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From: joes <noreply@example.org>
Newsgroups: comp.theory
Subject: Re: DDD simulated by HHH cannot possibly halt (Halting Problem) ---
 mindless robots
Date: Mon, 14 Apr 2025 12:33:05 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Mon, 14 Apr 2025 06:46:20 -0500 schrieb olcott:
> On 4/13/2025 9:12 PM, dbush wrote:
>> 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
>>>>
> Such an HHH works fine when the input DD is not attempting to do the
> opposite of whatever this HHH reports. This is not a problem though. DD
> merely changes its own behavior through the pathological self-reference
> that it implements.
DD doesn’t change anything. It is completeley determined by the return
value of HHH. Either it halts or it doesn’t, and HHH returns the wrong
result.

> Then HHH simply reports on this changed behavior. HHH need not even know
> that DD is calling itself. It only need to know that the behavior of DD
> would prevent its own termination.
If HHH reports on what DD *would* do *if* HHH returned the other value,
that’s changing the input. (HHH doesn’t „know” anything at all.)

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.