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On 3/11/2024 12:13 PM, Richard Damon wrote:OF course there is.On 3/11/24 6:19 AM, olcott wrote:There is no such thing as a sub-machine.On 3/11/2024 1:02 AM, Richard Damon wrote:>On 3/10/24 10:44 PM, olcott wrote:>
>*Every implementation of Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ gets the wrong answer*>
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨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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Yes, you have rotely repeated that many times, not knowing what that implies, or doesn't imply.
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Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨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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*Every implementation of Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ gets the wrong answer*
*Every implementation of Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ gets the wrong answer*
*Every implementation of Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ gets the wrong answer*
Really?
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A "submachine" doesn't have a requirement except to act as the machine it is a copy of.
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No, there IS a 'Correct answer', it just isn't the one that that H gives.So, what you are REALLY Saying is that:Both answers of YES and NO are incorrect for any H ⟨Ĥ⟩ ⟨Ĥ⟩
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H (H^) (H^) gets the wrong answer for every implementation of H,
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that is inconsistent with the behavior of Ĥ ⟨Ĥ⟩ when an
exact copy of this same H is embedded within Ĥ.
Because both YES and NO are the wrong answer for this HBut not for the question to have a correct answer.
it is a logical impossibility H to answer that question
correctly.
It is much easier to see that it is a logical impossibilityyes, there IS a correct answer, but H doesn't give it, so H is just wrong.
for Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ to provide an YES NO answer that corresponds
to the behavior of Ĥ ⟨Ĥ⟩.
But that isn't the question, so you are admitting to using a Strawman.but then we see that you are changing the input across you arguement, and thus it doesn't show an invalid questin.Both YES and NO are the wrong answer to the question:
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There are Many H' that can get the answer to the question that this H is being asked, so the question is valid.
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Does Ĥ ⟨Ĥ⟩ halt? for every implementation of Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩.
Thus when we do not ignore the context of who is asked
Does Ĥ ⟨Ĥ⟩ halt? <is> an incorrect question for: Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩.
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