G asserts its own unprovability in F

[Skepdick]

I spent 20 years boiling the whole thing down to this:
G asserts its own unprovability in F.

Whether G asserts its own unprovability in F.
Or whether you assert that G is unprovable in F.

It makes no difference if "G is unprovable in F" is a tautology e.g true in all models.

It is true in some models usually referred to as Meta_F.

The reason that G cannot be proved in F is that this requires
a sequence of inference steps in F that proves no such sequence
of inference steps exists in F.

And you are back on the merry go-round. L[Redacted]

Prove that there are no sequence of steps which proves that there are no sequence of steps.


[Edited by iMod]

[PeteOlcott]

I propose that it is impossible to correctly provide any sequence of
inference steps in F that proves in F that there is no such sequence
of inference steps in F.

No shit! An object can’t prove its own non-existence.

G asserts its own unprovability in F

The reason that G cannot be proved in F is that this requires a
sequence of inference steps in F that proves no such sequence
of inference steps exists in F.

Thus the reason that G cannot be proved in F is NOT that F is
incomplete as Göde'l's Incompleteness Theorem concludes.
If the conclusion of a proof is incorrect then the whole proof has been refuted.

[PeteOlcott]

We must first agree on definitions of the pertinent, some more than others, words that appear in Gödel's proof. Second step is to exhaust all possible inferences.

I'm no fan of this method, but all philosophers ultimately end up using it, especially when they're cornered,

I spent 20 years boiling the whole thing down to this:
G asserts its own unprovability in F.

When we even hypothesize that it is a correct basis it refutes Gödel's
proof (within this hypothesis) in a few more sentences .

I suggest that you keep Gödel and his incompleteness theorems on the backburner - for at least a week, say - and sink yer teeth into paradoxes in general. What can we learn from other antinomies? Go for the 10,000 feet view.

I have been working on these things for twenty years and created a new logic system
https://www.researchgate.net/publicatio ... y_YACC_BNF
This logic system is named Minimal Type Theory and translates logic expressions
into directly graphs. Every logic expression having an infinite cycle is erroneous.

I am already taking a break from my halting problem proofs to work on Gödel
https://www.researchgate.net/publicatio ... lem_Proofs

My other reviewer on this forum already acknowledged that I am correct
about Gödel the message that I just quoted of his.

[Skepdick]

The reason that G cannot be proved in F is that this requires a
sequence of inference steps in F that proves no such sequence
of inference steps exists in F.

[Redacted]

What sequence of steps is required in order to prove that no roads on Earth lead to Australia?

Describe the algorithm to a human who undertakes the task.


[Edited by iMod]

[PeteOlcott]

The reason that G cannot be proved in F is that this requires a
sequence of inference steps in F that proves no such sequence
of inference steps exists in F.

[Redacted]

What sequence of steps is required in order to prove that no roads on Earth lead to Australia?

Yet the paragraph that you denigrate you already agreed to thus
seem be be proving your namesake as an obnoxious skeptic.

The fact is that the above paragraph cannot be proved in F
because its proof is contradictory in F is the real reason why
it cannot be proved in F thus not the reason that Gödel gave.

Gödel "Incompleteness" Theorem is more accurately named
Formal systems are not supposed to prove contradictions theorem.

[Skepdick]

The fact is that the above paragraph cannot be proved in F
because its proof is contradictory in F is the real reason why
it cannot be proved in F thus not the reason that Gödel gave.

Gödel "Incompleteness" Theorem is more accurately named
Formal systems are not supposed to prove contradictions theorem.

The implication perfectly agrees with Godel's theorem.

The fact that G can't be proved in F is true.
Which is the same thing as saying that G is unprovable.

Which is the same thing as saying that if "G is provable" then "G can't be proved in F would be false".

[Redacted] you can't escape your own circular reasoning.


[Edited by iMod]

[PeteOlcott]

The fact is that the above paragraph cannot be proved in F
because its proof is contradictory in F is the real reason why
it cannot be proved in F thus not the reason that Gödel gave.

Gödel "Incompleteness" Theorem is more accurately named
Formal systems are not supposed to prove contradictions theorem.

