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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory,comp.ai.philosophy,sci.logic
Subject: Re: Halting Problem Proof ERROR
Date: Sun, 20 Jul 2025 09:54:46 +0200
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Op 19.jul.2025 om 16:23 schreef olcott:
> On 7/19/2025 3:26 AM, Fred. Zwarts wrote:
>> Op 18.jul.2025 om 18:09 schreef olcott:
>>> On 7/18/2025 6:17 AM, Fred. Zwarts wrote:
>>>> Op 17.jul.2025 om 16:44 schreef olcott:
>>>>> 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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