XPost: comp.theory, sci.logic   
   From: polcott333@gmail.com   
      
   On 8/1/2025 6:15 PM, Richard Damon wrote:   
   > On 8/1/25 6:54 PM, olcott wrote:>>   
   >> ⟨Ĥ⟩ ⟨Ĥ⟩ simulated by embedded_H determines the   
   >> behavior that *THE ACTUAL INPUT* to embedded_H   
   >> specifies. Ĥ ⟨Ĥ⟩ is not and cannot possibly be   
   >> *AN ACTUAL INPUT* to embedded_H so its differing   
   >> behavior *DOES NOT COUNT*.   
   >>   
   >   
   > NO!!!!   
   >   
   > By that standard, any input could mean anything becuase the machine it   
   > is being given can do whatever it wants with it.   
   >   
      
   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⟩   
      
   Yes if you ignore that I said that Ĥ.embedded_H   
   is based on a UTM and ignore the above is the   
   definition of machine Ĥ that could be true.   
      
   > But then, that IS how you consider logic to work, so it makes sense that   
   > is what you would think.   
   >   
   > The *DEFINITION* of the "behavior of this input", for a halting decider,   
   > is the behavior of the machine that input represent.   
   >   
      
   "Represents" is a vague weasel word that has been   
   used historically. "Specifies" is what has always   
   been meant.   
      
   > Anything else is just an admission of lying, as the problem statement is   
   > to decide on the behavior of the machine that input represents.   
   >   
   > Sorry, you just admitted you are just a blantant liar that doesn't   
   > respect definitions, and thus NOTHING you say should be considered usable.   
   I don't worship textbook authors as infallible Gods.   
   Even definitions can be proved wrong when they are   
   proved to contradict other definitions.   
      
   --   
   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)