XPost: comp.theory, sci.logic   
   From: polcott333@gmail.com   
      
   On 8/6/2025 6:01 AM, Richard Damon wrote:   
   > On 8/5/25 10:56 PM, olcott wrote:   
   >>   
   >> It is a requirement of the aspect of Ĥ named Ĥ.embedded_H.   
   >>   
   >   
   > Depends on which system you are working in.   
   >   
   > IF you are talking about Linz system, where H *IS* a Halt Decider,   
   If H *is* a halt decider then the proof that no halt   
   decider exists is done.   
      
   Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.∞,   
   if Ĥ applied to ⟨Ĥ⟩ halts, and   
   Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn   
   if Ĥ applied to ⟨Ĥ⟩ does not halt.   
      
   *Lines 2 and 4 above*   
   *Does insist that Ĥ.embedded_H report on its own behavior*   
      
       "The contradiction in Linz's (or Turing's) self-referential   
        halting construction only appears if one insists that the   
        machine can and must decide on its own behavior, which is   
        neither possible nor required."   
      
   https://chatgpt.com/share/6890ee5a-52bc-8011-852e-3d9f97bcfbd8   
      
   --   
   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   
    * Origin: you cannot sedate... all the things you hate (1:229/2)