XPost: comp.theory, sci.logic

G := ~(F ⊢ G)
When G asserts its own unprovability in F the proof of G in F requires a sequence of inference steps in F that prove that they themselves do not
exist. *This nullifies the whole notion of mathematical incompleteness*

It is dead obvious that G is unprovable in F because its proof would be contradictory in F thus the reason is not that 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

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XPost: comp.theory, sci.logic

On 8/9/2023 4:07 PM, olcott wrote:

G := ~(F ⊢ G)
When G asserts its own unprovability in F the proof of G in F requires a sequence of inference steps in F that prove that they themselves do not exist. *This nullifies the whole notion of mathematical incompleteness*

It is dead obvious that G is unprovable in F because its proof would be contradictory in F thus the reason is not that F is incomplete.

Any expression of language that asserts its own unprovability in F
proves that the essential notion of mathematical incompleteness is
incorrect whether or not this expression is isomorphic to the Gödel
sentence.

Because G is neither provable nor refutable in F thus exactly meeting
the mathematical definition of incompleteness, yet we can also see that
G is unprovable because this proof would be contradictory then we know
that the reason is not that F is incomplete, thus the essential notion
of mathematical incompleteness is incorrect.




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

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XPost: comp.theory, sci.logic

On 8/9/23 5:07 PM, olcott wrote:

G := ~(F ⊢ G)

INCORRECT!!!

When G asserts its own unprovability in F the proof of G in F requires a sequence of inference steps in F that prove that they themselves do not exist. *This nullifies the whole notion of mathematical incompleteness*

No, G does NOT assert its own unprovability.

G asserts that there does not exist a Natural number that satisfies a
certain primative recursive relationship.

It is only with knowledge from the meta-theory that created that
primative recursive relationship in F that we can deduce that this means
that the existance of such a number directly correelates to the ability
to prove G in F.

It is dead obvious that G is unprovable in F because its proof would be contradictory in F thus the reason is not that F is incomplete.

Since you don't have the right statement for G, your "logic" just proves
your ignorance and stupdity.

The fact that you keep repeating it shows you are just a hypocritical liar.

You clearly do not understand how logic works.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XPost: comp.theory, sci.logic

On 8/9/23 7:04 PM, olcott wrote:

On 8/9/2023 4:07 PM, olcott wrote:

G := ~(F ⊢ G)
When G asserts its own unprovability in F the proof of G in F requires a
sequence of inference steps in F that prove that they themselves do not
exist. *This nullifies the whole notion of mathematical incompleteness*

It is dead obvious that G is unprovable in F because its proof would be
contradictory in F thus the reason is not that F is incomplete.

Any expression of language that asserts its own unprovability in F
proves that the essential notion of mathematical incompleteness is
incorrect whether or not this expression is isomorphic to the Gödel sentence.

So, I guess you are proving that you can't read.

G does NOT assert its own unprovability, so you logic is immaterial.

You are just proving that you have very limited understand of language.

Because G is neither provable nor refutable in F thus exactly meeting
the mathematical definition of incompleteness, yet we can also see that
G is unprovable because this proof would be contradictory then we know
that the reason is not that F is incomplete, thus the essential notion
of mathematical incompleteness is incorrect.

Since you have the wrong statement for G, and have been told that, you
are just proving that your BRAIN is incomplete, and that you are just an ignorant pathological lying idoit.

You will undoubtedly repeat your statement again, just strengthing that
proof.

Note, the fact that you answer NOT by replt to the message with the
comments, because to do so would just show your ignorance, this proves
that the lying is deliberate.

You have KILLED your reputation and will go down in history as a total
idiot.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Wednesday, August 9, 2023 at 6:26:35 PM UTC-5, Richard Damon wrote:

On 8/9/23 7:04 PM, olcott wrote:

On 8/9/2023 4:07 PM, olcott wrote:

G := ~(F ⊢ G)
When G asserts its own unprovability in F the proof of G in F requires a >> sequence of inference steps in F that prove that they themselves do not >> exist. *This nullifies the whole notion of mathematical incompleteness* >>
It is dead obvious that G is unprovable in F because its proof would be >> contradictory in F thus the reason is not that F is incomplete.

Any expression of language that asserts its own unprovability in F
proves that the essential notion of mathematical incompleteness is incorrect whether or not this expression is isomorphic to the Gödel sentence.

So, I guess you are proving that you can't read.

G does NOT assert its own unprovability, so you logic is immaterial.

You are just proving that you have very limited understand of language.

Because G is neither provable nor refutable in F thus exactly meeting
the mathematical definition of incompleteness, yet we can also see that
G is unprovable because this proof would be contradictory then we know that the reason is not that F is incomplete, thus the essential notion
of mathematical incompleteness is incorrect.

Since you have the wrong statement for G, and have been told that, you
are just proving that your BRAIN is incomplete, and that you are just an ignorant pathological lying idoit.

You will undoubtedly repeat your statement again, just strengthing that proof.

Note, the fact that you answer NOT by replt to the message with the comments, because to do so would just show your ignorance, this proves
that the lying is deliberate.

You have KILLED your reputation and will go down in history as a total idiot.

none of that puts food on the table.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Wednesday, August 9, 2023 at 6:26:35 PM UTC-5, Richard Damon wrote:

On 8/9/23 7:04 PM, olcott wrote:

On 8/9/2023 4:07 PM, olcott wrote:

G := ~(F ⊢ G)
When G asserts its own unprovability in F the proof of G in F requires a >> sequence of inference steps in F that prove that they themselves do not >> exist. *This nullifies the whole notion of mathematical incompleteness* >>
It is dead obvious that G is unprovable in F because its proof would be >> contradictory in F thus the reason is not that F is incomplete.

Any expression of language that asserts its own unprovability in F
proves that the essential notion of mathematical incompleteness is incorrect whether or not this expression is isomorphic to the Gödel sentence.

So, I guess you are proving that you can't read.

G does NOT assert its own unprovability, so you logic is immaterial.

You are just proving that you have very limited understand of language.

Because G is neither provable nor refutable in F thus exactly meeting
the mathematical definition of incompleteness, yet we can also see that
G is unprovable because this proof would be contradictory then we know that the reason is not that F is incomplete, thus the essential notion
of mathematical incompleteness is incorrect.

Since you have the wrong statement for G, and have been told that, you
are just proving that your BRAIN is incomplete, and that you are just an ignorant pathological lying idoit.

You will undoubtedly repeat your statement again, just strengthing that proof.

Note, the fact that you answer NOT by replt to the message with the comments, because to do so would just show your ignorance, this proves
that the lying is deliberate.

You have KILLED your reputation and will go down in history as a total idiot.

we don't have anything useful to do so, let's debate.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)