A proof of G in F cannot exist in F

[olcott]

*The scope of this post is* ∃G ∈ F (G ↔ ¬(F ⊢ G))

There exists a G in F such that G is logically equivalent to its own
unprovability in F.

It makes no difference at all even if Gödel explicitly stated that he
isn't talking about anything like this.

The idea here is to examine the philosophical foundation of the
mathematical notion of incompleteness making sure that it is coherent.

A proof of G in F that proves that G cannot be proved in F is simply
self-contradictory, thus no such G exists in F.

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

Thus proving that when the above G is neither provable nor refutable in
F it is because G is self-contradictory in F thus not because F is
incomplete.


--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

[Richard Damon]

On 3/26/23 4:38 PM, olcott wrote:
> *The scope of this post is*  ∃G ∈  F (G ↔ ¬(F ⊢ G))

So, nothing to do with Godels Incompletnes proof.

An thus you trying to connect it to Godel is just a Strawman Error.

>
> There exists a G in F such that G is logically equivalent to its own
> unprovability in F.
>
> It makes no difference at all even if Gödel explicitly stated that he
> isn't talking about anything like this.

But it does, you can't put words in another persons mouth and be correct.

You are just admitting that you system is based on LIES.

>
> The idea here is to examine the philosophical foundation of the
> mathematical notion of incompleteness making sure that it is coherent.

Which actually just proves that YOUR concepts are incoherent.

>
> A proof of G in F that proves that G cannot be proved in F is simply
> self-contradictory, thus no such G exists in F.

Which since Godel never claimed a proof of G in F, in fact he claims
that such a proof can not exist, so your logic is proved to b UNSOUND,
and that you are an idiot.

>
> The conventional definition of incompleteness:
> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>
> Thus proving that when the above G is neither provable nor refutable in
> F it is because G is self-contradictory in F thus not because F is
> incomplete.
>
>

Based on what?

You LIES?

Of course if you start from the wrong G, your break proof. Since you "G"
isn't Gode's G, you just commited the Stram man error, and to claim
otherwords just proves you are a LIAR.


Please show the exact location in Godels ACTUAL PROOF where he makes the
claim you say hbe does.

FAILURE TO REPLY IS ADMISSION YOU ARE A LIAR.