XPost: comp.theory, comp.ai.philosophy, sci.math   
   From: polcott333@gmail.com   
      
   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.   
      
      
   --   
   Copyright 2025 Olcott

   
      
   My 28 year goal has been to make 
   
   "true on the basis of meaning expressed in language"
   
   reliably computable.

   
      
   This required establishing a new foundation
   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)