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

On 3/8/24 8:41 PM, olcott wrote:

On 3/8/2024 10:28 PM, Richard Damon wrote:

On 3/8/24 8:05 PM, olcott wrote:

On 3/8/2024 9:48 PM, Richard Damon wrote:

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
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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.

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

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But it needs to get the RIGHT answer to be correct.

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*Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ <Ĥ> must have some basis for its wrong answer*
*Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ <Ĥ> must have some basis for its wrong answer*
*Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ <Ĥ> must have some basis for its wrong answer*
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But if it is the wrong answer, it is wrong.
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Why don't you understand that?
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 It is only wrong for the input and not the external decider.

It is WRONG.
DEFINITIOBN.

 The criteria is very very special in the the same criteria that lets
the input derive some answer lets the external decider derive the
correct answer.

No, the criteria for H to be a Halt Decider is PRECISELY Defined.
IF H gives the wrong answer, ANYWHERE, if FAILS to be a Halt Decider.

 When each H determines the halt status of its input from its own point
of view then the external one corresponds to the actual behavior of the
input when it is directly executed.
 

But it isn't to answer "From its own point view". It is to answer according to the REQUIREMENT to compute the MAPPING, which is OBJECTIVE.
You don't get to convert the OBJECTIVE standard to a SUBJECTIVE standard, that is just a LIE.
They ALL must be correct, not just the top level.
You are just proving you don't understand the definition of a COMPUTATION.
That is your downfall, you just don't know the rules of what you are talking about, and think it ok to LIE about what you are doing.