In epistemology (theory of knowledge), a self-evident proposition is a
proposition that is known to be true by understanding its meaning
without proof ... (Wikipedia: Self-evidence)

Self-evident(A) Every simulation of input P that never halts unless
simulating halt decider H aborts this simulation <is> a non-halting
computation. This remains true even after H stops simulating P.

Because we know that the only difference in the behavior of a simulating
halt decider and a simulator is that the simulating halt decider stops
simulating some of its inputs we can examine the behavior of these
inputs in a simulator to determine whether or not a simulating halt
decider would stop simulating these inputs.

If the simulation of input P to simulator S would never terminate then
we can know that simulating halt decider H must stop simulating input P.

∃H ∈ Simulating_Halt_Deciders
∀P ∈ Turing_Machine_Descriptions
∀I ∈ Finite_Strings
(UTM(P,I) = ∞) ⊢ (H(P,I) = 0)

In English it says that whenever the input (P,I) to UTM would never halt
then a simulating halt decider correctly decides not halting on this input.

The behavior of the proxy computation forms the halt deciding basis for
the inputs that would otherwise specify the pathological self-reference
error.

http://www.liarparadox.org/Halting_problem_undecidability_and_infinitely_nested_simulation.pdf

Wikipedia contributors. Self-evidence. Wikipedia, The Free Encyclopedia.
May 17, 2021, 19:44 UTC. Available at:
https://en.wikipedia.org/w/index.php?title=Self-evidence&oldid=1023688680.
Accessed May 22, 2021.

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

On 5/22/2021 1:04 PM, André G. Isaak wrote:
> On 2021-05-22 11:46, olcott wrote:
>> In epistemology (theory of knowledge), a self-evident proposition is a
>> proposition that is known to be true by understanding its meaning
>> without proof ... (Wikipedia: Self-evidence)
>>
>> Self-evident(A) Every simulation of input P that never halts unless
>> simulating halt decider H aborts this simulation <is> a non-halting
>> computation. This remains true even after H stops simulating P.
>>
>> Because we know that the only difference in the behavior of a
>> simulating halt decider and a simulator is that the simulating halt
>> decider stops simulating some of its inputs we can examine the
>> behavior of these inputs in a simulator to determine whether or not a
>> simulating halt decider would stop simulating these inputs.
>
> Or, of course, we could just run the computation directly. Your
> fascination with simulation is odd to say the least...
>
> Either way, though,
>
> Your H(H_Hat, H_Hat) claims that H_Hat(H_Hat) doesn't halt.
>
> BUT
>
> If we run H_Hat(H_Hat) it *does* halt.
>
> Similarly, if we run
>
> S(H_Hat, H_Hat), it also halts.
>
> You are determined to instead run
>
> S(S_Hat, S_Hat), which admittedly does not halt, but S_Hat(S_Hat) is an
> *entirely* *different* computation from H_Hat(H_Hat).
>
> According to your own description "we can examine the behavior of THESE
> INPUTS [caps mine] in a simulator to determine whether or not a
> simulating halt decider would stop simulating these inputs."
>
> The input to H(H_Hat, H_Hat) is H_Hat, H_Hat. It isn't S_Hat, S_Hat. So
> by the very logic you give above you must give your simulator H_Hat,
> H_Hat as its input, not S_Hat, S_Hat.
>
> André
>

Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qy ∞
Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn

You have to examine the rest of what I said before the point that I am
making is complete.

Until we have a mutual understanding on all the points in this thread
you will not be able to understand how it provides the correct basis for
the embedded halt decider at state Ĥ.qx to correctly decide not halting
on its input: ([Ĥ],[Ĥ]).

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

On 5/22/2021 2:05 PM, Richard Damon wrote:
> On 5/22/21 1:46 PM, olcott wrote:
>> In epistemology (theory of knowledge), a self-evident proposition is a
>> proposition that is known to be true by understanding its meaning
>> without proof ... (Wikipedia: Self-evidence)
>
> Again, your trying to get things by that you want by claiming you don't
> need to prove them. We will not clarifications needed to definitions as
> we go.
>
>>
>> Self-evident(A) Every simulation of input P that never halts unless
>> simulating halt decider H aborts this simulation <is> a non-halting
>> computation. This remains true even after H stops simulating P.
>
> Yes, If H is simulating <[P],[I]>, and it can PROVE that P(I) will not
> halt, it can abort the simlulation of <[P],{I]> and doing so doesn't
> make P(I) halting.
>
> This action DOES change the value of Halting for the computation that H
> is in, as if it did not stop the simulation, H would be non-halting, but
> now it is Halting.
>
> Important note, as this means any proof that H uses, that passes through
> a copy of something like H that simulates and might abort, H in proving
> the non-Halting of P, needs to take that action into count.
>
> (Your 'proof' of H^ fails here).
>
>>
>> Because we know that the only difference in the behavior of a simulating
>> halt decider and a simulator is that the simulating halt decider stops
>> simulating some of its inputs we can examine the behavior of these
>> inputs in a simulator to determine whether or not a simulating halt
>> decider would stop simulating these inputs.
>>
>> If the simulation of input P to simulator S would never terminate
>> then we can know that simulating halt decider H must stop simulating
>> input P.

