Re: Working out the details of the steps of Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ <Ĥ> ⊢* Ĥ.Hqn

On 3/9/24 8:53 AM, olcott wrote:

On 3/9/2024 10:21 AM, immibis wrote:

On 9/03/24 17:00, olcott wrote:

On 3/9/2024 1:05 AM, Richard Damon wrote:

On 3/8/24 10:40 PM, olcott wrote:

On 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⟩.

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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?

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Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ cannot just sit around scratching its head it
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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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.
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 Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ can fool itself yet cannot possibly fool an external H ⟨Ĥ⟩ ⟨Ĥ⟩.
 

Why not?
Are you thinking H will just simulate until H^.H makes its decision?
We know the outcome of that, never answering, and thus failing.