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On 11/03/24 14:19, olcott wrote:This proves that both Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ are being asked*Every implementation of Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ gets the wrong answer*You agree. And since every implementation of Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ gets the same answer as H ⟨Ĥ⟩ ⟨Ĥ⟩ (it is stipulated) then obviously H ⟨Ĥ⟩ ⟨Ĥ⟩ also gets the wrong answer.
Whenever anyone or anything is asks a YES/NO questionso what is wrong with it?It is also true that every instance of that question has a right answer, it just isn't the one that H gives.>
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Every decision problem that includes undecidable instances only has
these instances because there is something wrong with the decision
problem specification.
The gist of his idea is correct even if the exact words are not.The proof of the halting problem assumes a universal haltIf you tell me a consistent universal halt test I will tell you a consistent program that the test cannot handle. It will definitely be a program. There will be no valid rebuttal that it isn't a program at all.
test exists and then provides S as an example of a program
that the test cannot handle. But S is not a program at all.
It is not even a conceptual object, and this is due to
inconsistencies in the specification of the halting function.
(Stoddart: 2017)
When we ask Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ whether Ĥ halts on input ⟨Ĥ⟩*This is my unique contribution to the field of the Halting Problem*We do not ask it that. We ask it whether Ĥ halts on input ⟨Ĥ⟩. This is an objective specification, not subjective.
*This is my unique contribution to the field of the Halting Problem*
*This is my unique contribution to the field of the Halting Problem*
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When we ask H ⟨Ĥ⟩ ⟨Ĥ⟩:
Does your input halt on its input?
H(D,D) and H1(D,D) are fully implemented to answer that questionmeaning: Would Ĥ ⟨Ĥ⟩ halt on its input, then H gets the wrong answer.We can't ask that question because it is subjective. And that is a different question.
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When we ask the exact same question meaning:
Will you halt if you never abort your simulation?
H(D,D) and H1(D,D) correctly answer that question for threeThen every H always gets the right answer.If you ask me to recite Einstein's equations, I will answer wrong. If you ask me 1+1, I will answer right. That I answer correctly to one question has no relevance to that I answer incorrectly to another question.
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