The above <is> a self-evident truth, thus impossibly incorrect.

> Incorrect. BECAUSE the simulating Halt decider can convert a non-halting
> computation that the simulator would be part of into a Halting
> Computaton (note, not of the machine being simulated, but of the machine
> DOING the simulation) we need to take this into account when deciding a
> machine that does this.
>

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

On 5/22/21 3:24 PM, olcott wrote:
> The above <is> a self-evident truth, thus impossibly incorrect.

You might try actually saying something about what I said rather than
just reiterate your position. Just repeating yourself tend to imply that
you can't actually rebut what was said.

I will note that there is a name for people who see things that no one
else sees. And a name for system that can prove a statement and its
opposite.

Even YOU have agreed that H^([H^]) does Halt when run, and there is the
definition/Truism that a computation that halts is a Halting Computation.

On 5/22/2021 3:42 PM, Richard Damon wrote:
> On 5/22/21 3:24 PM, olcott wrote:
>> The above <is> a self-evident truth, thus impossibly incorrect.
>
> You might try actually saying something about what I said rather than
> just reiterate your position. Just repeating yourself tend to imply that
> you can't actually rebut what was said.
>
> I will note that there is a name for people who see things that no one
> else sees.

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

> And a name for system that can prove a statement and its
> opposite.
>

Inconsistent.

> Even YOU have agreed that H^([H^]) does Halt when run, and there is the
> definition/Truism that a computation that halts is a Halting Computation.
>
We have to go through all the steps one-at-a-time. That you insist on
skipping to the end blocks your path to understanding the truth.

That you insist on skipping to the end prevents you from paying enough
attention.

We must have mutual agreement on every single line of V8 before you will
understand. This may require a few more versions of improved wording.

That I am not a very good communicator makes improved wordings a pure
matter of trial-and-error.

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

On 5/22/2021 1:04 PM, André G. Isaak wrote:
> On 2021-05-22 11:46, olcott wrote:
>> In epistemology (theory of knowledge), a self-evident proposition is a
>> proposition that is known to be true by understanding its meaning
>> without proof ... (Wikipedia: Self-evidence)
>>
>> Self-evident(A) Every simulation of input P that never halts unless
>> simulating halt decider H aborts this simulation <is> a non-halting
>> computation. This remains true even after H stops simulating P.
>>
>> Because we know that the only difference in the behavior of a
>> simulating halt decider and a simulator is that the simulating halt
>> decider stops simulating some of its inputs we can examine the
>> behavior of these inputs in a simulator to determine whether or not a
>> simulating halt decider would stop simulating these inputs.
>
> Or, of course, we could just run the computation directly. Your
> fascination with simulation is odd to say the least...
>
> Either way, though,
>
> Your H(H_Hat, H_Hat) claims that H_Hat(H_Hat) doesn't halt.
>
This is not any part of the focused analysis that I have listed below.

> BUT
>
> If we run H_Hat(H_Hat) it *does* halt.
>
This is not any part of the focused analysis that I have listed below.

> Similarly, if we run
>
> S(H_Hat, H_Hat), it also halts.
>
This is not any part of the focused analysis that I have listed below.

> You are determined to instead run
>
> S(S_Hat, S_Hat), which admittedly does not halt, but S_Hat(S_Hat) is an
> *entirely* *different* computation from H_Hat(H_Hat).

This <is> part of the focused analysis listed below
Yes it <is> a different computation.
It is not an entirely different computation.

The <only> difference is shown below in (a).
The <only> difference is shown below in (a).
The <only> difference is shown below in (a).

> According to your own description "we can examine the behavior of THESE
> INPUTS [caps mine] in a simulator to determine whether or not a
> simulating halt decider would stop simulating these inputs."
>
> The input to H(H_Hat, H_Hat) is H_Hat, H_Hat. It isn't S_Hat, S_Hat. So
> by the very logic you give above you must give your simulator H_Hat,
> H_Hat as its input, not S_Hat, S_Hat.
>
> André
>

I have changed the wording and now have specifically named machines.

(a) The only difference between a simulating halt decider and a
UTM/simulator is that the former stops its simulation at some point.

(b) Where a computation P has an embedded simulating halt decider H we
create proxy computation P2 replacing every instance of H with simulator S.

The following two points are the key basis of my whole proof, so far
they have proved far too subtle for anyone here to begin to grasp.

(c) Because of (a) when P2 is a halting computation then H does not need
to stop P and H decides halting.

(d) Because of (a) when P2 is an infinite computation then H must stop P
and H decides not halting.

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein