XPost: comp.theory, sci.logic, sci.math

On 2/28/2022 4:08 PM, André G. Isaak wrote:

This reminded me of Olcott

<https://xkcd.com/2566/>

André

You still have not shown that I am incorrect.

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

It is the case than unless embedded_H aborts the simulation of its input
that this input would never stop running.

It is also the case that the fact that this
IS A REASONABLE MEASURE THAT THIS INPUT SPECIFIES A NON HALTING SEQUENCE
OF CONFIGURATIONS.

The above two facts taken together prove that the essence of my idea is correct.

--
Copyright 2021 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

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XPost: comp.theory, sci.logic, sci.math

On 3/1/2022 3:27 AM, Mikko wrote:

On 2022-02-28 22:47:44 +0000, olcott said:

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

These two lines contradict each other,
so at least one of them is false,
possibly both.

Mikko

It is a paraphrase of Linz bottom of page 319. https://www.liarparadox.org/Peter_Linz_HP_317-320.pdf

--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer

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XPost: comp.theory, sci.logic, sci.math

On 3/1/2022 6:02 AM, Ben Bacarisse wrote:

Mikko <mikko.levanto@iki.fi> writes:

On 2022-02-28 22:47:44 +0000, olcott said:

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

These two lines contradict each other,
so at least one of them is false,
possibly both.

PO makes a habit of omitting the key conditions under which each line applies. This has been pointed out so often that it must be
deliberate. The trouble is that the conditions are what shows PO to be
wrong so he's spent some time trying to find words for his own
conditions that make it sound a bit like he is still talking about a
halt decider. The conditions are

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞ if H applied to ⟨Ĥ⟩ halts, and
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn if H applied to ⟨Ĥ⟩ does not halt.

Those are not the conditions.
The copy of the simulating halt decider H embedded at Ĥ.qx will be
called embedded_H

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
if embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ determines that its simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ will
halt without aborting the simulation of its input

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
if embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ determines that its simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ will NOT
halt without aborting the simulation of its input



--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer

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XPost: comp.theory, sci.logic, sci.math

On 3/1/2022 10:04 AM, Ben Bacarisse wrote:

olcott <NoOne@NoWhere.com> writes:

On 3/1/2022 6:02 AM, Ben Bacarisse wrote:

Mikko <mikko.levanto@iki.fi> writes:

On 2022-02-28 22:47:44 +0000, olcott said:

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

These two lines contradict each other,
so at least one of them is false,
possibly both.

PO makes a habit of omitting the key conditions under which each line
applies. This has been pointed out so often that it must be
deliberate. The trouble is that the conditions are what shows PO to be
wrong so he's spent some time trying to find words for his own
conditions that make it sound a bit like he is still talking about a
halt decider. The conditions are
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞ if H applied to ⟨Ĥ⟩ halts, and
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn if H applied to ⟨Ĥ⟩ does not halt.

Those are not the conditions.

Indeed they are not. I made a typo. You, however, cannot give the
correct ones because they show you to be wrong. Instead you must pile
on the verbiage:

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
if embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ determines that its simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ will
halt without aborting the simulation of its input

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
if embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ determines that its simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ will
NOT halt without aborting the simulation of its input

If these were same as those in Linz you would use the far simpler
conditions from Linz, but in actual fact you are re-defining what
halting means hoping that you won't be called out on it.

I'll call you out on it: you have not changed your stance since you made
the fatal mistake of being crystal clear:

Me: do you still assert that H(P,P) == false is the "correct" answer
even though P(P) halts?

You: Yes that is the correct answer even though P(P) halts.

Until to accept that this is simply wrong, everything you say on the
topic is just hot air.

I explain your mistake about this in terms of Turing machine deciders:
On 2/28/2022 11:59 AM, olcott wrote:
Concise refutation of halting problem proofs V63 [ Linz Proof ][ Ben's
mistake ]


--
Copyright 2021 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

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XPost: comp.theory, sci.logic, sci.math

On 3/1/2022 5:57 PM, Ben Bacarisse wrote:

olcott <polcott2@gmail.com> writes:

I explain your mistake about this in terms of Turing machine deciders:
On 2/28/2022 11:59 AM, olcott wrote:
Concise refutation of halting problem proofs V63 [ Linz Proof ][ Ben's
mistake ]

You can't even be bothered to learn how to cite a Usenet post (it's not hard).

But that suits me fine. You appear to want to talk forever, whereas all
I want to do is remind readers that you are not addressing the halting problem,

I pointed out your mistake On 2/28/2022 11:59 AM
Concise refutation of halting problem proofs V63 [ Linz Proof ][ Ben's
mistake ]

and that you have been 100% clear about this in the past:

Me: do you still assert that H(P,P) == false is the "correct" answer
even though P(P) halts?
You: Yes that is the correct answer even though P(P) halts.

I have not been talking about H(P,P) for many months.
I point out your mistake in terms of Linz.

You apparently don't really know how deciders work, otherwise you would
not have made this mistake.

--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer

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XPost: comp.theory, sci.logic, sci.math

On 3/2/2022 4:10 PM, Ben Bacarisse wrote:

olcott <NoOne@NoWhere.com> writes:

On 3/2/2022 11:07 AM, Ben Bacarisse wrote:

olcott <NoOne@NoWhere.com> writes:

Linz confuses himself my making the TM descriptions less than a clear
as possible.

Have you looked at Linz's actual proof yet? It's theorem 12.2, a page
further on from the one you seem to be obsessed by.

Like I said my only reply to you will be to keep repeating the key
points that you failed to address until you address them completely.

I can't parse that sentence but it contains no hint that you have looked
at Linz's proof yet.

Do you understand that a decider computes the mapping ONLY from its
inputs to an accept or reject state and does not compute any other mapping?

--
Copyright 2021 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

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