Gödel sentence in the 1931 incompleteness proof is not a truth bearer thus simply untrue

[olcott]

The conventional definition of incompleteness:
Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))

When we see that the following Prolog expressions satisfy the above
definition of incompleteness then we can see that they are equivalent to
the Gödel sentence in the 1931 incompleteness proof.

?- G = not(provable(F, G)). % G = ¬(F ⊢ G)
?- G = not(provable(F, not(G))). % G = ¬(F ⊢ ¬G)

When we test the above pair of expressions we find that neither of them
are provable in the Prolog formal system: (SWI-Prolog (threaded, 64
bits, version 7.6.4)

?- unify_with_occurs_check(G, not(provable(F, G))).false.
?- unify_with_occurs_check(G, not(provable(F, not(G)))).false.

Thus fulfilling the conventional definition of incompleteness, and
proving equivalence to the 1931 Gödel “Incompleteness” sentence. The
1931 Gödel Incompleteness theorem correctly concludes that neither G nor
¬G are provable in F.

The key detail that it leaves out is that neither G nor ¬G are provable
in F because both are erroneous cyclic terms that cannot be resolved in
any formal system what-so-ever.

Prolog detects [and rejects] pathological self reference in the Gödel
sentence

https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
Gödel analyzed within Wittgenstein's controversial formalization of true
and false: (thus also defeating the Tarski Undefinability theorem)

'True in Russell's system' means, as was said: proved in Russell's
system; and
'false in Russell's system' means: the opposite has been proved in
Russell's system.

Then the above minimal essence of Gödel's logic sentence: φ is construed
as neither true nor false thus (like the liar paradox) simply not a
truth bearer. Gödel would construe this same case as Incomplete(T).

https://www.liarparadox.org/Wittgenstein.pdf

Thus the simplest way to understand Gödel 1931 Incompleteness is to
understand that is is nothing more than the mistake of trying to
correctly determine the truth value of an expression of language that is
not a truth bearer.


--
Copyright 2022 Pete Olcott

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

[olcott]

On 11/28/2022 3:46 AM, Julio Di Egidio wrote:

> On Monday, 28 November 2022 at 01:20:41 UTC+1, olcott wrote:
>
>> "Gödel sentence in the 1931 incompleteness proof

>> is not a truth bearer thus simply untrue"
>
> Prove it... Moron.
>
> Corollary: model theory my ass.
>
> Julio

Prolog detects [and rejects] pathological self reference in the Gödel
sentence

https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence

I already proved my point to everyone knowing Prolog. I reiterated this
same point in Minimal Type Theory in my above paper.

*Here is how Wittgenstein ties to model theory*
<Wittgenstein>
8. I imagine someone asking my advice; he says: "I have constructed a
proposition (I will use 'P' to designate it) in Russell's symbolism, and
by means of certain definitions and transformations it can be so
interpreted that it says: 'P is not provable in Russell's system'.
</Wittgenstein>

The following says that:
there exists an φ such that φ is neither provable nor refutable in T:

The conventional definition of incompleteness:
Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))

When we see that the following Prolog expressions satisfy the above
definition of incompleteness then we can see that they are equivalent to
the Gödel sentence in the 1931 incompleteness proof.

?- G = not(provable(F, G)). % G = ¬(F ⊢ G)
?- G = not(provable(F, not(G))). % G = ¬(F ⊢ ¬G)

When we test the above pair of expressions we find that neither of them
are provable in the Prolog formal system: (SWI-Prolog (threaded, 64
bits, version 7.6.4)

?- unify_with_occurs_check(G, not(provable(F, G))).false.
?- unify_with_occurs_check(G, not(provable(F, not(G)))).false.

Thus fulfilling the conventional definition of incompleteness, and
proving equivalence to the 1931 Gödel “Incompleteness” sentence. The
1931 Gödel Incompleteness theorem correctly concludes that neither G nor
¬G are provable in F.

The key detail that it leaves out is that neither G nor ¬G are provable
in F because both are erroneous cyclic terms that cannot be resolved in
any formal system what-so-ever.

Gödel analyzed within Wittgenstein's controversial formalization of true
and false: (thus also defeating the Tarski Undefinability theorem)

'True in Russell's system' means, as was said: proved in Russell's
system; and
'false in Russell's system' means: the opposite has been proved in
Russell's system.

Then the above minimal essence of Gödel's logic sentence: φ is construed

as *neither true nor false* thus (*like the liar paradox*) simply not a

truth bearer. Gödel would construe this same case as Incomplete(T)

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius

[olcott]

On 11/28/2022 11:51 AM, Julio Di Egidio wrote:

> On Monday, 28 November 2022 at 18:31:28 UTC+1, _ Olcott wrote:
>> On 11/28/2022 3:46 AM, Julio Di Egidio wrote:
>>> On Monday, 28 November 2022 at 01:20:41 UTC+1, olcott wrote:
>>>
>>>> "Gödel sentence in the 1931 incompleteness proof
>>>> is not a truth bearer thus simply untrue"
>>>
>>> Prove it... Moron.
>
> Moron.
>
>>> Corollary: model theory my ass.
>>

>> *Here is how Wittgenstein ties to model theory*
>

> There is how you quote Wittgenstein *out of context*,
> to make him say the exact opposite of what he said.
>
> You bloody troll and spammer.
>
> *Plonk*
>
> Julio


When I provide word-for-word everything that Wittgenstein said I am
providing the complete context. https://www.liarparadox.org/Wittgenstein.pdf

I know that Wittgenstein is correct because I formulated his entire
rebuttal shortly before I ever heard of him.

Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))

It is common knowledge that the above definition correctly formalizes
the notion of incompleteness.

What is not common knowledge is that every self-contradictory expression
of language fulfills the above logic sentence.

[olcott]

On 11/28/2022 4:44 PM, Don Stockbauer wrote:

> Have you heard of Wittgenstein's poker?
>
> It was a card game he was involved in.

https://www.youtube.com/watch?v=Mj5omcY21bE

[Artist (nickis jobsearchespage)]

On Wednesday, November 30, 2022 at 6:56:31 AM UTC, Don Stockbauer wrote:

> OMG it wasn't about a card game at all it was about a philosophical argument not an intellectual argument but one that could have resulted in a philosopher with a red hot post poker driven into his eye
>
> have a nice day
Don old chap, these men are serious researchers, quit disturbing them I plea, they could just discover something extraordinarily significant....and whilenI'm here how much did your ex-missus swindle from you, its had an extraordinary effect on your personal communications ?

[Artist (nickis jobsearchespage)]

On Wednesday, December 7, 2022 at 3:27:05 PM UTC, Don Stockbauer wrote:
> On Tuesday, December 6, 2022 at 12:04:01 PM UTC-6, Don Stockbauer wrote:
> > On Tuesday, December 6, 2022 at 10:20:50 AM UTC-6, Don Stockbauer wrote:
> > > On Tuesday, December 6, 2022 at 2:46:22 AM UTC-6, Don Stockbauer wrote:
> > > > On Monday, December 5, 2022 at 9:31:21 AM UTC-6, Don Stockbauer wrote:

> > > > > Dealbreaker i'm
> > > >
> > > > So , with those words you're aiming for a reconciliation, Nic?
> > > >
> > > > Found your passport yet?
> > > yeah I do that too I kind of keep trying and trying to maintain the relationship and then it becomes obvious that it's doomed so then I lash out in horrible things against my conversational opponent and then that's it you know there's 8 million other people to go and have a conversation with you so it's absolutely no big thing right? Have a nice day.
> > >
> > > The Apple dictation keeps putting down million instead of billion it's really irritating.
> > yeah, it's really hard for me to have a relationship because I just get irritated with people too easily and in this modern lobotomize sheep world we live in you get irritated at somebody they're just gone and if somebody stops communicating with you there's nothing on earth that can get them to communicate again because all they have to do is be lazy and not deal with you I thought of this one funny thing suppose your conversational opponent refuses to talk to you but then you find out information where they can get a kid needs to save their lives so you write to them about that they still won't contact you did rather die than contact you have a nice day I want my Dolly
>
> so what is the lesson learned? if you try to get your conversational opponent to establish a video link with you in order to reduce the possibility that they might be a scammer and that person refuses dont actually call that person a scammer because that ends the relationship immediately, what you should do is not call that person a scammer and then just wait and see if that person ever asks you for money , then the relationship is immediately over.
Since you have found somebody to talk physics and computers with you, there seems no o alterior motive and write to comp.ai.philosophy.

nope I have not found my passport and travelling to the states seems like a dumb idea.

[Artist (nickis jobsearchespage)]

Don Stockbauer,
Cease your confabulations. I quit, as you know I'm married.