XPost: comp.theory, sci.logic, sci.math   
   From: 643-408-1753@kylheku.com   
      
   On 2025-11-18, Mike Terry  wrote:   
   > On 18/11/2025 03:10, dart200 wrote:   
   >> yes i meant generally   
   >>   
   >> you also can't compute generally whether you can or cannot compute whether   
   a an machine description   
   >> halts or not   
   >   
   > What does that mean though?   
   >   
   > It sounds like you're asking for a /single/ TM that given /any/ machine   
   description D, must compute   
   > "whether or not D's halting is computable".  [And saying no such single TM   
   exists?]   
      
   Since the halting of any machine /is/ individually computable, then that   
   appears false. We can compute whether it is computable whether a single,   
   given machine halts. We can compute that with the word "True".   
      
     for_all (M) : is_halting_computable(M) = T   
      
   For every machine, halting is computable --- just not by   
   an algorithm that also works for all other machines since there   
   is no such thing.   
      
   Another way to look at an existential rephrasing:   
      
     not ( some (M) : is_halting_computable(M) = F )   
      
   It is false that there exist machines whose halting is   
   individually incomputable.   
      
   That has been specific misconception that Olcott labored under for   
   many years. He showed clear signs of believing that the D template   
   program is /one/ function which is not decidable by any H.   
      
   It's not clear if he has been fully disabused of this notion,   
   years of unbridled abuse notwithstanding.   
      
      
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