XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   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.   
      
   The system that the halting problem assumes is   
   logically incoherent when you simply don't ignore   
   what it entails even within the domain of pure math.   
      
      "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."   
      
   Carefully study the last five steps.   
      
   > Moreover it is painfully obvious that simulation is /not/ the way toward   
   > calculating halting.   
   >   
   > Simulation is precisely the same thing as execution. Programs are   
   > abstract; the machines we have built are all simulators. Simulation is   
   > not software running on a non-simulator. Simulation is hardware also.   
   > An ARM64 core is a simulator; Python's byte code machine is a simulator;   
   > a Lisp-in-Lisp metacircular interpreter is a simulator, ...   
   >   
   > We /already know/ that when we execute, i.e. simulate, programs, that they   
   > sometimes do not halt. The halting question is concerned entirely with   
   > the question whether we can take an algorithmic short-cut toward knowing   
   > whether every program will halt or not.   
   >   
   > We already knew when asking this question for the first time that   
   > simulation is not the answer. Simulation is exactly that process which   
   > does not terminate for non-terminating programs and that we need to   
   > /avoid doing/ in order to decide halting.   
   >   
   > The abstract halting function is well-defined by the fact that every   
   > machine is deterministic, and either halts or does not halt.  A machine   
   > that halts always halts, and one which does not halt always fails to   
   > halt.   
   >   
   > If it ever seems as if the same machine both halts and does not   
   > halt, we have made some mistake in our reasoning or symbol   
   > manipulation; if we take a fresh, correct look, we will find that   
   > we have been working with two machines.   
   >   
   >> That is a stronger critique than “the definition doesn’t match   
   reality.”   
   >   
   > I'm not convinced You have no intellectual capacity for measuring the   
   > relative strength of a critique.   
   >   
   > You have a long track record of dismissing perfectly correct, valid,   
   > and on-point/relevant critiques.   
   >   
      
   --   
   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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