XPost: comp.theory, sci.logic, sci.math   
   From: 643-408-1753@kylheku.com   
      
   On 2025-10-15, olcott  wrote:   
   > On 10/14/2025 9:46 PM, Kaz Kylheku wrote:   
   >> On 2025-10-15, olcott  wrote:   
   >>> 5. In short   
   >>>   
   >>> The halting problem as usually formalized is syntactically consistent   
   >>> only because it pretends that U(p) is well-defined for every p.   
   >>>   
   >>> If you interpret the definitions semantically — as saying that   
   >>> U(p) should simulate the behavior   
   >>   
   >> ... then you're making a grievous mistake. The halting function doesn't   
   >> stipulate simulation.   
   >>   
   >   
   > None-the-less it is a definitely reliable way to   
   > discern the actual behavior that the actual input   
   > actually specifies.   
      
   No, it isn't.  When the input specifies halting behavior   
   then we know that simulation will terminate in a finite number   
   of steps. In that case we discern that the input has terminated.   
      
   When the input does not terminate, simulation does not inform   
   about this.   
      
   No matter how many steps of the simulation have occurred,   
   there are always more steps, and we have no idea whether   
   termination is coming.   
      
   In other words, simulation is not a halting decision algorithm.   
      
   Exhaustive simulation is what we must desperately avoid   
   if we are to discern the halting behavior that   
   the actual input specifies.   
      
   You are really not versed in the undergraduate rudiments   
   of this problem, are you!   
      
   > The system that the halting problem assumes is   
   > logically incoherent when  ...   
      
   when it is assumed that halting can be decided; but that inconsitency is   
   resolved by concluding that halting is not decidable.   
      
   ... when you're a crazy crank on comp.theory, otherwise all good.   
      
   >    "You’re making a sharper claim now — that even   
   >     as mathematics, the halting problem’s assumed   
   >     system collapses when you take its own definitions   
   >     seriously, without ignoring what they imply."   
   >   
      
   I don't know who is supposed to be saying this and to whom;   
   (Maybe one of your inner vocies to the other? or AI?)   
      
   Whoever is making this "sharper claim" is an absolute dullard.   
      
   The halting problem's assumed system does positively /not/   
   collapse when you take its definitions seriously,   
   and without ignoring what they imply.   
      
   (But when have you ever done that, come to think of it.)   
      
   --- SoupGate-Win32 v1.05   
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