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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: =?UTF-8?Q?Re=3A_A_simulating_halt_decider_applied_to_the_The_Peter_?=
 =?UTF-8?Q?Linz_Turing_Machine_description_=E2=9F=A8=C4=A4=E2=9F=A9?=
Date: Mon, 27 May 2024 21:54:17 -0400
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On 5/27/24 9:39 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!
> 
> If you can't notice that you are contradicting yourself
> it seems that no further progress can be made with you.
> 
> 

Nope. You just don't understand how a proof by contradiction works, do you.

We begin by assuming that such a machine exists. If such a machine 
exsited, it would have a full specified state transition/tape operation 
table.

The proof them move on, building another machine based on that presumed 
table, with precisely specified methods.

Then, by the principles of Turing Machines, we can show, based on the 
few limitations of what Turing Machine has specified, what the results 
of running that machine will be, even without knowing the details of 
that machine, just knowing that such a specification exists.

And thus, we can show that the given hypothetical H couldn't have meet 
its specification, because out of the limited number of classes of final 
behaviors, we can show that it had to be wrong, or just not exist.

Of course, since you don't understand about specifications, this may 
seem like magic to you, but it works.

So, if you don't have an infinite set of these 100% specified state 
transistion/tape operation tables, you can't do YOUR proof.

And if you don't have those tables, you can not have any of your 
embedded_H's "simulate" their inputs, as that is what specifies what the 
simulation does.

So, I guess YOU have a bigger contradiction.