The implication perfectly agrees with Godel's theorem.

The fact that G can't be proved in F is true is materially equivalent to G is unprovable.

The "reason" it's unprovable is immaterial if it's true THAT it's unprovable.

Yet Gödel says the reason that G cannot be proved in F is that there is
something wrong with F when in reality there is something wrong with G
and nothing wrong with F.

This means that the conclusion of his proof is incorrect thus refuting the entire proof.

[Skepdick]

Yet Gödel says the reason that G cannot be proved in F is that there is
something wrong with F when in reality there is something wrong with G
and nothing wrong with F.

This means that the conclusion of his proof is incorrect thus refuting the entire proof.

There's nothing "wrong" with F. It's incomplete. Incompleteness is a property of F.
There's nothing "wrong" with G either. It's unprovable. Unprovability is a property of G.

If you expect/want/desire F to be complete, then the fact that F is incomplete might disappoint you. And you might say that there's something "wrong" with F.
If you expect/want/desire G to be provable, then the fact that G is unprovable might disappoint you. And you might say that there's something "wrong" with C.

It's like a TV that doesn't turn on. There's only something "wrong" with it because you expect it to turn on and it doesn't.

[Redacted]you can't semantically separate your expectations from your assertions.


[Edited by iMod]

[PeteOlcott]

I propose that it is impossible to correctly provide any sequence of inference steps in F that proves in F that there is no such sequence of inference steps in F.

No shit! An object can’t prove its own non-existence.

When G asserts its own unprovability in F is proven this requires a sequence of
inference steps in F that proves that there is no such sequence of inference steps in F.

Can you understand this much?

[Skepdick]

When G asserts its own unprovability in F is proven...

G doesn't assert its own unprovability in F is proven.
G asserts its own unprovability in F is true.

[Redacted]


[Edited by iMod]

[PeteOlcott]

When G asserts its own unprovability in F is proven...

G doesn't assert its own unprovability in F is proven.
G asserts its own unprovability in F is true.

You are an idiot for conflating truth and provability.

If we hypothesize that G is asserting its own unprovability in F
then the proof of this does require a sequence of inference steps
in F that proves there is no such sequence of inference steps in F
thus proving that G is unprovable in F only because the proof of
G is contradictory in F.

That Gödel sums up the essence of his G in F as:
"...a proposition which asserts its own unprovability." 15 (Gödel 1931:39-41)

Is a reasonable basis to conclude that:
G asserts its own unprovability in F
Is a reasonably equivalent summation of his actual G.

Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And Related Systems

[Skepdick]

If we hypothesize that G is asserting its own unprovability in F
then the proof of this...

[Redacted

There is no "proof of this."
That is why it's true.


[Edited by iMod]

[PeteOlcott]

If we hypothesize that G is asserting its own unprovability in F
then the proof of this...

Idiot.

There is no "proof of this."
That is why it's true.

Circular reasoning is incorrect reasoning.

When G asserts its own unprovability in F
The proof of G in F requires a sequence of inference steps in F
that proves there is no such sequence of inference steps in F.

Gödel understood this so he proved that there are no such sequence
of inference steps in F in Meta-F.

[PeteOlcott]

I am not the one resorting to Ad Hominem attacks. You cannot show an actual mistake in my reasoning only because there are no mistakes.

Most often (from many prior discussions) Ad Hominem attacks are what people that don't have a clue use to try to hide the fact that they don't have a clue.


[Edited by iMod]

[Skepdick]

I am not the one resorting to Ad Hominem attacks.
You cannot show an actual mistake in my reasoning only because there are no mistakes.

I've pointed out the mistake enough times to be certain you don't want to acknowledge it.

True doesn't imply provable and truth doesn't require provability - therefore G's unprovability (being true) doesn't require a proof.

Most often (from many prior discussions) Ad Hominem attacks are what people that don't have a clue use to try to hide the fact that they don't have a clue.

You don't even understand what an ad hominem attack is.

An ad hominem looks like "your argument is wrong BECAUSE you are an idiot". I am not saying such a thing.

[Redacted]


[Edited by iMod]