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On 9/03/24 17:00, olcott wrote:
> On 3/9/2024 1:05 AM, Richard Damon wrote:
>> On 3/8/24 10:40 PM, olcott wrote:
>>> On 3/9/2024 12:25 AM, Richard Damon wrote:
>>>> On 3/8/24 9:55 PM, olcott wrote:
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn   // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>>>
>>>>> Expecting Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ to correctly report on the behavior of
>>>>> Ĥ ⟨Ĥ⟩ is a little nuts because Ĥ contradicts Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩.
>>>>
>>>> But that is the job it signed up for when it tried to call itself a 
>>>> Halt Decider.
>>>>
>>>
>>> There is no correct answer that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ can possibly
>>> provide that corresponds to the behavior of this Ĥ ⟨Ĥ⟩.
>>> Therefore it must have a basis for its wrong answer.
>>>
>>>
>>
>> WHY?
>>
>> What is the actual grounds for that statement?
> 
> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ cannot just sit around scratching its head it
> must do something. As soon as we have the basis for what
> it will do, then H ⟨Ĥ⟩ ⟨Ĥ⟩ has its basis to correctly
> decide halting.

H ⟨A⟩ ⟨B⟩ cannot just sit around scratching its head, it must do 
something. As soon as we have the basis for what H will do, then we have 
a basis to construct an Ĥ where H ⟨Ĥ⟩ ⟨Ĥ⟩ is wrong.