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From: olcott <polcott2@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: =?UTF-8?Q?Re=3A_Working_out_the_details_of_the_steps_of_=C4=A4=2EH_?=
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Date: Sat, 9 Mar 2024 10:53:52 -0600
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On 3/9/2024 10:21 AM, immibis wrote:
> 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.
> 

Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ can fool itself yet cannot possibly fool an external H ⟨Ĥ⟩ ⟨Ĥ⟩.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer