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On 3/9/2024 1:05 AM, Richard Damon wrote:H ⟨A⟩ ⟨B⟩ cannot just sit around scratching its head, it must do something. As soon as we have the basis for what H will do, then we have a basis to construct an Ĥ where H ⟨Ĥ⟩ ⟨Ĥ⟩ is wrong.On 3/8/24 10:40 PM, olcott wrote:Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ cannot just sit around scratching its head itOn 3/9/2024 12:25 AM, Richard Damon wrote:>On 3/8/24 9:55 PM, olcott wrote:>Ĥ.q0 ⟨Ĥ⟩ ⊢* ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩ halts>
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn // Ĥ applied to ⟨Ĥ⟩ does not halt
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Expecting Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ to correctly report on the behavior of
Ĥ ⟨Ĥ⟩ is a little nuts because Ĥ contradicts Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩.
But that is the job it signed up for when it tried to call itself a Halt Decider.
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There is no correct answer that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ can possibly
provide that corresponds to the behavior of this Ĥ ⟨Ĥ⟩.
Therefore it must have a basis for its wrong answer.
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WHY?
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What is the actual grounds for that statement?
must do something. As soon as we have the basis for what
it will do, then H ⟨Ĥ⟩ ⟨Ĥ⟩ has its basis to correctly
decide halting.
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