XPost: comp.theory, sci.logic
From: polcott333@gmail.com
On 7/20/2025 3:39 AM, Mikko wrote:
> On 2025-07-19 15:11:21 +0000, olcott said:
>
>> 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 wrote:
>>>>>> On 7/6/2025 5:16 AM, Alan Mackenzie wrote:
>>>>>>> olcott 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.
>>>
>>> This means nothing as long as symbols are undefined.
>>
>> They are defined on the link provided on the next line.
>
> That was not said in the quoted message, and some of the symbols
> are not defined there.
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