XPost: comp.theory, sci.logic, comp.lang.c++   
   From: mikko.levanto@iki.fi   
      
   On 15/12/2025 16:31, olcott wrote:   
   > On 12/15/2025 3:20 AM, Mikko wrote:   
   >> On 15/12/2025 02:15, olcott wrote:   
   >>> On 12/14/2025 4:46 AM, Mikko wrote:   
   >>>> On 11/12/2025 16:38, olcott wrote:   
   >>>>> On 12/11/2025 2:53 AM, Mikko wrote:   
   >>>>>> olcott kirjoitti 10.12.2025 klo 18.27:   
   >>>>>>>   
   >>>>>>> DD() executed from main() calls HHH(DD) thus is   
   >>>>>>> not one-and-the-same-thing as an argument to HHH.   
   >>>>>>   
   >>>>>> If the last sentence is true then this is not the counter exmaple   
   >>>>>> mentioned in certain proofs of noncomputability of halting and   
   >>>>>> therefore not relevant in that context. The halting problem reuqires   
   >>>>>> that HHH can determine whether the counter example halts. That is,   
   >>>>>> you must be able to replace "???" in   
   >>>>>>   
   >>>>>>    #include  // or your replacement   
   >>>>>>    int main (void)   
   >>>>>>    {   
   >>>>>>      int Halt_Status = HHH(???); // put the correct argument here   
   >>>>>>      printf("HHH says: %s\n", Halt_Status ? "halts" : "does not   
   >>>>>> halt");   
   >>>>>>      return Halt_Status;   
   >>>>>>    }   
   >>>>>>   
   >>>>>> with whatever specifies the behaviour of DD to HHH. If you can't   
   >>>>>> do this then HHH is not a halt decider nor a partial halt decider.   
   >>>>   
   >>>>> When the halting problem requires a halt decider   
   >>>>> to report on the behavior of a Turing machine this   
   >>>>> is always a category error.   
   >>>>   
   >>>> That you don't know what "category error" means does not justify your   
   >>>> claim. Apparently you can't apply definitions.   
   >>>   
   >>> Turing machines only compute functions from finite   
   >>> strings they never compute functions from Turing   
   >>> machines.   
   >>   
   >> True, but irrelevant to questions about category errors.   
   >>   
   >>> A halt decider can at best compute the behavior of   
   >>> a Turing machine through the proxy of a finite   
   >>> string machine description it never computes it   
   >>> directly from another Turing machine.   
   >>>   
   >>> Whenever any textbook says that a halt decider   
   >>> must compute halting for machine M on input w   
   >>> is it wrong.   
   >>   
   >> Which textbook actually says "must"? It is not wrong to say "must" in   
   >> the sense that any decider that does not compute whether machine M   
   >> halts on input w is not a halt decider. But using "must" is not the   
   >> clearest way to say it because the word "must" other meanings.   
   >>   
   >>  > It actually computes halting that this input pair specifies (⟨M⟩,   
   w).   
   >>   
   >> There is an unbalanced parenthesis above.   
   >   
   > No halt decider ever computes the halt status   
   > of a machine except through the proxy of finite   
   > strings.   
      
   No halt decider computes anything because there are not halt deciders.   
   But we may compare to univerals Turing machines, which do exist.   
   A finite string tells to a universal Turing machine everything needed   
   to fully simulate the behaviour of any Turing machine with any input.   
      
   > Because all computation only transforms finite   
   > strings the result of this transformation is the   
   > ultimate correct answer.   
      
   No, it is not the ultimate correct answer to every question. In   
   particular, it differes from the ultimate correct answer to at   
   least one halting question.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
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