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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: DDD simulated by HHH cannot possibly halt (Halting Problem) ---
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Date: Sun, 13 Apr 2025 22:12:45 -0400
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On 4/13/2025 10:09 PM, olcott wrote:
> On 4/13/2025 6:51 PM, dbush wrote:
>> On 4/13/2025 7:32 PM, olcott wrote:
>>> On 4/13/2025 4:03 PM, dbush wrote:
>>>> On 4/13/2025 5:00 PM, olcott wrote:
>>>>> On 4/13/2025 3:00 PM, dbush wrote:
>>>>>> On 4/13/2025 3:59 PM, olcott wrote:
>>>>>>> On 4/13/2025 3:54 AM, joes wrote:
>>>>>>>> Am Fri, 11 Apr 2025 10:56:32 -0500 schrieb olcott:
>>>>>>>>> On 4/11/2025 3:24 AM, Richard Heathfield wrote:
>>>>>>>>>> On 11/04/2025 08:57, Mikko wrote:
>>>>>>>>
>>>>>>>>>>> No proof of this principle has been shown so its use is not 
>>>>>>>>>>> valid.
>>>>>>>>>>
>>>>>>>>>> No proof of Peano's axioms or Euclid's fifth postulate has 
>>>>>>>>>> been shown.
>>>>>>>>>> That doesn't mean we can't use them.
>>>>>>>>>> Mr Olcott can have his principle if he likes, but only by EITHER
>>>>>>>>>> proving it (which, as you say, he has not yet done) OR by 
>>>>>>>>>> taking it as
>>>>>>>>>> axiomatic, leaving the world of mainstream computer science 
>>>>>>>>>> behind him,
>>>>>>>>>> constructing his own computational 'geometry' so to speak, and
>>>>>>>>>> abandoning any claim to having overturned the Halting Problem. 
>>>>>>>>>> Navel
>>>>>>>>>> contemplation beckons.
>>>>>>>>>> Axioms are all very well, and he's free to invent as many as 
>>>>>>>>>> he wishes,
>>>>>>>>>> but nobody else is obliged to accept them.
>>>>>>>>>>
>>>>>>>>> *Simulating termination analyzer Principle*
>>>>>>>>> It is always correct for any simulating termination analyzer to 
>>>>>>>>> stop
>>>>>>>>> simulating and reject any input that would otherwise prevent 
>>>>>>>>> its own
>>>>>>>>> termination.
>>>>>>>> Sure. Why doesn’t the STA simulate itself rejecting its input?
>>>>>>>>
>>>>>>>
>>>>>>> Because that is a STUPID idea and categorically impossible
>>>>>>> because the outermost HHH sees its needs to stop simulating
>>>>>>> before any inner HHH can possibly see this.
>>>>>>>
>>>>>>
>>>>>> In other words, you agree that Linz and others are correct that no 
>>>>>> H exists that satisfies these requirements:
>>>>>>
>>>>>>
>>>>>> Given any algorithm (i.e. a fixed immutable sequence of 
>>>>>> instructions) X described as <X> with input Y:
>>>>>>
>>>>>> A solution to the halting problem is an algorithm H that computes 
>>>>>> the following mapping:
>>>>>>
>>>>>> (<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
>>>>>> (<X>,Y) maps to 0 if and only if X(Y) does not halt when executed 
>>>>>> directly
>>>>>>
>>>>>
>>>>> No stupid! Those freaking requirements are wrong 
>>>>
>>>> In other words, you have no interest in something that would make 
>>>> all truth provable.
>>>>
>>>
>>> It will remain forever impossible to prove that five minutes
>>> ago ever existed. This is empirical truth mislabeled as synthetic truth.
>>>
>>> Semantic truth poorly labeled as analytic truth is the only
>>> truth that is either provable else untrue. It is {provable}
>>> on the basis of semantic connections to expressions that are
>>> stipulated as true.
>>>
>>
>> So you do want something that would make all truth provable.  An H 
>> that meets the following requirements would do that, therefore these 
>> requirements are not "wrong":
>>
> 
> *Ignorance on your part about this*
> https://philosophy.stackexchange.com/questions/43748/how-do-we-know- 
> the--wasnt-created-5-minutes-ago#:~:text=Ask%20Question,non- 
> falsifiable%20and%20all).

None-the-less an H that meets the requirements below would make all 
formal systems complete.  That makes such an H *very* useful, and 
therefore the requirements are not "wrong".

> 
>>
>> Given any algorithm (i.e. a fixed immutable sequence of instructions) 
>> X described as <X> with input Y:
>>
>> A solution to the halting problem is an algorithm H that computes the 
>> following mapping:
>>
>> (<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
>> (<X>,Y) maps to 0 if and only if X(Y) does not halt when executed 
>> directly
>>
>>
> 
>