Re: ZFC solution to incorrect questions: reject them

On 3/12/24 12:57 PM, olcott wrote:

On 3/12/2024 1:41 PM, Richard Damon wrote:

On 3/12/24 11:12 AM, 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)
>
When we disallow decider/input pairs that are incorrect
questions where both YES and NO are the wrong answer
(the same way the ZFC disallowed self-referential sets) then
pathological inputs are not allowed to come into existence.

>
But each of the questions in your set, that for each H^ built on each SPECIFIC H, there is a correct answer, just not the one that H gives, so the ALL the questions are correct.
>

 *Halts(TMD) means true if TMD actually halts and false otherwise*
∀ H ∈ Turing_Machine_Deciders
∃ TMD ∈ Turing_Machine_Descriptions  |
(H TMD ⊢* H.qy != Halts(TMD)) ∧ (H TMD ⊢* H.qn != Halts(TMD))
 The questions in my set are only the H/TMD pairs specified above.
 

Right, so for Each H, we can find a TMD, which could be the H^ built on THAT H.
then if H goes to qy, then HALTS(TMD) is false, so that H was wrong, but there was a correct answer.
and if H goes to qn, then HALTD(TMD) is true, so that H was wrong, but there was a correct answer.
So, for EACH INDIVIDUAL H, which is what the conditions look at, there IS a correct answer for that input we foud, just not the one that THAT H gave.
No one claims that no Halt Decider can get any correct decisions, which seems to be what you are trying to claim.
You don't seem to understand logical categorical operations.