Re: ZFC solution to incorrect questions: reject them

On 3/12/2024 6:11 PM, Richard Damon wrote:

On 3/12/24 3:53 PM, olcott wrote:

On 3/12/2024 5:30 PM, Richard Damon wrote:

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.
>

∀ H ∈ Turing_Machines_Returning_Boolean
∃ TMD ∈ Turing_Machine_Descriptions  |
Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>
Every H/TMD pair (referenced in the above set) has a
corresponding H/TMD pair that only differs by the return
value of its Boolean_TM.

 That isn't in the set above.
 

>
That both of these H/TMD 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.
>
>

Nope, since both aren't in the set selected.
 

When they are deciders that must get the correct answer both
of them are not in the set.
When they are Turing_Machines_Returning_Boolean the this
set inherently includes identical pairs that only differ
by return value.

You just don't understand what that statement is saying.
 I've expalined it, but it seems over you head.
 

No the problem is that you are not paying attention.

For Every H, we show we can find at least one input (chosen just for that machine) that it will get wrong.
 

When we use machine templates then we can see instances of
the same machine that only differs by return value where both
get the wrong answer on the same input. By same input I mean
the same finite string of numerical values.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer