General Undecidable Axiom (V2)

[wij]

Since the conventional HP only mentions a specific halting problem, which is
often believed to be an invalid proof and limited in use.
See https://groups.google.com/g/comp.theory/c/RO9Z9eCabeE/m/Ka8-xS2rdEEJ

I hereby proudly claims the General Undecidable Axiom (2021 WIJ):
+--------------------------------------------------------------------------------+
| No TM U can decide the property of a TM P if that property can be defied by TM P. |
+--------------------------------------------------------------------------------+

// Example1:
// [Ret] true: f prints 'Y'
// false: f does not print 'Y'
//
bool U(Func f);

void P() {
if(U(P)) {
printf("b");
} else {
printf("Y");
}
}
//---
// Example2:
// [Ret] true: f is a "pathological input" function
// false: otherwise
//
bool U(Func f);

void P() {
if(U(P)) {
return;
} else {
P(); // if "pathological input" is so defined, whatever.
}
};

--
The construct of P (proof of General Undecidable Axiom) is 100% correct,
intuitive and above all, REPRODUCIBLE, VERIFIABLE.

// [Ret] true: f has the (dynamic)property Q
// false: otherwise
//
bool U(Func f);

void P() {
if(U(P)) {
// do whatever Q defines false
} else {
// do whatever Q defines
}
};

Note: I would like to acknowledge Olcott tirelessly refuted various wrong
conventional HP proofs over these years for me. So I need not to do the
same work again, though not necessary.

--
Copyright 2021 WIJ
"If I can see further it is by standing on top of the tower of dwarfs."

[olcott]

You have merely copied Sipser
http://www.liarparadox.org/Sipser_165_167.pdf

D(⟨M⟩) = {accept if M does not accept ⟨M⟩
{reject if M accepts ⟨M⟩

Sipser has merely copied the Liar Paradox.
The Liar Paradox is merely erroneous because it is self-contradictory

Thus the whole concept of undecidability that is based on pathological
self-reference(Olcott 2004) is merely a misconception and nothing more.

It is just like asking:
What is the length of you car in colors of the rainbow?
The issue is not that people cannot make up their mind (decide) about
the correct answer the issue is that the question is incorrect.

This issue has snuck past human comprehension because we tolerate
terms-of the-art being assigned meanings that are incompatible with
their common meanings.

When we allow the term-of-the-art meaning to be assigned to the common
word "decidable" people are fooled. If we assign this same meaning
accurately people would not be fooled.

The correct name for undecidable decision problems that are based on the
pathological self-reference error is not "undecidable" the accurate name
for them is {erroneous}.

To eliminate these problems all knowledge must be organized as an
inheritance hierarchy that disallows overriding existing meanings.

If we did it this way then Russell's paradox would have never come into
existence. People would know that no physical or conceptual object can
ever possibly totally contain itself. A set as a member of itself would
then be immediately understood as incoherent.

> Note: I would like to acknowledge Olcott tirelessly refuted various wrong
> conventional HP proofs over these years for me. So I need not to do the
> same work again, though not necessary.
>
> --
> Copyright 2021 WIJ
> "If I can see further it is by standing on top of the tower of dwarfs."
>

--
Copyright 2021 Pete Olcott

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

[wij]

The quoted is an INSTANCE of GUA, my own independent invention.
Your H(P,P) is also an instance governed by GUA, too. But, according to GUA,
H(P,P) is undecidable, your conclusion is incorrect.

GUA is REPRODUCIBLE, VERIFIABLE, period.
Your following statement does not seem to firm-grounded. Let's say, it is just
pathological misconception talking about pathological misconception.

People will continue to use GUA, not your 'self-talk', or fantasy.

[olcott]

Because it has identical semantic meaning to Sipser and you fail to give
Sipser credit it is merely Plagiarism.

> Your H(P,P) is also an instance governed by GUA, too. But, according to GUA,
> H(P,P) is undecidable, your conclusion is incorrect.
>
> GUA is REPRODUCIBLE, VERIFIABLE, period.
> Your following statement does not seem to firm-grounded. Let's say, it is just
> pathological misconception talking about pathological misconception.
>
> People will continue to use GUA, not your 'self-talk', or fantasy.
>

It took me years to track down the original author.
Although he calls it: "The Psychology of Self-Reference"
It is actually the pathology of self-reference.

Pathological self-reference(Olcott 2004) makes both yes and no incorrect
answers to yes/no question thus proving that the question itself is
incorrect.

The Psychology of Self-Reference
Daryl McCullough
Jun 25, 2004, 6:30:39 PM

You ask someone (we'll call him "Jack") to give a truthful
yes/no answer to the following question:

Will Jack's answer to this question be no?

Jack can't possibly give a correct yes/no answer to the question.
https://groups.google.com/g/sci.logic/c/4kIXI1kxmsI/m/hRroMoQZx2IJ




Flibble is the only one that understands this besides me:

On 7/10/2021 12:00 PM, Mr Flibble wrote:
> I agree with Olcott that a halt decider can NOT be part
> of that which is being decided (see [Strachey 1965])
> which, if Olcott is correct, falsifies a collection of
> proofs (which I don't have the time to examine) which
> rely on that mistake.

