XPost: comp.theory, sci.logic, sci.math   
   From: news.dead.person.stones@darjeeling.plus.com   
      
   On 19/11/2025 00:13, Kaz Kylheku wrote:   
   > 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.   
      
   Right, I realise that.   
      
   So my question "What does that mean though?" is still to be answered (by   
   nick).  If Nick's reply is   
   that it means what I described, then that will mark Nick's claim as false.   
      
   Maybe nick meant something else though.   
      
   >   
   > 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.   
      
   Well, he still chooses wordings that invite that confusion, when he has been   
   presented with   
   alternatives that are both neutral and correct.  I would say he does that,   
   because one of his   
   underlying confusions is exactly what you describe.  He wants to say something   
   that will /sound/   
   reasonable to casual listeners, but also keeps his confusion "on the table".   
      
      
   Mike.   
      
   --- SoupGate-Win32 v1.05   
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