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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: =?utf-8?Q?Re:_A_simulating_halt_decider_applied_to_the_The_Peter_Linz_Turing_Machine_description_=E2=9F=A8=C4=A4=E2=9F=A9?=
Date: Thu, 30 May 2024 10:06:38 +0300
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On 2024-05-29 13:13:13 +0000, olcott said:

> On 5/29/2024 3:37 AM, Mikko wrote:
>> On 2024-05-28 11:34:24 +0000, Richard Damon said:
>> 
>>> On 5/27/24 10:59 PM, olcott wrote:
>>>> On 5/27/2024 9:52 PM, Richard Damon wrote:
>>>>> On 5/27/24 10:41 PM, olcott wrote:
>>>>>> On 5/27/2024 9:23 PM, Richard Damon wrote:
>>>>>>> On 5/27/24 10:01 PM, olcott wrote:
>>>>>>>> On 5/27/2024 8:24 PM, Richard Damon wrote:
>>>>>>>>> On 5/27/24 9:04 PM, olcott wrote:
>>>>>>>> 
>>>>>>>>>>>> I totally do. Can you please write down the
>>>>>>>>>>>> "completely specified state transition/tape operation table."
>>>>>>>>>>>> of this specific (thus uniquely identifiable) machine I would
>>>>>>>>>>>> really like to see it.
>>>>>>>>>>>> 
>>>>>>>>>>> 
>>>>>>>>>>> But it was proven that no such machine exists!
>>>>>>>>>>> 
>>>>>>>>>>> Remember, the proof starts with the hypothetical that such a machine 
>>>>>>>>>>> exists. Such a machine WOULD HAVE a completely specified state 
>>>>>>>>>>> transition/tape operation table.
>>>>>>>>>>> 
>>>>>>>>>> 
>>>>>>>>>> That is not what you said.
>>>>>>>>>>  >>>>> There doesn't need to be a unique finite string, but it is a 100%
>>>>>>>>>>  >>>>> completely specified state transition/tape operation table.
>>>>>>>>>> 
>>>>>>>>>> "a 100% completely specified state transition/tape operation table"
>>>>>>>>>> of a non-existent machine.
>>>>>>>>> 
>>>>>>>>> Right, by presuming that you have a Turing Machine, you have a 
>>>>>>>>> completly specified state transition/tape operation table.
>>>>>>>>> 
>>>>>>>>> You may not KNOW what that table is if you don't know what the exact 
>>>>>>>>> machine is, but you know it exists.
>>>>>>>> 
>>>>>>>>  >>> But it was proven that no such machine exists!
>>>>>>>>  > ... but you know it exists.
>>>>>>>> 
>>>>>>>>  >>> But it was proven that no such machine exists!
>>>>>>>>  > ... but you know it exists.
>>>>>>>> 
>>>>>>>>  >>> But it was proven that no such machine exists!
>>>>>>>>  > ... but you know it exists.
>>>>>>>> 
>>>>>>>> 
>>>>>>> 
>>>>>>> 
>>>>>>> Really, then show that one exists!
>>>>>>> 
>>>>>> 
>>>>>> *I am quoting your words. You did contradict yourself*
>>>>>> *I am quoting your words. You did contradict yourself*
>>>>>> *I am quoting your words. You did contradict yourself*
>>>>>> *I am quoting your words. You did contradict yourself*
>>>>>> *I am quoting your words. You did contradict yourself*
>>>>>> *I am quoting your words. You did contradict yourself*
>>>>>> *I am quoting your words. You did contradict yourself*
>>>>>> *I am quoting your words. You did contradict yourself*
>>>>>> *I am quoting your words. You did contradict yourself*
>>>>>> *I am quoting your words. You did contradict yourself*
>>>>>> 
>>>>> 
>>>>> 
>>>>> Really, where did I say that H exists?
>>>>> 
>>>>> I said that if a Turing Machine exists, then its transition table does too.
>>>>> 
>>>> 
>>>> OK my mistake this time. I did not take into account the full context.
>>>> I will go back an read the Linz proof and see if he said anything
>>>> about a specific machine.
>>> 
>>> Read the DEFINITION of the problem. He talks about "a" machine. Using a 
>>> singular article means you are working with just one.
>>> 
>>> 
>>> Taking stuff out of context is a common problem with you, when you 
>>> don't understand something, you just make up what it must mean, and 
>>> stick to that. That isn't the way to learn.
>>> 
>>> 
>>>> 
>>>> None of the proofs ever try to show that there exists one machine that
>>>> gets the wrong answer. They are always at least trying to prove that no
>>>> machine of the infinite set of machine gets the right answer.
>>>> 
>>> 
>>> What I see, is they always start with a prototypical single machine, 
>>> and show that it gets the answer wrong, and then they use categorical 
>>> logic to say that we can do this same thing for all of them.
>> 
>> It is possible to formulate the claim and proof so that H is an universally
>> quantified variable. But the usual way is apparently equally good for the
>> target audience.
>> 
> 
> *Formalizing the Linz Proof structure*
> ∃H  ∈ Turing_Machines
> ∀x  ∈ Turing_Machines_Descriptions
> ∀y  ∈ Finite_Strings
> such that H(x,y) = Halts(x,y)

That is not a proof structure. That is the counter-hypothesis of Linz' proof.
Also note that both x and y are finite strings.

-- 
Mikko