G asserts its own unprovability in F

[PeteOlcott]

"argumentum ad verecundiam is not a fallacy within inductive inference, yet it must be a qualified authority."

indeed peter.

skepdick wasted no time reminding me of the fact that just becuz i might think of wtf as a person who by his mathematical knowledge would be an authority on the matter, it doesn't mean that he would be right.

"That a broad consensus of physicians agree on a medical opinion provides strong evidence (yet zero proof) that the opinion is correct."

indeed peter.

just becuz a couple or more people consistently disagree with skepdick, I'd not be justified in claiming that it's more likely that he's wrong therefore.

On the other hand my claim is proven analytically.
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.

The standard definition of mathematical incompleteness:
Incomplete(T) ↔ ∃φ ∈ F((T ⊬ φ) ∧ (T ⊬ ¬φ))
requires formal systems to do the logically impossible:
to prove self-contradictory expressions of language.

So formal systems are "incomplete" in the same sense that we determine
that a baker that cannot bake a proper angel food cake using ordinary
red house bricks as the only ingredient lacks sufficient baking skill.

[Agent Smith]

Skepdick had made an interesting comment which, ex mea sententia, amounts to saying there really is no difference between the two/more systems in re G (the Gödel sentence) that are at play here.

[PeteOlcott]

Skepdick had made an interesting comment which, ex mea sententia, amounts to saying there really is no difference between the two/more systems in re G (the Gödel sentence) that are at play here.

I didn't notice that he said anything like that.
The key aspect of this is whether or not Gödel's G has unprovability
equivalence to my: G asserts its own unprovability in F.

Gödel's G was in the language of arithmetic that can't directly represent
anything like provability, so he had to fake provability using Arithmetization.
https://encyclopediaofmath.org/wiki/Arithmetization

My much more powerful F has its own provability predicate, thus does
no need Arithmetization or Diagonalization (defined in link)
https://www.cs.cornell.edu/courses/cs48 ... lec-23.pdf

[Agent Smith]

Skepdick had made an interesting comment which, ex mea sententia, amounts to saying there really is no difference between the two/more systems in re G (the Gödel sentence) that are at play here.

I didn't notice that he said anything like that.
The key aspect of this is whether or not Gödel's G has unprovability
equivalence to my: G asserts its own unprovability in F.

Gödel's G was in the language of arithmetic that can't directly represent
anything like provability. My much more powerful F has its own provability
predicate.

For me the nature of the problem is such that all one needs to do is let Gödel compromise his own position.

[PeteOlcott]

Skepdick had made an interesting comment which, ex mea sententia, amounts to saying there really is no difference between the two/more systems in re G (the Gödel sentence) that are at play here.

I didn't notice that he said anything like that.
The key aspect of this is whether or not Gödel's G has unprovability
equivalence to my: G asserts its own unprovability in F.

Gödel's G was in the language of arithmetic that can't directly represent
anything like provability. My much more powerful F has its own provability
predicate.

For me the nature of the problem is such that all one needs to do is let Gödel compromise his own position.

This is the crux of the whole error:
The standard definition of mathematical incompleteness:
Incomplete(T) ↔ ∃φ ∈ F((T ⊬ φ) ∧ (T ⊬ ¬φ))

Requires formal systems to do the logically impossible:
to prove self-contradictory expressions of language.

So formal systems are "incomplete" in the same sense that we determine
that a baker that cannot bake a proper angel food cake using ordinary
red house bricks as the only ingredient lacks sufficient baking skill.

Everything else about the Gödel proof is correct.

[Agent Smith]

I didn't notice that he said anything like that.
The key aspect of this is whether or not Gödel's G has unprovability
equivalence to my: G asserts its own unprovability in F.

Gödel's G was in the language of arithmetic that can't directly represent
anything like provability. My much more powerful F has its own provability
predicate.

For me the nature of the problem is such that all one needs to do is let Gödel compromise his own position.

This is the crux of the whole error:
The standard definition of mathematical incompleteness:
Incomplete(T) ↔ ∃φ ∈ F((T ⊬ φ) ∧ (T ⊬ ¬φ))

Requires formal systems to do the logically impossible:
to prove self-contradictory expressions of language.

So formal systems are "incomplete" in the same sense that we determine
that a baker that cannot bake a proper angel food cake using ordinary
red house bricks as the only ingredient lacks sufficient baking skill.

Everything else about the Gödel proof is correct.

As it seems to me you're on the right track. Poor baker!

[Skepdick]

This is the crux of the whole error:
The standard definition of mathematical incompleteness:
Incomplete(T) ↔ ∃φ ∈ F((T ⊬ φ) ∧ (T ⊬ ¬φ))

Requires formal systems to do the logically impossible:
to prove self-contradictory expressions of language.

So formal systems are "incomplete" in the same sense that we determine
that a baker that cannot bake a proper angel food cake using ordinary
red house bricks as the only ingredient lacks sufficient baking skill.

Everything else about the Gödel proof is correct.

I don't think I've stressed this enough....[Redacted]
Proving self-contradictory expressions can't be "logically impossible" because it's factually possible.

