Re: Working out the details of the steps of Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ <Ĥ> ⊢* Ĥ.Hqn

On 3/8/24 7:14 PM, olcott wrote:

On 3/8/2024 9:03 PM, Richard Damon wrote:

On 3/8/24 6:34 PM, olcott wrote:

On 3/8/2024 8:24 PM, Richard Damon wrote:

The Mapping describes the answer that we want for ALL possible inputs. It becomes the specification of the problem.
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You still can't understand how computing the mapping
from all inputs to final state Ĥ.Hqn or non final state
Ĥ.Hqy on the basis of the indirect criteria also causes
H ⟨Ĥ⟩ ⟨Ĥ⟩ <H> to correctly compute halting.
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Because your "indirect Criteria" map differs from the DEFINED DIRECT Criteria map.
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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
 The indirect criteria provides Ĥ.H the basis for
which wrong answer it must return and provides
H with the basis to return the correct halt status.

And if it gives a WRONG answer, then H is just WRONG.

 So far everyone in world the has no idea what
basis Ĥ.H could use to determine its wrong answer.
*They leave it wide open with a question mark*

But it needs to get the RIGHT answer to be correct.
And we KNOW the "basis" it is what H does.

 When we hypothesize a basis such that H gets
the correct answer and Ĥ.H can provide some
answer then this question mark is resolved.
 

But you don't seem to understand that H^.H IS an instance of the computation of H, and as such, MUST deliver the "right" answer per the mapping that H is DEFINED to give.
You aren't allowed to LIE here.
The algorithm of H computes some mapping of (M) d <TMD> to accept / reject.
This mapping, for ALL inputs, must match the HALTING mapping.
Thus the algorithm of H, which is at H^.H must go to qy if M d will halt, and to qn if M d will not halt.
Since M = H^ and d = (H^)
This means that, as you comment says
H^.H (H^) (H^) <H^> should have gone to qy if H^ (H^) halts, which it did, so the algorithm of H is proven to be WRONG.
You are just showing you don't understand what you are doing.