XPost: comp.theory, sci.logic   
   From: polcott333@gmail.com   
      
   On 8/4/2025 5:34 PM, Mr Flibble wrote:   
   > On Mon, 04 Aug 2025 13:29:04 -0500, olcott wrote:   
   >   
   >> Diagonalization only arises when one assumes that a Turing machine   
   >> decider must report on its own behavior instead of the behavior   
   >> specified by its machine description.   
   >>   
   >> Everyone assumes that these must always be the same.   
   >> That assumption is proven to be incorrect.   
   >>   
   >> When one assumes a halt decider based on a UTM then the simulated input   
   >> remains stuck in recursive simulation never reaching simulated states   
   >> ⟨Ĥ.∞⟩ or ⟨Ĥ.qn⟩.   
   >>   
   >> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.∞ Ĥ.q0   
   ⟨Ĥ⟩ ⊢*   
   > Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩   
   >> ⊢* Ĥ.qn   
   >>   
   >> (a) Ĥ copies its input ⟨Ĥ⟩   
   >> (b) Ĥ invokes embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩   
   >> (c) embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩   
   >> (d) simulated ⟨Ĥ⟩ copies its input ⟨Ĥ⟩   
   >> (e) simulated ⟨Ĥ⟩ invokes simulated embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩   
   >> (f) simulated embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩   
   >> on and on never reaching any simulated final state of ⟨Ĥ.qn⟩   
   >>   
   >> When embedded_H aborts its simulation and transitions to Ĥ.qn on the   
   >> basis that its simulated input cannot possibly reach its own simulated   
   >> final halt state of ⟨Ĥ.qn⟩ embedded_H is correct.   
   >>   
   >> This causes embedded_H itself to halt, thus contradicting its result   
   >> *only if a Turing machine decider can be applied to its actual self* and   
   >> not merely its own machine description.   
   >   
   > Your Ĥ is not a halt decider as defined by the Halting Problem so has   
   > nothing to do with the Halting Problem.   
   >   
   > /Flibble   
      
   You have this part incorrectly. Ask Richard because   
   of what he explained to you the other night he may   
   correct you on this.   
      
   --   
   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)