Re: A simulating halt decider applied to the The Peter Linz Turing Machine description ⟨Ĥ⟩

On 5/29/24 9:13 AM, olcott wrote:

On 5/29/2024 3:37 AM, Mikko wrote:

On 2024-05-28 11:34:24 +0000, Richard Damon said:
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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:

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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.
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But it was proven that no such machine exists!
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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.
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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.
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"a 100% completely specified state transition/tape operation table"
of a non-existent machine.

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Right, by presuming that you have a Turing Machine, you have a completly specified state transition/tape operation table.
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You may not KNOW what that table is if you don't know what the exact machine is, but you know it exists.

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 >>> But it was proven that no such machine exists!
 > ... but you know it exists.
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 >>> But it was proven that no such machine exists!
 > ... but you know it exists.
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 >>> But it was proven that no such machine exists!
 > ... but you know it exists.
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Really, then show that one exists!
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*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*
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Really, where did I say that H exists?
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I said that if a Turing Machine exists, then its transition table does too.
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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.

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Read the DEFINITION of the problem. He talks about "a" machine. Using a singular article means you are working with just one.
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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.
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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.
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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.

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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.
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 *Formalizing the Linz Proof structure*
∃H  ∈ Turing_Machines
∀x  ∈ Turing_Machines_Descriptions
∀y  ∈ Finite_Strings
such that H(x,y) = Halts(x,y)
 

And Linz shows how to construct an x, y pair for ANY H that makes the final condition false, thus there does NOT exist any H that make it true for ALL inputs.