XPost: comp.theory   
   From: acm@muc.de   
      
   [ Followup-To: set ]   
      
   In comp.theory olcott  wrote:   
      
   > Summary of the key point:   
   > The halting problem's self-referential construction creates two distinct   
   > computational entities:   
      
   There is no self reference in the statement of the halting problem.   
      
   > Input (DD-as-simulated-by-HHH): Shows non-halting behavior - recursive   
   > pattern that HHH correctly identifies   
   > Non-input (DD-as-directly-executed): Halts because HHH returns 0   
      
   > The category error occurs when the halting problem asks HHH to report on   
   > the direct execution behavior, which:   
      
   The halting problem does no such thing.  If anything, it is your   
   constructions of HHH and DD which have the category error, not the   
   statement of the problem.  But there is no such error.   
      
   > Depends on HHH's own return value   
   > Is therefore not a property of the input HHH analyzes   
   > Represents a different computational object than what HHH can examine   
   > through simulation   
      
   What your purported decider decides on is a pure function.  This is an   
   abstract mathematical entity, which retains its identity regardless of   
   whether its a "computational object" or just a specification written on   
   paper with a pencil.   
      
   It's the same thing.   
      
   > The philosophical point: A Turing machine decider should only be   
   > expected to report on properties determinable from its input.   
      
   There's no "expected" about it.  A turing machine does what it does, and   
   is incapable, by its very construction, of reporting on anything apart   
   from its input.   
      
   > When the halting problem construction makes the "actual behavior"   
   > dependent on the decider's output, it's asking the decider to report   
   > on something outside its input - hence, a category error.   
      
   No, the purported decider's input is a pure function, the same thing   
   which is also used elsewhere.   
      
   > This reframes the "impossibility" of the halting problem not as a   
   > limitation of computation per se, but as a conflation between what an   
   > analyzer observes about its input versus what happens when that input is   
   > executed with the analyzer's answer embedded in it.   
      
   You're wide of the mark.  The input is the same pure function in both   
   cases.   
      
   > The distinction between input-behavior and non-input-behavior is the   
   > crux of resolving the apparent paradox.   
      
   The "paradox" is entirely in your own mistaken analysis.   
      
   > https://claude.ai/share/6e4ccef9-9749-4fb4-b58d-946fe18e7c73   
      
   > --   
   > Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius   
   > hits a target no one else can see." Arthur Schopenhauer   
      
   --   
   Alan Mackenzie (Nuremberg, Germany).   
      
   --- SoupGate-Win32 v1.05   
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