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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Claude.ai provides reasoning why I may have defeated the
 conventional HP proof
Date: Mon, 7 Jul 2025 08:57:28 -0500
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On 7/7/2025 3:20 AM, Mikko wrote:
> On 2025-07-06 14:48:45 +0000, olcott said:
> 
>> On 7/6/2025 3:30 AM, Mikko wrote:
>>> On 2025-07-05 15:18:46 +0000, olcott said:
>>>
>>>> On 7/5/2025 4:06 AM, Mikko wrote:
>>>>> On 2025-07-04 20:16:34 +0000, olcott said:
>>>>>
>>>>>> https://claude.ai/share/48aab578-aec3-44a5-8bb3-6851e0f8b02e
>>>>>
>>>>> Perhaps an artificial idiot can think better than you but it does
>>>>> not think better than most participants of these discussions.
>>>>
>>>> Yet you cannot point out any actual error.
>>>
>>> There is no error in your above quoted words.
>>>
>>>>> What is not provable is not analytic truth.
>>>
>>>> I totally agree. Not only must it be provable it must
>>>> be provable semantically not merely syntactically.
>>>
>>> In order to prove anything a proof must be syntactically correct.
>>> Then the conclusion is semantically true if the premises are.
>>
>> Not exactly. Some of logic is wrong.
> 
> There is no example where ordinary logic derives a false conclusion from
> true premises. Other logics may contain mistakes so they should not be
> used unless proven valid.
> 

The one that I have in mind derives a true conclusion
from false premises.

>> An analytic proof requires a semantic connection
>> from a set of expressions of language that are
>> stipulated to be true.
> 
> It requires a syntactic connection. A semantic connection can always
> be expressed with a syntactic connection. Other ways of expression
> tend to lead to errors.
> 

It can be a semantics connection express syntactically.
Unless all of the relevant semantics are included terrible
mistakes are made. For example type mismatch errors.

>> I used C and x86 as my proof
>> languages.
> 
> They cannot be used as proof languages as they don't have any concept of 
> inference. In addition, they don't have any reasonable interrpetation as
> truth-bearer languages.
> 

The semantics of the x86 language specifies every single
detail of each state transition such that disagreement
is inherently incorrect.

>>>> Claude does provide the proof on the basis of understandings
>>>> that I provided to it.
> 
> Which are not acceptable premises for those reader who undrstand
> the halting problem and related topics.
> 

*This definition has proven to be perfectly fine*
Termination Analyzer HHH simulates its input until
it detects a non-terminating behavior pattern. When
HHH detects such a pattern it aborts its simulation
and returns 0.

That people disagree with the result of that merely
proves that they have poor understanding of programming.

>>>> Here is the key new one:
>>>>
>>>> Since no Turing machine can take another directly executing
>>>> Turing machine as an input they are outside of the domain
>>>> of any Turing machine based decider.
>>>
>>> By the same reasning there are no universal Turing machines.
>>
>> Counter-factual. UTMs are easy.
> 
> Indeed. If your reasoning were correct an universal Turing
> machine would be impossible but there are universal Turing
> machines so (by the inference rule known as modus tollens)
> your reasoning is not correct.
> 

A UTM is one thing. A UTM that can watch the behavior
of its input detecting non-terminating patterns is
something else.

>>> But the reasoning is not correct. The halting problem requires
>>> that a halt decider must predict what happens later ir the
>>> descirbed comutation is performed.
>>
>> That is an incorrect requirement.
> 
> A requirement is correct if it is possible to determine whether
> it is satisfied. If the prediction is "does not halt" and a
> direct execution halts then the requirement is 

proven to be incorrect. Halt deciders have never actually
been required to report on elements outside of their domain
of TMs encoded as finite strings. When textbooks say otherwise
they are wrong. Because you only learn these things by rote
memorization and have no actual depth of understanding you may
never get this.

> not met and the
> predicting machien is not a halt decider, because that is what
> the words mean.
> 

Predicting the behavior specified by their input.
Not predicting the behavior of things that are not
TMs encoded as finite strings.

>> Partial halt deciders can only report on the actual
>> behavior that their actual input actually specifies.
> 
> They cannot do even that for every possible behaviour. Some of
> them can determine more cases than some others but none of them
> can determine all cases.
> 

For the crucial counter-example input DD emulated by
HHH cannot possibly reach its own final halt state.

>>>> The requirement that a partial halt decider to report on the
>>>> behavior of a directly executed machine has always been bogus.
> 
> No, it is not:
> 

You already know that TMs can only take finite string
encodings of TMs. The directly executed machine is not
a finite string at all.

>>> The Wikipeda page https://en.wikipedia.org/wiki/Halting_problem confirms
>>> what I said above. The magic word "bogus" has no effect, no matter how
>>> may times you say it.
> 
>> All of the halting problem proofs depend on an input
>> to a partial halt decider doing the opposite of whatever
>> the decider decides. No such input exists.
> 
> An analytic truth is that such input is constructible.
> 

Unless you try to actually do it and find that all such
cases do not involve actual inputs.

>> *The standard halting problem proof cannot even be constructed*
> 
> It has been constructed and published and checked and found good.
> But the proof does not apply to your work because your work is
> not about the halting problem.
> 

https://www.liarparadox.org/Peter_Linz_HP_317-320.pdf

When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.∞
   if Ĥ applied to ⟨Ĥ⟩ halts
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
   if Ĥ applied to ⟨Ĥ⟩ does not halt

When Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ transitions to Ĥ.qn it is correct.
The computation that Ĥ.embedded_H is contained within:
========== REMAINDER OF ARTICLE TRUNCATED ==========