Re: ZFC solution to incorrect questions: reject them --Gödel--

On 12/03/24 21:11, olcott wrote:

On 3/12/2024 2:40 PM, Richard Damon wrote:

On 3/12/24 12:02 PM, olcott wrote:

On 3/12/2024 1:31 PM, immibis wrote:

On 12/03/24 19:12, olcott wrote:

∀ H ∈ Turing_Machine_Deciders
∃ TMD ∈ Turing_Machine_Descriptions  |
Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>
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.
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When we disallow decider/input pairs that are incorrect
questions where both YES and NO are the wrong answer

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Once we understand that either YES or NO is the right answer, the whole rebuttal is tossed out as invalid and incorrect.
>

>
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
BOTH YES AND NO ARE THE WRONG ANSWER FOR EVERY Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩

>
No, because a given H will only go to one of the answers. THAT will be wrong, and the other one right.
>

 ∀ H ∈ Turing_Machine_Deciders
∃ TMD ∈ Turing_Machine_Descriptions  |
Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
 Not exactly. A pair of otherwise identical machines that
(that are contained within the above specified set)
only differ by return value will both be wrong on the
same pathological input.

You know this is not true so why lie? One of them will be correct on that input. If Ĥ is the function D from x86utm, then Ĥ applied to ⟨Ĥ⟩ does halt, YES is the correct answer, and any decider which returns YES on this input is correct on this input.