XPost: comp.theory, sci.logic   
   From: polcott333@gmail.com   
      
   On 8/6/2025 5:54 AM, Richard Damon wrote:   
   > On 8/5/25 11:47 PM, olcott wrote:   
   >>   
   >> It corrects the error of the requirement that   
   >> a halt decider reports on its own behavior.   
   >   
   > But it isn't an error.   
   >   
   > Halt Deciders need to answer about *ANY* program, and they are programs.   
   >   
   >>   
   >>     "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   
   >>   
   >   
   > Because you lied to it and said it was an error.   
   >   
      
   The above paragraph is proved true by the meaning of its words.   
   When we ask a Turing machine to report on its own behavior we   
   are assuming that its Turing Machine description is an accurate   
   proxy for this behavior. When there are exceptions to this rule   
   then we cannot possibly ask a Turing machine about its own behavior.   
   This is easily corrected:   
      
   Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.∞   
       if ⟨Ĥ⟩ ⟨Ĥ⟩ simulated by Ĥ.embedded_H reaches   
       its simulated final halt state of ⟨Ĥ.qn⟩, and   
      
   Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn   
       if ⟨Ĥ⟩ ⟨Ĥ⟩ simulated by Ĥ.embedded_H cannot possibly   
       reach its simulated final halt state of ⟨Ĥ.qn⟩.   
      
   When we use the above standard then a halt decider   
   will always report on the actual behavior that its   
   input actually specifies.   
      
   --   
   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)