G asserts its own unprovability in F

[PeteOlcott]

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.

Gödel's arithmetization was ingenious, he was able to make G say
something like "G is unprovable in F" when G cannot express anything
like that, it is only the language of arithmetic.

If he started with a language that has its own unprovability operator
his proof would have been 100,000 times less complex and then his trick
would be exposed as the baker that can't bake a cake from house bricks.

When F asserts its own unprovability in F the proof of G in F is analogous
to a person trying to prove that they themselves never existed and math
calling them stupid because they cant do this.

[Agent Smith]

"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.

Gödel's arithmetization was ingenious, he was able to make G say
something like "G is unprovable in F" when G cannot express anything
like that, it is only the language of arithmetic.

If he started with a language that has its own unprovability operator
his proof would have been 100,000 times less complex and then his trick
would be exposed as the baker that can't bake a cake from house bricks.

When F asserts its own unprovability in F the proof of G in F is analogous
to a person trying to prove that they themselves never existed and math
calling them stupid because they cant do this.

I said what I thought was the right thing to say. Take it from there.

[PeteOlcott]

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.

Gödel's arithmetization was ingenious, he was able to make G say
something like "G is unprovable in F" when G cannot express anything
like that, it is only the language of arithmetic.

If he started with a language that has its own unprovability operator
his proof would have been 100,000 times less complex and then his trick
would be exposed as the baker that can't bake a cake from house bricks.

When F asserts its own unprovability in F the proof of G in F is analogous
to a person trying to prove that they themselves never existed and math
calling them stupid because they cant do this.

I said what I thought was the right thing to say. Take it from there.

I think this means that as long as my analogy is correct then my conclusion is
correct. We wouldn't expect a baker to be able to bake a cake from house bricks
thus we shouldn't expect mathematical systems to do the equally impossible.

[Agent Smith]

Gödel's arithmetization was ingenious, he was able to make G say
something like "G is unprovable in F" when G cannot express anything
like that, it is only the language of arithmetic.

If he started with a language that has its own unprovability operator
his proof would have been 100,000 times less complex and then his trick
would be exposed as the baker that can't bake a cake from house bricks.

When F asserts its own unprovability in F the proof of G in F is analogous
to a person trying to prove that they themselves never existed and math
calling them stupid because they cant do this.

I said what I thought was the right thing to say. Take it from there.

I think this means that as long as my analogy is correct then my conclusion is
correct. We wouldn't expect a baker to be able to bake a cake from house bricks
thus we shouldn't expect mathematical systems to do the equally impossible.

The analogy holds, yep!

However, how do "true" logician-phikosophers tackle Gödel. Sorry, hadta make the distinction there - you obviously know why.

[Skepdick]

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".

It's difficult to tell which version of "reasobleness" you actually endorse on any given day.

Reasonable peaople don't commit ad hominems...

But, of course the principle of charity compells me to assume you had the best intentions at heart, so I'll just assume you meant it as a compliment. Thanks!

The reasonable man adapts himself to the world; the unreasonable one persists in trying to adapt the world to himself. Therefore, all progress depends on the unreasonable man. --George Bernard Shaw

[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".

It's difficult to tell which version of "reasobleness" you actually endorse on any given day.

Reasonable peaople don't commit ad hominems...

But, of course the principle of charity compells me to assume you had the best intentions at heart, so I'll just assume you meant it as a compliment. Thanks!

The reasonable man adapts himself to the world; the unreasonable one persists in trying to adapt the world to himself. Therefore, all progress depends on the unreasonable man. --George Bernard Shaw

I reminded PeteOlcott of the inherent unpleasantness in the enterprise known as philosophy. I'm not really a likeable character myself in this universe and so it's likely that I have a lopsided smile so to speak

PeteOlcott has either received my package or is ignoring it. I can't tell at this point. In his favor, his interpretation, assuming it's his, of Gödel's theorems is simultaneously both clear and succinct, just the way I like it.

My own limited education precludes more from me by way of precise, to the point, observations. Suffice it to say that the liar sentence, from which G (the Gödel sentence) is adapted, is, to put it mildly, problematic.

