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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic,comp.ai.philosophy
Subject: Re: Halting Problem Proof ERROR
Date: Sat, 19 Jul 2025 13:31:41 -0400
Organization: i2pn2 (i2pn.org)
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On 7/19/25 11:11 AM, olcott wrote:
> On 7/19/2025 3:05 AM, Mikko wrote:
>> On 2025-07-17 14:44:23 +0000, olcott said:
>>
>>> On 7/6/2025 11:02 AM, Alan Mackenzie wrote:
>>>> [ Followup-To: set ]
>>>>
>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>> On 7/6/2025 5:16 AM, Alan Mackenzie wrote:
>>>>>> olcott <polcott333@gmail.com> wrote:
>>>>>>> On 7/5/2025 2:07 PM, Alan Mackenzie wrote:
>>>>
>>>>>>>> You lie.  You don't have a proof.  Many people in this group 
>>>>>>>> have pointed
>>>>>>>> out lots of errors in various versions of your purported proof, 
>>>>>>>> which you
>>>>>>>> just ignore.  The section in Professor Linz's book you used to 
>>>>>>>> be so fond
>>>>>>>> of citing will contain plenty of details, if only you would take 
>>>>>>>> the
>>>>>>>> trouble to understand it (assuming you're capable of such 
>>>>>>>> understanding).
>>>>
>>>>>>> I have addressed ....
>>>>
>>>>>> Meaningless pompous word.
>>>>
>>>>>>> .... all of those details that you make sure to ignore so that 
>>>>>>> you can
>>>>>>> baselessly claim that I am wrong.
>>>>
>>>>>> I vaguely remember rolling my eyes at your hopeless lack of
>>>>>> understanding.  It was like watching a 7 year old trying to do 
>>>>>> calculus.
>>>>>> The basic understanding was simply not there.  Years later, it's 
>>>>>> still
>>>>>> not there.
>>>>
>>>>>> And yes, you are wrong.  The proofs of the halting theorem which 
>>>>>> involve
>>>>>> constructing programs which purported halting deciders cannot decide
>>>>>> correctly are correct.
>>>>
>>>>> Yet you cannot point to even one mistake because there are none.
>>>>
>>>> That's what I'm saying.  Those proofs of the halting theorem are free
>>>> from mistakes.
>>>>
>>>> More to the point, it is YOU who cannot point to any mistakes in them.
>>>> They are valid proofs.  Your work, if it contradicts those proofs 
>>>> (which
>>>> isn't at all clear) can thus be dismissed without further 
>>>> consideration.
>>>>
>>>>>>> There cannot possibly be *AN ACTUAL INPUT* that does the
>>>>>>> opposite of whatever its decider decides. All of the examples
>>>>>>> of this have never been *ACTUAL INPUTS*
>>>>
>>>>>> That's so sloppily worded, it could mean almost anything.
>>>>
>>>>> The standard halting problem proof cannot even be constructed.
>>>>
>>>> It has been constructed, and is valid.  But one would normally talk 
>>>> about
>>>> formulating a proof, rather than constructing one.
>>>>
>>>> [ .... ]
>>>>
>>>>>>> No Turing machine can possibly take another directly executing
>>>>>>> Turing machine as in input, thus removing these from the
>>>>>>> domain of every halt decider.
>>>>
>>>>>> And that, too.
>>>>
>>>>>>> *Thus the requirement that HHH report on the behavior*
>>>>>>> *of the directly executed DD has always been bogus*
>>>>
>>>>>> And that makes your hat trick.
>>>>
>>>>>>> Turing machine partial halt deciders compute the mapping
>>>>>>> from their actual inputs to the actual behavior that these
>>>>>>> inputs specify.
>>>>
>>>>>> And a fourth.  There's some semblance of truth in there, but it's 
>>>>>> very
>>>>>> confused.
>>>>
>>>>
>>>>> It is not at all confused. I know exactly what it means.
>>>>
>>>> It's very confused to everybody but you, then.
>>>>
>>>>>> Sloppy wording is your technique to get people to go down to your 
>>>>>> level
>>>>>> of discussion.  That involves many posts trying just to tie you 
>>>>>> down to
>>>>>> specific word meanings, and is very tiresome and unrewarding.  I 
>>>>>> decline
>>>>>> to get involved any further.
>>>>
>>>>
>>>>> *Yet as I claimed you found no actual mistake*
>>>>
>>>> I've found plenty of actual mistakes.  I was a software developer by
>>>> profession.
>>>>
>>>>> Let me tell you the punchline so that you can
>>>>> see why I said those things.
>>>>
>>>> Despite what I said last post, I will actually go to the trouble of
>>>> analysing your sloppy expression.
>>>>
>>>>> Because directly executed Turing machines cannot
>>>>> possibly be inputs to Turing machine deciders this
>>>>> makes them outside of the domain of these deciders.
>>>>
>>>> It's entirely unclear what a "directly executed Turing machine" is. 
>>>> Most
>>>> of the time turing machines are theoretical constructs used for proving
>>>> theorems.  They can be executed, but rarely are.
>>>>
>>>> It's unclear what you mean by a turing machine being an input to a 
>>>> turing
>>>> machine.  Read up about universal turing machines to get a bit of
>>>> background.
>>>>
>>>>> When a partial halt decider is required to report
>>>>> on the direct execution of a machine this requirement
>>>>> is bogus.
>>>>
>>>> See above.  That paragraph is meaningless.
>>>>
>>>>> This means that the behavior of DD() is none of the damn
>>>>> business of HHH, thus does not contradict HHH(DD)==0.
>>>>> *If you disagree this only proves that you do not understand*
>>>>
>>>> It's fully obscure what DD() and HHH mean, and thus impossible to
>>>> affirm or contradict the meaningless "HHH(DD)==0".
>>>>
>>>>> HHH(DD) does correctly detect that DD simulated by HHH
>>>>> according to the semantics pf the C programming language
>>>>> cannot possibly reach its own "return"statement final
>>>>> halt state.
>>>>
>>>> See above.  By the way, people concerned with computation theory use
>>>> turing machines, which are well-defined, simple, and powerful.  They 
>>>> lack
>>>> the complexity, ambiguity, and unsuitability for theoretical work of 
>>>> real
>>>> world programming languages like C.
>>>>
>>>>> *If you disagree this only proves that you do not understand*
>>>>
>>>>> Any mindless idiot can disagree. Showing an error and proving
>>>>> that it is an actual mistake requires much more than this.
>>>>
>>>> Indeed.  All you have done is disagree with one of the proofs of the
>>>> halting theorem.  You have yet to show an error in it.  That will be
>>>> difficult, because there aren't any.
>>>
>>> q0 WM ⊢* Ĥq0 WM WM ⊢* Ĥ∞,
>>>     if M applied to WM halts, and
>>> q0 WM ⊢* Ĥq0 Wm WM ⊢* Ĥ y1 qn y2,
>>>     if M applied to WM does not halt.
>>
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