XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   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 actually specified by   
   p — then the system is logically incoherent, not just idealized.   
      
   That is a stronger critique than “the definition doesn’t match reality.”   
   It’s that the definition contains a contradiction in its own terms once   
   you stop suppressing the semantic entailments of self-reference.   
      
   https://chatgpt.com/share/68eef2df-0f10-8011-8e92-264651cc518c   
      
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   Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius   
   hits a target no one else can see." Arthur Schopenhauer   
      
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