Too, I hadta make the distinction real vs. pseudo philosophers. It should've pointed the spotlight in the right directions. It either has or hasn't! Me and me plans!

[PeteOlcott]

I said what I thought was the right thing to say. Take it from there.

I think this means that as long as my analogy is correct then my conclusion is
correct. We wouldn't expect a baker to be able to bake a cake from house bricks
thus we shouldn't expect mathematical systems to do the equally impossible.

The analogy holds, yep!

However, how do "true" logician-phikosophers tackle Gödel. Sorry, hadta make the distinction there - you obviously know why.

A very famous philosophy of logic guy Ludwig Wittgenstein rejects Gödel's Incompleteness
https://www.liarparadox.org/Wittgenstein.pdf
I figured out his whole proof months before I ever heard of him.

He is considered by some to be the greatest philosopher of the 20th century.
The first and best-known of this posthumous series is the 1953 book Philosophical Investigations. A survey among American university and college teachers ranked the Investigations as the most important book of 20th-century philosophy, standing out as "the one crossover masterpiece in twentieth-century philosophy, appealing across diverse specializations and philosophical orientations".
https://en.wikipedia.org/wiki/Ludwig_Wittgenstein

[Agent Smith]

I think this means that as long as my analogy is correct then my conclusion is
correct. We wouldn't expect a baker to be able to bake a cake from house bricks
thus we shouldn't expect mathematical systems to do the equally impossible.

The analogy holds, yep!

However, how do "true" logician-phikosophers tackle Gödel. Sorry, hadta make the distinction there - you obviously know why.

A very famous philosophy of logic guy Ludwig Wittgenstein rejects Gödel's Incompleteness
https://www.liarparadox.org/Wittgenstein.pdf
I figured out his whole proof months before I ever heard of him.

He is considered by some to be the greatest philosopher of the 20th century.
The first and best-known of this posthumous series is the 1953 book Philosophical Investigations. A survey among American university and college teachers ranked the Investigations as the most important book of 20th-century philosophy, standing out as "the one crossover masterpiece in twentieth-century philosophy, appealing across diverse specializations and philosophical orientations".
https://en.wikipedia.org/wiki/Ludwig_Wittgenstein

I'm not as enamored by Wittgenstein's take on language-philosophy as many seem to be. He has quite a following I'm told. That's alright, part of the territory, nothing at all surprising about it. In a nutshell, Wittgenstein shoots himself in the foot in a rather elaborate and fanciful way which is, paradoxically, the very point he wishes to make. In short Wittgensteinism self-destructs and you come away from it as if someone just told you "that was the plan ... from the very beginning". Stuff like this happen ... on a regular basis ... in philosophy and, perhaps, mathematics, Gödel's theorems being a good example, per you of course.

[PeteOlcott]

The analogy holds, yep!

However, how do "true" logician-phikosophers tackle Gödel. Sorry, hadta make the distinction there - you obviously know why.

A very famous philosophy of logic guy Ludwig Wittgenstein rejects Gödel's Incompleteness
https://www.liarparadox.org/Wittgenstein.pdf
I figured out his whole proof months before I ever heard of him.

He is considered by some to be the greatest philosopher of the 20th century.
The first and best-known of this posthumous series is the 1953 book Philosophical Investigations. A survey among American university and college teachers ranked the Investigations as the most important book of 20th-century philosophy, standing out as "the one crossover masterpiece in twentieth-century philosophy, appealing across diverse specializations and philosophical orientations".
https://en.wikipedia.org/wiki/Ludwig_Wittgenstein

I'm not as enamored by Wittgenstein's take on language-philosophy as many seem to be. He has quite a following I'm told. That's alright, part of the territory, nothing at all surprising about it. In a nutshell, Wittgenstein shoots himself in the foot in a rather elaborate and fanciful way which is, paradoxically, the very point he wishes to make. In short Wittgensteinism self-destructs and you come away from it as if someone just told you "that was the plan ... from the very beginning". Stuff like this happen ... on a regular basis ... in philosophy and, perhaps, mathematics, Gödel's theorems being a good example, per you of course.

Please carefully study this 1/2 page
https://www.liarparadox.org/Wittgenstein.pdf

All that it says is that when expressions of language form something like
the Liar Paradox where they cannot possibly be resolved to true or false
then the expression (rather than the formal system) must be rejected.

