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On 3/12/2024 1:31 PM, immibis wrote:Once we understand that either YES or NO is the right answer, the whole rebuttal is tossed out as invalid and incorrect.On 12/03/24 19:12, olcott wrote:Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩ halts∀ H ∈ Turing_Machine_Deciders>
∃ TMD ∈ Turing_Machine_Descriptions |
Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
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There is some input TMD to every H such that
Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
And it can be a different TMD to each H.
>When we disallow decider/input pairs that are incorrect>
questions where both YES and NO are the wrong answer
Once we understand that either YES or NO is the right answer, the whole rebuttal is tossed out as invalid and incorrect.
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Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn // Ĥ applied to ⟨Ĥ⟩ does not halt
BOTH YES AND NO ARE THE WRONG ANSWER FOR EVERY Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩
Naive set theory says that for every predicate P, the set {x | P(x)} exists. This axiom was a mistake. This axiom is not in ZFC.Russell's paradox did not allow this answer within Naive set theory.Does the barber that shaves everyone that does not shave>
themselves shave himself? is rejected as an incorrect question.
The barber does not exist.
The barber does not exist and the proposition does not exist.The following is true statement:That might be correct I did not check it over and over
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∀ Barber ∈ People. ¬(∀ Person ∈ People. Shaves(Barber, Person) ⇔ ¬Shaves(Person, Person))
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The following is a true statement:
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¬∃ Barber ∈ People. (∀ Person ∈ People. Shaves(Barber, Person) ⇔ ¬Shaves(Person, Person))
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again and again to make sure.
The same reasoning seems to rebut Gödel Incompleteness:
...We are therefore confronted with a proposition which
asserts its own unprovability. 15 ... (Gödel 1931:43-44)
¬∃G ∈ F | G := ~(F ⊢ G)
Any G in F that asserts its own unprovability in F is
asserting that there is no sequence of inference steps
in F that prove that they themselves do not exist in F.
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