XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 10/14/2025 10:34 PM, Kaz Kylheku wrote:   
   > 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!   
   >   
      
   *Five different systems could figure it all out from this*   
   They are 67-fold smarter than last year.   
      
      
      
   Please think this all the way through without making any guesses   
      
   Simulating Termination Analyzer HHH correctly simulates its input until:   
   (a) Detects a non-terminating behavior pattern:   
        abort simulation and return 0.   
   (b) Simulated input reaches its simulated "return" statement:   
        return 1.   
   (c) If HHH must abort its simulation to prevent its own non-termination   
        then HHH is correct to abort this simulation and return 0.   
      
   typedef int (*ptr)();   
   int HHH(ptr P);   
      
   int DD()   
   {   
      int Halt_Status = HHH(DD);   
      if (Halt_Status)   
        HERE: goto HERE;   
      return Halt_Status;   
   }   
      
   int main()   
   {   
      HHH(DD);   
   }   
      
   What value should HHH(DD) correctly return?   
      
      
   >> 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.)   
      
      
   --   
   Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius   
   hits a target no one else can see." Arthur Schopenhauer   
      
   --- SoupGate-Win32 v1.05   
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