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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Claude.ai provides reasoning why I may have defeated the
 conventional HP proof
Date: Mon, 7 Jul 2025 19:10:55 -0400
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On 7/7/25 9:57 AM, olcott wrote:
> 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.

Which is just an unsound argument that just happens to reach a correct 
solution.

> 
>>> 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.

NO, in Formal Logic, *ALL* semantics can be expressed syntactically.

> 
>>> 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.

Right, such as a call instuction will ALWAYS be followed by the 
instruction addressed by it, and any other result is an error.

> 
>>>>> 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 if it stops before finishing the simulation, it isn't a UTM.

That is like saying that your street legal car is still street legal 
after removing the headlight and brakes.

> 
>>>> 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.

And their domain include finite strings that encode Turing Machines, 
from which the full behavior of that machine is defined, and thus that 
behavior is subject to being asked for.



> 
>> 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.

So, you think UTMs don't exist? That Turing Machine can't be encoded as 
a finite string and have *ALL* of its behavior reconstructed from that 
finite string?

Then I guess you don't think simulation is possible, and thus simulators 
and Stimulating Halt Decider don't exist.

See all the problems your lies create, you just prove that you arguement 
is a lie.

> 
>>> 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.

But DD correctly emuated does.

The fact that no Decider HHH can do a correct simulation means it can't 
be the source of defining non-halting.

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