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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
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Date: Mon, 11 Mar 2024 23:03:00 -0700
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On 3/11/24 9:08 PM, olcott wrote:
> On 3/11/2024 10:57 PM, Richard Damon wrote:
>> On 3/11/24 8:37 PM, olcott wrote:
>>> On 3/11/2024 10:31 PM, Richard Damon wrote:
>>>> On 3/11/24 7:52 PM, olcott wrote:
>>>>> On 3/11/2024 9:32 PM, immibis wrote:
>>>>>> On 12/03/24 03:24, olcott wrote:
>>>> \
>>>>>>> Troll detected.
>>>>>>>
>>>>>>
>>>>>> Once we understand that either YES or NO is the right answer
>>>>>
>>>>> Not for this decider/input question: Ĥ.H / ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>> For that decider/input question both YES and NO are the wrong answer.
>>>>
>>>> The problem that you keeep on missing is that by the point we can 
>>>> ask this question, H and H^ are FULLY CODED, and thus we know their 
>>>> behavirs.
>>>
>>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy // Ĥ applied to ⟨Ĥ⟩ halts
>>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>
>>> Since you know that is false why lie?
>>> ⊢* specifies an infinite set of encodings.
>>
>> Nope, read him again, not just skim and assume.
>>
> 
> In other words you are claiming that Linz proved there is at least
> one H that does not decide halting correctly on at least one input?
> 
> If Linz proved the there does not exist any H that gets every input
> correctly then ⊢* specifies every possible encoding of H.
> 
> 

No, in first part of the proof, he proved that you can take ANY 
arbitrary machine that claimes to be a Halt Decider, and then show there 
is at least input it doesn't get correct.

That is most of the words where he talks about H, and H^ and the like.

THEN at the end, he points out that because we did this to ONE ARBITRARY 
decider, we can do it to ANY and ALL deciders, thus none exist.

I thought you understood exhaustive categorical analysis?