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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 19:51:48 -0400
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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":


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