Re: ZFC solution to incorrect questions: reject them

On 3/12/24 2:34 PM, olcott wrote:

On 3/12/2024 4:23 PM, Richard Damon wrote:

On 3/12/24 1:11 PM, 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.
>

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.
>

>
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 mean a pair of DIFFERENT machines. Any difference is different.

 Every decider/input pair (referenced in the above set) has a
corresponding decider/input pair that only differs by the return
value of its decider.

Nope.
Lets break it down.
FIRST, we go through each of the H's due to:
∀ H ∈ Turing_Machine_Deciders
Then for Each of them we find that we can find an input, that might be a different input of each decider:
∃ TMD ∈ Turing_Machine_Descriptions
The Results of which, that decider give a wrong answer for that input:
Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
So, in no case do we have an assertioig that it is the SAME input for anytwo deciders that we chose.
Thus, you have NO basis for you claim that there is ANY pairing of two deciders, that answer differently of getting the same input.

 That both of these decider/input pairs get the wrong answer proves
that their question was incorrect because the opposite answer to the
same question is also proven to be incorrect.
 

But that isn't claimed, so your logic is baseless.