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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 12:45:04 -0600
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On 3/9/2024 12:17 PM, Richard Damon wrote:
> On 3/9/24 8:53 AM, olcott wrote:
>> 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⟩.
>>
> 
> Why not?
> 
> Are you thinking H will just simulate until H^.H makes its decision?
> 
> We know the outcome of that, never answering, and thus failing.

Please switch over to this new post that addresses all of your
objections in advance.
[Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior]

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