I always assess what is actually said rather than reject what is said based
on my opinion of the person saying it, this latter would be ad hominem.

[Agent Smith]

A very famous philosophy of logic guy Ludwig Wittgenstein rejects Gödel's Incompleteness
https://www.liarparadox.org/Wittgenstein.pdf
I figured out his whole proof months before I ever heard of him.

He is considered by some to be the greatest philosopher of the 20th century.
The first and best-known of this posthumous series is the 1953 book Philosophical Investigations. A survey among American university and college teachers ranked the Investigations as the most important book of 20th-century philosophy, standing out as "the one crossover masterpiece in twentieth-century philosophy, appealing across diverse specializations and philosophical orientations".
https://en.wikipedia.org/wiki/Ludwig_Wittgenstein

I'm not as enamored by Wittgenstein's take on language-philosophy as many seem to be. He has quite a following I'm told. That's alright, part of the territory, nothing at all surprising about it. In a nutshell, Wittgenstein shoots himself in the foot in a rather elaborate and fanciful way which is, paradoxically, the very point he wishes to make. In short Wittgensteinism self-destructs and you come away from it as if someone just told you "that was the plan ... from the very beginning". Stuff like this happen ... on a regular basis ... in philosophy and, perhaps, mathematics, Gödel's theorems being a good example, per you of course.

Please carefully study this 1/2 page
https://www.liarparadox.org/Wittgenstein.pdf

All that it says is that when expressions of language form something like
the Liar Paradox where they cannot possibly be resolved to true or false
then the expression (rather than the formal system) must be rejected.

That's one of probably many ways to trip Gödel, but - the million dollar question is - are we in the same boat as Gödel?

[PeteOlcott]

Please carefully study this 1/2 page
https://www.liarparadox.org/Wittgenstein.pdf

All that it says is that when expressions of language form something like
the Liar Paradox where they cannot possibly be resolved to true or false
then the expression (rather than the formal system) must be rejected.

That's one of probably many ways to trip Gödel, but - the million dollar question is - are we in the same boat as Gödel?

We only need that one way to conclusively prove that Gödel's conclusion
that F is incomplete is completely incorrect.

[Agent Smith]

Please carefully study this 1/2 page
https://www.liarparadox.org/Wittgenstein.pdf

All that it says is that when expressions of language form something like
the Liar Paradox where they cannot possibly be resolved to true or false
then the expression (rather than the formal system) must be rejected.

That's one of probably many ways to trip Gödel, but - the million dollar question is - are we in the same boat as Gödel?

We only need that one way to conclusively prove that Gödel's conclusion
that F is incomplete is completely incorrect.

I see, didn't know that!

[Skepdick]

Please carefully study this 1/2 page
https://www.liarparadox.org/Wittgenstein.pdf

All that it says is that when expressions of language form something like
the Liar Paradox where they cannot possibly be resolved to true or false
then the expression (rather than the formal system) must be rejected.

I always assess what is actually said rather than reject what is said based
on my opinion of the person saying it, this latter would be ad hominem.

Olcott, [Redacted]

Wittgenstein's critique of Russel's system is bases on Classical logic e.g a setting where excluded middle holds.
Godel's proof of the incompleteness theorem is done in Intuitionistic logic e.g it's done WITHOUT using excluded middle.

Using less axioms makes it a stronger result - irrespective of what Wittgenstein says.

[Redacted]
https://www.jamesrmeyer.com/ffgit/intuitionism.php

If we are to reject expressions which cannot be resolved to true or false then we have to reject ALL open problem in Mathematics.

[Redacted


[Edited by iMod]

[PeteOlcott]

The same nitwit that honestly believes that
FALSE <proves> Donald Trump is the Christ

also believes that expressions of language with currently unknown truth values
(conjectures in math) are IMPOSSIBLE TO RESOLVE TO TRUE OR FALSE.

[Agent Smith]

We all seem (so) lost. The wilderness of ideas is a dangerous place. I'm sure there's a parallel we can all relate to. If only we could find it. A certain European philosopher got it right when he said philosophy merely replaces and without much to show for it.