XPost: comp.theory, comp.lang.c++, comp.lang.c
From: polcott333@gmail.com
On 10/12/2025 11:22 PM, dbush wrote:
> On 10/13/2025 12:12 AM, olcott wrote:
>> On 10/12/2025 10:49 PM, dbush wrote:
>>> On 10/12/2025 11:43 PM, olcott wrote:
>>>> On 10/12/2025 9:59 PM, dbush wrote:
>>>>> On 10/12/2025 10:57 PM, olcott wrote:
>>>>>> On 10/12/2025 9:40 PM, dbush wrote:
>>>>>>> On 10/12/2025 10:34 PM, olcott wrote:
>>>>>>>> On 10/12/2025 9:29 PM, dbush wrote:
>>>>>>>>> On 10/12/2025 10:20 PM, olcott wrote:
>>>>>>>>>> On 10/12/2025 9:15 PM, dbush wrote:
>>>>>>>>>>> On 10/12/2025 9:56 PM, olcott wrote:
>>>>>>>>>>>> On 10/12/2025 8:22 PM, dbush wrote:
>>>>>>>>>>>>> On 10/12/2025 9:20 PM, olcott wrote:
>>>>>>>>>>>>>> On 10/12/2025 3:11 PM, dbush wrote:
>>>>>>>>>>>>>>> On 10/12/2025 11:47 AM, olcott wrote:
>>>>>>>>>>>>>>>> On 10/12/2025 9:19 AM, dbush wrote:
>>>>>>>>>>>>>>>>> On 10/12/2025 9:50 AM, olcott wrote:
>>>>>>>>>>>>>>>>>> Please think this all the way through without making
>>>>>>>>>>>>>>>>>> any guesses
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Simulating Termination Analyzer HHH correctly
>>>>>>>>>>>>>>>>>> simulates its input until:
>>>>>>>>>>>>>>>>>> (a) Detects a non-terminating behavior pattern:
>>>>>>>>>>>>>>>>>> abort simulation and return 0.
>>>>>>>>>>>>>>>>>> (b) Simulated input reaches its simulated "return"
>>>>>>>>>>>>>>>>>> statement:
>>>>>>>>>>>>>>>>>> return 1.
>>>>>>>>>>>>>>>>>> (c) If HHH must abort its simulation to prevent its
>>>>>>>>>>>>>>>>>> own non- termination
>>>>>>>>>>>>>>>>>> then HHH is correct to abort this simulation and
>>>>>>>>>>>>>>>>>> return 0.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> These conditions make HHH not a halt decider because
>>>>>>>>>>>>>>>>> they are incompatible with the requirements:
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> It is perfectly compatible with those requirements
>>>>>>>>>>>>>>>> except in the case where the input calls its own
>>>>>>>>>>>>>>>> simulating halt decider.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> In other words, not compatible. No "except".
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Given any algorithm (i.e. a fixed immutable sequence of
>>>>>>>>>>>>>>>>> instructions) X described as with input Y:
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> A solution to the halting problem is an algorithm H
>>>>>>>>>>>>>>>>> that computes the following mapping:
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> (,Y) maps to 1 if and only if X(Y) halts when
>>>>>>>>>>>>>>>>> executed directly
>>>>>>>>>>>>>>>>> (,Y) maps to 0 if and only if X(Y) does not halt
>>>>>>>>>>>>>>>>> when executed directly
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> typedef int (*ptr)();
>>>>>>>>>>>>>>>>>> int HHH(ptr P);
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> int DD()
>>>>>>>>>>>>>>>>>> {
>>>>>>>>>>>>>>>>>> int Halt_Status = HHH(DD);
>>>>>>>>>>>>>>>>>> if (Halt_Status)
>>>>>>>>>>>>>>>>>> HERE: goto HERE;
>>>>>>>>>>>>>>>>>> return Halt_Status;
>>>>>>>>>>>>>>>>>> }
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> int main()
>>>>>>>>>>>>>>>>>> {
>>>>>>>>>>>>>>>>>> HHH(DD);
>>>>>>>>>>>>>>>>>> }
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> What value should HHH(DD) correctly return?
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Error: assumes it's possible to design HHH to get a
>>>>>>>>>>>>>>>>> correct answer.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> HHH(DD) gets the correct answer within its set
>>>>>>>>>>>>>>>> of assumptions / premises
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Which is incompatible with the requirements for a halt
>>>>>>>>>>>>>>> decider:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Yes, but the requirements for a halt decider are inconsistent
>>>>>>>>>>>>>> with reality.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> In other words, you agree with Turing and Linz that the
>>>>>>>>>>>>> following requirements cannot be satisfied:
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Sure and likewise no Turing machine can
>>>>>>>>>>>> give birth to a real live fifteen story
>>>>>>>>>>>> office building. All logical impossibilities
>>>>>>>>>>>> are exactly equally logical impossible.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> So we're in agreement: no algorithm exists that can tell us
>>>>>>>>>>> if any arbitrary algorithm X with input Y will halt when
>>>>>>>>>>> executed directly, as proven by Turning and Linz.
>>>>>>>>>>
>>>>>>>>>> In exactly the same way that: "this sentence is not true"
>>>>>>>>>> cannot be proven true or false. It is a bogus decision
>>>>>>>>>> problem anchored in
>>>>>>>>
>>>>>>>> a fundamentally incorrect notion of truth.
>>>>>>>>> The false assumption that such an algorithm *does* exist.
>>>>>>>>
>>>>>>>> Can we correctly say that the color of your car is fifteen feet
>>>>>>>> long?
>>>>>>>> For the body of analytical truth coherence is the key and
>>>>>>>> incoherence rules out truth.
>>>>>>>>
>>>>>>>
>>>>>>> There is nothing incoherent about wanting to know if any
>>>>>>> arbitrary algorithm X with input Y will halt when executed directly.
>>>>>>>
>>>>>>
>>>>>> Tarski stupidly thought this exact same sort of thing.
>>>>>> If a truth predicate exists then it could tell if the
>>>>>> Liar Paradox is true or false. Since it cannot then
>>>>>> there must be no truth predicate.
>>>>>
>>>>> Correct. If you understood proof by contradiction you wouldn't be
>>>>> questioning that.
>>>>>
>>>>
>>>> It looks like ChatGPT 5.0 is the winner here.
>>>> It understood that requiring HHH to report on
>>>> the behavior of the direct execution of DD()
>>>> is requiring a function to report on something
>>>> outside of its domain.
>>>
>>> False. It is proven true by the meaning of the words that a finite
>>> string description of a Turing machine specifies all semantic
>>> properties of the machine it describes, including whether that
>>> machine halts when executed directly.
>>>
>>
>> ChatCPT 5.0 was the first LLM to be able to prove
>> that is counter-factual.
>
> Ah, so you don't believe in semantic tautologies?
>
*They are the foundation of this whole system*
Any system of reasoning that begins with a consistent
system of stipulated truths and only applies the truth
preserving operation of semantic logical entailment to
this finite set of basic facts inherently derives a
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