XPost: comp.theory, sci.logic   
   From: polcott333@gmail.com   
      
   On 8/7/2025 4:11 AM, Fred. Zwarts wrote:   
   > Op 07.aug.2025 om 05:15 schreef olcott:   
   >>   
   >> 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.   
   >>   
   >> The Linz proof has Ĥ take its own machine description   
   >> as input (this is fine) yet requires Ĥ.embedded_H to   
   >> directly report on its own behavior. No TM can ever   
   >> do that.   
   > That is your mistake. It does not require to report on its own   
   > behaviour, but on the behaviour of Ĥ.   
      
   That *is* its own behavior.   
   Ĥ.embedded_H *is* an aspect of Ĥ.   
   Ĥ.embedded_H does correctly report on the behavior   
   specified by its input ⟨Ĥ⟩ ⟨Ĥ⟩ as measured by its   
   correct simulation of this input.   
      
   > It is irrelevant whether the   
   > behaviour of Ĥ resembles that of embedded_H.   
      
      
      
   --   
   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)