XPost: comp.theory, comp.ai.philosophy, sci.math   
   From: mikko.levanto@iki.fi   
      
   On 13/12/2025 17:50, olcott wrote:   
   > On 12/13/2025 4:58 AM, Mikko wrote:   
   >> 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.   
   >   
   > Best First Principle   
   > All Turing machines only compute the mapping   
   > from an input finite string to some value.   
   >   
   > It is very difficult to see that the halting   
   > problem definition breaks that rule.   
   >   
   > I will work on making this more clear now that   
   > I have the best first principle.   
      
   None of above gives any reason to revise my comment. You don't say   
   anything about category errors.   
      
   The rule (or "principle") you present only says what a Turing macnine   
   can do, which is already known anyway. It does not restrict what a   
   problem statement can say, so it is irrelevant to the topic of this   
   discussion as specified on the subject line.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
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