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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: HP counter-example INPUT cannot possibly exist
Date: Wed, 18 Jun 2025 09:39:02 -0500
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On 6/16/2025 3:21 AM, Mikko wrote:
> On 2025-06-15 14:44:47 +0000, olcott said:
> 
>> On 6/15/2025 4:19 AM, Mikko wrote:
>>> On 2025-06-13 15:33:45 +0000, olcott said:
>>>
>>>> On 6/13/2025 5:37 AM, Mikko wrote:
>>>>> On 2025-06-12 15:18:30 +0000, olcott said:
>>>>>
>>>>>> On 6/12/2025 3:23 AM, Mikko wrote:
>>>>>>> On 2025-06-11 14:34:41 +0000, olcott said:
>>>>>>>
>>>>>>>> On 6/11/2025 4:19 AM, Mikko wrote:
>>>>>>>>> On 2025-06-10 15:11:50 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>> On 6/10/2025 6:15 AM, Richard Damon wrote:
>>>>>>>>>>> On 6/9/25 8:34 PM, olcott wrote:
>>>>>>>>>>>> On 6/9/2025 7:16 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 6/9/25 3:16 PM, Mr Flibble wrote:
>>>>>>>>>>>>>> "big fat ignorant liar" -- Damon
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> There are no words.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> /Flibble
>>>>>>>>>>>>>
>>>>>>>>>>>>> Can you show me wrong?
>>>>>>>>>>>>>
>>>>>>>>>>>>> Or are you complaining about me telling him the truth?
>>>>>>>>>>>>
>>>>>>>>>>>> What about this paper that I wrote?
>>>>>>>>>>>>
>>>>>>>>>>>> Severe anthropogenic climate change proven entirely with 
>>>>>>>>>>>> verifiable facts
>>>>>>>>>>>>
>>>>>>>>>>>> https://www.researchgate.net/ 
>>>>>>>>>>>> publication/336568434_Severe_anthropogenic_climate_change_proven_entirely_with_verifiable_facts
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Which just shows you don't know the meaning of the word "prove".
>>>>>>>>>>
>>>>>>>>>> What specifically do you believe is not proven?
>>>>>>>>>
>>>>>>>>> The article makes no attempt to prove anything.
>>>>>>>>
>>>>>>>> That is a dishonest or stupid thing to say.
>>>>>>>
>>>>>>> On what page and line there is the end of the conclusion of
>>>>>>> a proof?
>>>>>>
>>>>>> Maybe you don't know what a verified fact is?
>>>>>
>>>>> Irrepevant.
>>>>
>>>> That you don't know what a verified fact is, cannot
>>>> possibly be more relevant.
>>>
>>> Indeed, but what is more relevant is that you don't know what a fact is.
>>>
>>>> It means that when I conclusively
>>>> prove that you are wrong you will still think that you are
>>>> correct because you lack the basis for dividing correct
>>>> from incorrect.
>>>
>>> Irrelevant as long as you don't prove anything.
>>
>> When I fully proven my claim and your lack of sufficient
>> technical knowledge fails to understand this proof that
>> is not any actual rebuttal at all.
> 
> Be specific. The relevant techincal knoledge is the knowloedge
> of what a proof is and how one looks like. That knowledge
> I have, so I know that you have not presented any proof.
> I have not failed to understand what does not exist.
> 

A proof is any sequence of statements that are
necessarily true and thus impossibly false.

>>>>> Your question "What specifically do you believe is not
>>>>> proven?" was about proofs, not about facts.
>>>>
>>>> Facts are the ultimate ground-of-being maximum foundational
>>>> basis of all proofs.
>>>
>>> No, they are not, just of proofs about the real world.
>>
>> So how many decades how you carefully studied the
>> philosophical foundation of analytical truth?
> 
> It doesn't take decades of study to learn that an analyitcal
> truth says nothing about the real world. That is one of the
> very first things teached and learned.
> 

That dogs are animals is an analytical truth
that does say something about the real world.
Like almost everyone you don't know much about
analytical truth.

>>>>> As you respond to my question without answering it it is
>>>>> obvious that you don't see any proofs in your article.
>>>>
>>>> It is a fact that there is no actual input D to any
>>>> termination analyzer H that does the opposite of
>>>> whatever value that H derives. The key element that
>>>> all conventional HP proofs depend on cannot possibly exist.
>>>
>>> Nonsense is not a fact.
>>
>> After studying these things for 22 years I found
>> that every conventional proof of the halting problem
>> never provides an actual input that would do the
>> opposite of whatever value that its partial halt
>> decider (PHD) returns.
> 
> The core part of those proofs is a constructive specification
> of that test case.
> 

Yet no one ever noticed that the counter-example input
cannot even be constructed thus the proof itself never
actually existed.

>> It is always the case that the computation the PHD
>> is embedded within or the function that calls the
>> PHD that does the opposite. It is never the input.
> 
> Doesn't matter. Those proofs prove that for any Turing machine there
> is an input that proves that the decider is not a halt decider.

*Counter-factual there never has been any such an input*
This may be difficult to understand.
A lack of comprehension does not count as a rebuttal.

When Ĥ is applied to ⟨Ĥ⟩     // *adapted from bottom of page 319*
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

(a) Ĥ copies its input ⟨Ĥ⟩
(b) Ĥ invokes embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
(c) embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩
(d) simulated ⟨Ĥ⟩ copies its input ⟨Ĥ⟩
(e) simulated ⟨Ĥ⟩ invokes simulated embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
(f) simulated embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩
(g) goto (d) with one more level of simulation until embedded_H
     sees the repeating pattern and transitions to Ĥ.qn.

⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by embedded_H cannot possibly
reach its own ⟨Ĥ.qy⟩ state or final halt state of ⟨Ĥ.qn⟩
thus can never do the opposite of whatever embedded_H decides.
https://www.liarparadox.org/Peter_Linz_HP_317-320.pdf

>  That
> is sufficient to prove that no Turing machine is a halt decider for
> Turing machines.
> 
>>> The expression "any termination analyzer H"
>>> does not mean anything in this context, which does not have the
>>> definitions that would give it a meaning.
>>
>> A termination analyzer is required to report on the
>> sequence of state transitions that its input specifies.
> 
> An analyzer is required to report on the program that the used wants
> to be analyed if that program is in the scope of the analyzer. How
> the input shall be constructed to enable that must be told in the
> instruction manual of the analyzer.
> 

*IT MUST BE AN ACTUAL INPUT AND NO SUCH INPUT CAN POSSIBLY EXIST*
========== REMAINDER OF ARTICLE TRUNCATED ==========