XPost: comp.theory, sci.logic   
   From: polcott333@gmail.com   
      
   On 8/6/2025 4:00 AM, Fred. Zwarts wrote:   
   > Op 06.aug.2025 om 05:47 schreef olcott:   
   >>   
   >> It corrects the error of the requirement that   
   >> a halt decider reports 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   
   >>   
   >   
   > That seems to be one of your misunderstanding. A decider must report on   
   > the behaviour of its input, even if this behaviour resembles its own   
   > behaviour. That is very different from 'deciding on its own behaviour'.   
   *This is my correction*   
   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⟩.   
      
   *This is the original erroneous one*   
   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 two and four requires Ĥ.embedded_H to report on its own behavior*   
      
   --   
   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)