G asserts its own unprovability in F

[PeteOlcott]

If we take the simplest possible essence of Gödel's logic sentence we have:
G asserts its own unprovability in F. This means that G is asserting
that there is no sequence of inference steps in F that derives G.

For G to be proved in F requires a sequence of
inference steps in F that proves there is no such
sequence of inference steps in F.

This is like René Descartes saying: “I think therefore thoughts do not exist”

Gödel knew about this contradiction:

..."there is also a close relationship with the “liar” antinomy,14" (Gödel 1931:39-41)

"14 Every epistemological antinomy can likewise be used for a similar
undecidability proof."(Gödel 1931:39-41)

So we can see from the above that it is true that G is unprovable in F, yet
without arithmetization and diagonalization or meta_F hiding the reason
why G is unprovable in F we can see that G is unprovable in F because G
is self-contradictory in F, not because F is in anyway incomplete.

Gödel sums up the essence of his own proof as:
"We are therefore confronted with a proposition which asserts its own
unprovability." (Gödel 1931:39-41)

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

[Agent Smith]

"There are 8 people in the room Watson," Sherlock Holmes was speaking to Dr. Watson. "Holmes, I know your method. Of course there are 8, look 8 pairs of shoes, one's sandals, but that doesn't affect the inference," Dr. Watson was absolutely sure. Sherlock Holmes looked at Watson and said, "Magnifique Watson! Magnifique! However, that's not it! Look at the sparrows Watson, the sparrows ... outside on the branches of the tree."

[PeteOlcott]

"There are 8 people in the room Watson," Sherlock Holmes was speaking to Dr. Watson. "Holmes, I know your method. Of course there are 8, look 8 pairs of shoes, one's sandals, but that doesn't affect the inference," Dr. Watson was absolutely sure. Sherlock Holmes looked at Watson and said, "Magnifique Watson! Magnifique! However, that's not it! Look at the sparrows Watson, the sparrows ... outside on the branches of the tree."

People on Stack Exchange seem to think that you are capable of more than this nonsense.

[Agent Smith]

"There are 8 people in the room Watson," Sherlock Holmes was speaking to Dr. Watson. "Holmes, I know your method. Of course there are 8, look 8 pairs of shoes, one's sandals, but that doesn't affect the inference," Dr. Watson was absolutely sure. Sherlock Holmes looked at Watson and said, "Magnifique Watson! Magnifique! However, that's not it! Look at the sparrows Watson, the sparrows ... outside on the branches of the tree."

People on Stack Exchange seem to think that you are capable of more than this nonsense.

You'll havta cut me some slack. Not exactly my best day or month or year. G (the Gödel sentence, the main protagonist in this tale of twisted logic) is an assertion. What does it assert?

[PeteOlcott]

"There are 8 people in the room Watson," Sherlock Holmes was speaking to Dr. Watson. "Holmes, I know your method. Of course there are 8, look 8 pairs of shoes, one's sandals, but that doesn't affect the inference," Dr. Watson was absolutely sure. Sherlock Holmes looked at Watson and said, "Magnifique Watson! Magnifique! However, that's not it! Look at the sparrows Watson, the sparrows ... outside on the branches of the tree."

People on Stack Exchange seem to think that you are capable of more than this nonsense.

You'll havta cut me some slack. Not exactly my best day or month or year. G (the Gödel sentence, the main protagonist in this tale of twisted logic) is an assertion. What does it assert?

G asserts that it cannot be proven.
This is analogous to the Liar Paradox.

A formal proof is simply a set of inference steps. (the simplest kind of formal proof)
https://en.wikipedia.org/wiki/Syllogism#Basic_structure

Major premise: All humans are mortal.
Minor premise: All Greeks are humans.
Conclusion: All Greeks are mortal.
The first two steps prove that the conclusion is true.

G asserts that there is a sequence of steps that proves
that there is no such sequence of steps. (a contradiction)
This tiny little insight overturns 92 years of math.
It has taken me 19 years to boil it down to that.

[Age]

People on Stack Exchange seem to think that you are capable of more than this nonsense.

You'll havta cut me some slack. Not exactly my best day or month or year. G (the Gödel sentence, the main protagonist in this tale of twisted logic) is an assertion. What does it assert?

G asserts that it cannot be proven.
This is analogous to the Liar Paradox.

A formal proof is simply a set of inference steps. (the simplest kind of formal proof)
https://en.wikipedia.org/wiki/Syllogism#Basic_structure

Major premise: All humans are mortal.
Minor premise: All Greeks are humans.
Conclusion: All Greeks are mortal.
The first two steps prove that the conclusion is true.

G asserts that there is a sequence of steps that proves
that there is no such sequence of steps. (a contradiction)
This tiny little insight overturns 92 years of math.
It has taken me 19 years to boil it down to that.

But to WORK OUT if the above 'major premise' is ACTUALLY True, ACTUAL CLARIFICATION to the QUESTION who and/or what are 'humans', EXACTLY, IS NEEDED, FIRSTLY. JUst like ACTUAL CLARIFICATION IS NEEDED as to what IS 'G', EXACTLY, FIRST, BEFORE we could ASCERTAIN that what 'G' 'asserts' is even ACTUALLY True or NOT.

