XPost: comp.theory, comp.ai.philosophy, comp.software-eng   
   From: 563-365-8930@kylheku.com   
      
   ["Followup-To:" header set to comp.theory.]   
   On 2021-05-21, olcott  wrote:   
   > (A) Every simulation of input P that never halts unless simulating halt   
   > decider H aborts this simulation  a non-halting computation. This   
   > remains true even after H stops simulating P.   
   >   
   > ∃H ∈ Simulating_Halt_Deciders   
   > ∀P ∈ Turing_Machine_Descriptions   
   > ∀I ∈ Finite_Strings   
   >    (UTM(P,I) = ∞) ⊢ (H(P,I) = 0)   
      
   This seems to be saying that there exists some simulating decider H such   
   that H will call all non-halting Turing machines non-halting.   
      
   The halting theorem shows that the above is false; and you have   
   no disproof.   
      
   Among those those  inputs there is one problematic pair:   
      
     =    
      
   and so on, whose calculation is such that UTM(H_Hat, H_Hat) = ∞ if,   
   and only if, H(H_Hat, H_Hat) /= 0. Therefore it cannot be true that   
      
     (UTM(P,I) = ∞) ⊢ (H(P,I) = 0)   
      
   For that  pair. UTM(P, I) only calculates forever if H(P, I) is   
   nonzero, otherwise not.   
      
   > In English it says that whenever the input (P,I) to UTM would never halt   
   > then a simulating halt decider correctly decides not halting on this input.   
      
   It says that a simulating halt decider exists whuich correctly ...   
      
   > By screening out the distinctly different behavior of a UTM from a   
   > simulating halt decider the pathological self-reference error of the   
   > halting theorem is eliminated.   
      
   You have not "screened out" (and must not) the fact that the set of   
    pairs contains the "eviL" .   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)