>> incorrect paraphrase. This is the strawman error.
>>>>>>>>>
>>>>>>>>> The complete and correct x86 emulation of the input to H(Px, Px)
>>>>>>>>> BY H
>>>>>>>>> BY H
>>>>>>>>> BY H
>>>>>>>>> BY H
>>>>>>>>> BY H
>>>>>>>>>
>>>>>>>>> cannot possibly contradict the easily verified fact that Px would
>>>>>>>>> never reach its "ret" instruction. This seems to be beyond your
>>>>>>>>> ordinary software engineering technical competence.
>>>>>>>> Px is defined to always halt; your H gets the answer wrong
>>>>>>>> saying Px
>>>>>>>> doesn't halt. QED.
>>>>>>>>
>>>>>>>> /Flibble
>>>>>>>
>>>>>>> Every technically competent software engineer can easily confirm
>>>>>>> that
>>>>>>> the correct and complete x86 emulation of the input to H(Px,Px) by H
>>>>>>> would never reach the "ret" instruction of Px.
>>>>>>>
>>>>>>> That you can not understand this proves that you are not a
>>>>>>> sufficiently technically competent software engineer on this point.
>>>>>>> Very good COBOL programmers might never be able to understand this.
>>>>>>>
>>>>>>> To anyone that writes or maintains operating systems what I am
>>>>>>> claiming would be as easy to verify as first grade arithmetic.
>>>>>> void Px(u32 x)
>>>>>> {
>>>>>>     H(x, x);
>>>>>>     return;
>>>>>> }
>>>>>>
>>>>>> int main()
>>>>>> {
>>>>>>     Output("Input_Halts = ", H((u32)Px, (u32)Px));
>>>>>> }
>>>>>>
>>>>>> ...[000013e8][00102357][00000000] 83c408          add esp,+08
>>>>>> ...[000013eb][00102353][00000000] 50              push eax
>>>>>> ...[000013ec][0010234f][00000427] 6827040000      push 00000427
>>>>>> ---[000013f1][0010234f][00000427] e880f0ffff      call 00000476
>>>>>> Input_Halts = 0
>>>>>> ...[000013f6][00102357][00000000] 83c408          add esp,+08
>>>>>> ...[000013f9][00102357][00000000] 33c0            xor eax,eax
>>>>>> ...[000013fb][0010235b][00100000] 5d              pop ebp
>>>>>> ...[000013fc][0010235f][00000004] c3              ret
>>>>>> Number of Instructions Executed(16120)
>>>>>>
>>>>>> It gets the answer wrong, i.e. input has not been decided correctly.
>>>>>> QED.
>>>>>>
>>>>>> /Flibble
>>>>>>
>>>>>>
>>>>>
>>>>> Get an operating system programmer to explain to you that the
>>>>> correct and complete x86 emulation of the input to H(Px,Px) by H
>>>>> would never reach the "ret" instruction of Px. *This is totally
>>>>> over your head*
>>>>>
>>>>> It is like I am saying that we know that black carts are cats and
>>>>> you disagree saying the a black cat might be some kind of dog.
>>>>>
>>>>> My whole system is now wrapped in 131K zip file as a Visual Studio
>>>>> project on a downloadable link.
>>>>>
>>>>
>>>> No, maybe you need an actual programmer to look at your logic.
>>>>
>>>> First, by definition correct emulation of a program will match the
>>>> behavior of the program.
>>>>
>>>
>>> When you disagree with this precisely stated verified fact you are
>>> either a liar or incompetent:
>>>
>>> the correct and complete x86 emulation of the input to H(Px,Px) by H
>>> would never reach the "ret" instruction
>>
>> When did you verify this statment for an H that returns 0?
>>
>
> When X is a cat then we know that X is an animal.
> What if X is a white cat?
>
> the correct and complete x86 emulation of the input to H(Px,Px) by H
> would never reach the "ret" instruction

Right, IF H actually does a correct and complete x86 emulation.

When H aborts to return 0, then H doesn't do a correct and complete x86
emualtion, and by your rule has nothing to show that it was correct.

>
> This is a truism thus remains true under all possible conditions.
>

Only in your mind. It is only a truism IF H actually does what you claim
H does, which means it can't abort its simulation and return 0.

You are creating your own liar's paradox, and are stuck in it.

Does H actually do a correct and complete emulation, if so, it can't
abort its simulation and return 0. If it aborts and returns 0, it didn't
do the correct and complete emulation it (falsesly) assumed that it
does, and thus it has used unsound logic.

H either uses UNSOUND logic or isn't a compution, either way you are
lying with yoru claims.

SubjectRepliesAuthor
o Halting Problem proof refutation is a tautology thus irrefutable

By: olcott on Sun, 19 Jun 2022

76olcott
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