The untyped lambda calculus does it.
Literally every Turing-complete system does it.

[Edited by iMod]

[PeteOlcott]

For me the nature of the problem is such that all one needs to do is let Gödel compromise his own position.

This is the crux of the whole error:
The standard definition of mathematical incompleteness:
Incomplete(T) ↔ ∃φ ∈ F((T ⊬ φ) ∧ (T ⊬ ¬φ))

Requires formal systems to do the logically impossible:
to prove self-contradictory expressions of language.

So formal systems are "incomplete" in the same sense that we determine
that a baker that cannot bake a proper angel food cake using ordinary
red house bricks as the only ingredient lacks sufficient baking skill.

Everything else about the Gödel proof is correct.

As it seems to me you're on the right track. Poor baker!

Don't believe anything that Skepdick says. He is getting some
things wrong. A self-contradictory expressions can never be proved.

[Agent Smith]

This is the crux of the whole error:
The standard definition of mathematical incompleteness:
Incomplete(T) ↔ ∃φ ∈ F((T ⊬ φ) ∧ (T ⊬ ¬φ))

Requires formal systems to do the logically impossible:
to prove self-contradictory expressions of language.

So formal systems are "incomplete" in the same sense that we determine
that a baker that cannot bake a proper angel food cake using ordinary
red house bricks as the only ingredient lacks sufficient baking skill.

Everything else about the Gödel proof is correct.

As it seems to me you're on the right track. Poor baker!

Don't believe anything that Skepdick says. He is getting some
things wrong. A self-contradictory expressions can never be proved.

Ok! I've read a few of Skepdick's posts. He sounds like a reasonable person.

Coming to Gödel, I find it extremely unlikely that he would've made a silly mistake like the ones most skeptical of his eponymous theorems say he made. I'd say Gödel is right even when he's wrong! I'm a big fan you see.

[Skepdick]

Don't believe anything that Skepdick says. He is getting some
things wrong. A self-contradictory expressions can never be proved.

I am not sure if anyone else has noticed but..[Redacted]

In an explosive system you can prove ALL expressions. That's literally how the principle of explosion works and what it entails.

What's a sufficient condition to prove all expressions? Conditionals: If C, then F; or Peirce's law in Classical logic.


[Edited by iMod]

[PeteOlcott]

As it seems to me you're on the right track. Poor baker!

Don't believe anything that Skepdick says. He is getting some
things wrong. A self-contradictory expressions can never be proved.

Ok! I've read a few of Skepdick's posts. He sounds like a reasonable person.

Coming to Gödel, I find it extremely unlikely that he would've made a silly mistake like the ones most skeptical of his eponymous theorems say he made. I'd say Gödel is right even when he's wrong! I'm a big fan you see.

"I'd say Gödel is right even when he's wrong! "
That kind of thinking can cause the end of life on Earth.
I am refuting Gödel as a proxy for refuting Tarski.

Unless humanity has a precise definition of
the notion of True(L, x) we have no definite
way of discerning truth from dangerous lies.

According to the principle of explosion:
FALSE proves that Donald Trump is the Christ.

My overarching principle is {correct reasoning} in this regard
some of classical logic is simply incorrect.

[FlashDangerpants]

Ok! I've read a few of Skepdick's posts. He sounds like a reasonable person.

Don't get me wrong, he's probably right about Olcott being totally wrong...
but he has a personality disorder so I can't endorse that misuse of the word "reasonable".

[PeteOlcott]

Ok! I've read a few of Skepdick's posts. He sounds like a reasonable person.

Don't get me wrong, he's probably right about Olcott being totally wrong...
but he has a personality disorder so I can't endorse that misuse of the word "reasonable".

Thanks for the clarification, that seems to make perfect sense and would
explain why he gets so angry over things that a reasonable person would not.

[Agent Smith]

Ok! I've read a few of Skepdick's posts. He sounds like a reasonable person.

Don't get me wrong, he's probably right about Olcott being totally wrong...
but he has a personality disorder so I can't endorse that misuse of the word "reasonable".

PeteOlcott has made a very specific claim. Either I missed the evidence for it or he hasn't provided it.

[Agent Smith]

Don't believe anything that Skepdick says. He is getting some
things wrong. A self-contradictory expressions can never be proved.

Ok! I've read a few of Skepdick's posts. He sounds like a reasonable person.

Coming to Gödel, I find it extremely unlikely that he would've made a silly mistake like the ones most skeptical of his eponymous theorems say he made. I'd say Gödel is right even when he's wrong! I'm a big fan you see.

"I'd say Gödel is right even when he's wrong! "
That kind of thinking can cause the end of life on Earth.
I am refuting Gödel as a proxy for refuting Tarski.

Unless humanity has a precise definition of
the notion of True(L, x) we have no definite
way of discerning truth from dangerous lies.

According to the principle of explosion:
FALSE proves that Donald Trump is the Christ.

My overarching principle is {correct reasoning} in this regard
some of classical logic is simply incorrect.

It was a tongue-in-cheek acknowledgment of Gödel's logical prowess. Nevertheless you have a point! History is on your side on that score.

Focus on the class of statements G, the Gödel sentence, belongs to.