[wij]

I have tons of books, steadily increasing by average 40 books every year. I just
skim most of them, I know where my knowledge is from. Hope you do.
(good you aware of this word 'Plagiarism')

> > Your H(P,P) is also an instance governed by GUA, too. But, according to GUA,
> > H(P,P) is undecidable, your conclusion is incorrect.
> >
> > GUA is REPRODUCIBLE, VERIFIABLE, period.
> > Your following statement does not seem to firm-grounded. Let's say, it is just
> > pathological misconception talking about pathological misconception.
> >
> > People will continue to use GUA, not your 'self-talk', or fantasy.
> >
> It took me years to track down the original author.
> Although he calls it: "The Psychology of Self-Reference"
> It is actually the pathology of self-reference.
>
> Pathological self-reference(Olcott 2004) makes both yes and no incorrect
> answers to yes/no question thus proving that the question itself is
> incorrect.
>
> The Psychology of Self-Reference
> Daryl McCullough
> Jun 25, 2004, 6:30:39 PM

You tend to throw irrelevant questions into discussion while you feel defeated.
What is this to do with psychology, again?

> You ask someone (we'll call him "Jack") to give a truthful
> yes/no answer to the following question:
>
> Will Jack's answer to this question be no?
>
> Jack can't possibly give a correct yes/no answer to the question.
> https://groups.google.com/g/sci.logic/c/4kIXI1kxmsI/m/hRroMoQZx2IJ

Many of your pathological questions can be expressed in formal logic and
evaluate. You seems not to know how, but keep on day dreaming and 'self-talk'.

>
>
> Flibble is the only one that understands this besides me:

Resorting the proof to an occasional bystander?
I can not imagine what kind of knowledge was built in your brain.

[olcott]

Systems of formal logic was very deliberately created to make sure that
actual self-reference is inexpressible so I created minimal type theory:

https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF

LP := ~True(LP) specifies infinite recursion and is thus unsound.
G := ~Provable(G) specifies infinite recursion and is thus unsound.

Minimal Type Theory translates its expressions into directed graphs.
The infinite cycled in these graphs proves that their expressions cannot
be evaluated and are therefore incorrect.

See page 5.
https://www.researchgate.net/publication/317953772_Provability_with_Minimal_Type_Theory

[wij]

I tell what: "LP:=~True(LP)" is a cyclic definition.

Tons of books/papers are 'manufactured' (roughly the same old thing with new
terms or author's own interpretation), for commercial,political, passing exam. ... reasons.
Few has true knowledge inside.

[olcott]

G is not provable in F
G := ~(F ⊢ G)

00 ~ 01
01 ⊢ 02 00
02 F
The above is a digraph with a cycle

[wij]

G(1/√2 |00> +1/√2 |10>)=1/2(|00> + |10> + |10> + |11>)
but |F>-<F⊕G> = (-1)ᴳ(|0> + |1>) ⊢ 1/2

∴ H is undecidable. Correct H(P,P) does not exist.
Your x86utm operating system is the physical proof that you are a liar.

[olcott]

The above seems to be incoherent gibberish.

Since I have proven that H(P,P) is correctly decided any "proof" to the
contrary must be equivalent to the nonesense proof that 1==0.

> ∴ H is undecidable. Correct H(P,P) does not exist.
> Your x86utm operating system is the physical proof that you are a liar.
>
> --
> Copyright 2021 WIJ
> "If I can see further it is by standing on top of the tower of dwarfs."
>

[wij]

I thought you were talking about quantum computing in digraph

> Since I have proven that H(P,P) is correctly decided any "proof" to the
> contrary must be equivalent to the nonesense proof that 1==0.

Is H(P,P) also a sub-instance of GUA? If not, why?

> > ∴ H is undecidable. Correct H(P,P) does not exist.
> > Your x86utm operating system is the physical proof that you are a liar.
> >
> > --
> > Copyright 2021 WIJ
> > "If I can see further it is by standing on top of the tower of dwarfs."
> >
> --
> Copyright 2021 Pete Olcott
>
> "Great spirits have always encountered violent opposition from mediocre
> minds." Einstein

[olcott]

Yes GUA is the generic case of the HP counter-examples.

>>> ∴ H is undecidable. Correct H(P,P) does not exist.
>>> Your x86utm operating system is the physical proof that you are a liar.
>>>
>>> --
>>> Copyright 2021 WIJ
>>> "If I can see further it is by standing on top of the tower of dwarfs."
>>>
>> --
>> Copyright 2021 Pete Olcott
>>
>> "Great spirits have always encountered violent opposition from mediocre
>> minds." Einstein
>
> --
> Copyright 2021 WIJ
> "If I can see further it is by standing on top of the tower of dwarfs."
>

[Richard Damon]

On 7/15/21 9:47 AM, olcott wrote:
>
> Since I have proven that H(P,P) is correctly decided any "proof" to the
> contrary must be equivalent to the nonesense proof that 1==0.

No, you haven't.

You have made a lot of badly argued claims about this, but you have
NEVER come close to a proof.