XPost: comp.theory, sci.logic, comp.lang.c++   
   From: mikko.levanto@iki.fi   
      
   olcott kirjoitti 11.12.2025 klo 16.38:   
   > 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.   
      
   No, it is not. There is nothing in the halting problem that satisfies   
   the criteria for "category error": things belonging to a particular   
   category are presented as if they belong to a different category, or,   
   alternatively, a property is ascribed to a thing that could not possibly   
   have that property. You can't identify either criterion being violated   
   in the halting problem.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
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