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

On 5/27/24 10:25 AM, olcott wrote:

On 5/27/2024 8:27 AM, Richard Damon wrote:

On 5/26/24 11:47 PM, olcott wrote:

On 5/26/2024 10:30 PM, Richard Damon wrote:

On 5/26/24 11:17 PM, olcott wrote:

On 5/26/2024 10:05 PM, Richard Damon wrote:

On 5/26/24 10:43 PM, olcott wrote:

On 5/26/2024 9:06 PM, olcott wrote:

When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
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  Ĥ copies its own Turing machine description: ⟨Ĥ⟩
  then invokes embedded_H that simulates ⟨Ĥ⟩ with ⟨Ĥ⟩ as input.
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It is an easily verified fact that ⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by
embedded_H cannot possibly reach its own simulated final state of
⟨Ĥ.qn⟩ in any finite sequence of steps.

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*To other reviewers that are not dishonest*
The complete proof of the above statement is that when we hypothesize
that embedded_H is a UTM we can see that:

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i.e. when we assume it is something it isn't, i.e we LIE to ourselves.
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If you assume embedded_H is something it isn't,

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Not at all.
*It looks like you may be utterly clueless about what-if scenarios*

You can only ask what-ifs about things that are possible.
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What-if embedded_H was a UTM would ⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated
by embedded_H reach its own simulated final state of ⟨Ĥ.qn⟩ ?
(a) YES
(b) NO
(c) DISHONEST HONEST ATTEMPT TO CHANGE THE SUBJECT

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So, If your H was a UTM, and H^ built on that, then embedded_H would be a UTM and H^ (H^) would be non-halting as would H (H^) (H^).
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*Great this is a step of progress*
This conclusively proves that ⟨Ĥ⟩ will not reach ⟨Ĥ.qn⟩ is less than
an infinite number of steps. A decider is not allowed to simulate
an infinite number of steps.

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First, it doesn't "Prove" it,

 *Sure it does, you just like to deny verified facts*

Nope, someone saying something doesn't prove it to be true.
Where has it actually been FORMALLY verified.
While I agree that *IF* H is a UTM / "Pure Simulator" (defined as a simulator that doesn't stop until it reaches a final state) that the D built on calling that H will be non-halting (and the H so built also non-halting) my agreement doesn't "Prove" the statement, only a formally writing out the of full set of steps that actually prove it will do so.

When ⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by embedded_H cannot possibly reach its
own simulated final state of ⟨Ĥ.qn⟩ and halt in an infinite number of
simulated steps

So, try to actually PROVE it (if you understand the definition of a proof)

 then it can't possibly reach its own simulated final state of ⟨Ĥ.qn⟩ and halt in less than an infinite (AKA a finite) number of simulated steps.
*When infinity is not enough then less than infinity is also not enough*
 

WHY do you say that? can you actually PROVE it.
That REQUIRES the explicit listing of a sequence of truth preserving operations from statements previously proven to be true (or taken as the fundamental truth-makers of the system) to arrive at your final statement. None of that has been done here, as you have never actually quoted the proper set of known true statements to base your argument on.
You seem to confuse the concept of "Proof" in a formal system to the more abstract concept in Philosophy, where the concept is a bit different, as there isn't the pre-agreed on set of truth-makers and truth-preserving operations like are present in Formal Systems. Philosophical "proofs" are merely just arguments, based largely on trying to convince the other person that the "truth-makers" you are basing your argument on are actually a true basis. In Formal systems that isn't required, as there is DEFINED the complete set of fundamental truth-makers for the system, and all other statement that are true, will have a truth-preserving path from those. (finite in length for those KNOWN to be true, possibly infinte in length for those that are true but not known).
Not understanding this difference has been your bane, as you are going into your argument unprepared to produce what is actually needed.
Your x point "proof" just high lights this. It is just a philosphical argument, trying to obtain agreement, not a Formal Proof of your statement. And since you argument is based on ideas that are NOT correct in the formal system, you are going to be unable to actually convert the whole thing into an actual Formal Proof.
We can honestly point out that the fundamental flaw in your argument is that you don't understand the formal meaning of Truth in Formal Systems. Which sort of makes it hard for you to prove that a statement is true, if you don't know what that means.