Also, what you CLAIM is 'tiny little insight' looks, at first appearances anyway, like a Truly ABSURD view and perspective to have and maintain. BUT, we do AWAIT CLARITY, FIRST.

[PeteOlcott]

G asserts that it cannot be proven.
This is analogous to the Liar Paradox.

A formal proof is simply a set of inference steps. (the simplest kind of formal proof)
https://en.wikipedia.org/wiki/Syllogism#Basic_structure

Major premise: All humans are mortal.
Minor premise: All Greeks are humans.
Conclusion: All Greeks are mortal.
The first two steps prove that the conclusion is true.

G asserts that there is a sequence of steps that proves
that there is no such sequence of steps. (a contradiction)
This tiny little insight overturns 92 years of math.
It has taken me 19 years to boil it down to that.

But to WORK OUT if the above 'major premise' is ACTUALLY True, ACTUAL CLARIFICATION to the QUESTION who and/or what are 'humans', EXACTLY, IS NEEDED, FIRSTLY. JUst like ACTUAL CLARIFICATION IS NEEDED as to what IS 'G', EXACTLY, FIRST, BEFORE we could ASCERTAIN that what 'G' 'asserts' is even ACTUALLY True or NOT.

Also, what you CLAIM is 'tiny little insight' looks, at first appearances anyway, like a Truly ABSURD view and perspective to have and maintain. BUT, we do AWAIT CLARITY, FIRST.

Major premise: All X are Y. // X ⊆ Y
Minor premise: All Z are X. // Z ⊆ X
Conclusion: All Z are Y. // ∴ Z ⊆ X

Gödel sums up his own G as:
...a proposition which asserts its own unprovability. 15 (Gödel 1931:39-41)

G is an expression of language that asserts there are no inference steps that derive G.
To prove G requires a sequence of inference steps that prove that there is no such sequence of steps.

That this is absurd is the whole point. No one ever noticed this before because
Gödel hid this absurdity behind a bunch of enormously complicated math steps
called arithmetization and diagonalization.

Gödel's proof was supposed to show that every system used to perform this proof
had something missing so he called this his incompleteness theorem, as if formal
systems are supposed to be able to prove gibberish.

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

[Age]

G asserts that it cannot be proven.
This is analogous to the Liar Paradox.

A formal proof is simply a set of inference steps. (the simplest kind of formal proof)
https://en.wikipedia.org/wiki/Syllogism#Basic_structure

Major premise: All humans are mortal.
Minor premise: All Greeks are humans.
Conclusion: All Greeks are mortal.
The first two steps prove that the conclusion is true.

G asserts that there is a sequence of steps that proves
that there is no such sequence of steps. (a contradiction)
This tiny little insight overturns 92 years of math.
It has taken me 19 years to boil it down to that.

But to WORK OUT if the above 'major premise' is ACTUALLY True, ACTUAL CLARIFICATION to the QUESTION who and/or what are 'humans', EXACTLY, IS NEEDED, FIRSTLY. JUst like ACTUAL CLARIFICATION IS NEEDED as to what IS 'G', EXACTLY, FIRST, BEFORE we could ASCERTAIN that what 'G' 'asserts' is even ACTUALLY True or NOT.

Also, what you CLAIM is 'tiny little insight' looks, at first appearances anyway, like a Truly ABSURD view and perspective to have and maintain. BUT, we do AWAIT CLARITY, FIRST.

Major premise: All X are Y. // X ⊆ Y
Minor premise: All Z are X. // Z ⊆ X
Conclusion: All Z are Y. // ∴ Z ⊆ X

Gödel sums up his own G as:
...a proposition which asserts its own unprovability. 15 (Gödel 1931:39-41)

G is an expression of language that asserts there are no inference steps that derive G.
To prove G requires a sequence of inference steps that prove that there is no such sequence of steps.

That this is absurd is the whole point. No one ever noticed this before because
Gödel hid this absurdity behind a bunch of enormously complicated math steps
called arithmetization and diagonalization.

But I NOTICED and could SEE that 'it' WAS Truly ABSURD, on FIRST SiGHT of 'it'.

Gödel's proof was supposed to show that every system used to perform this proof
had something missing so he called this his incompleteness theorem, as if formal
systems are supposed to be able to prove gibberish.

There was a fair bit of 'GIBBERISH' spoken, and written, back in the days when this was being written, in relation to 'gibberish', itself.

[PeteOlcott]

But to WORK OUT if the above 'major premise' is ACTUALLY True, ACTUAL CLARIFICATION to the QUESTION who and/or what are 'humans', EXACTLY, IS NEEDED, FIRSTLY. JUst like ACTUAL CLARIFICATION IS NEEDED as to what IS 'G', EXACTLY, FIRST, BEFORE we could ASCERTAIN that what 'G' 'asserts' is even ACTUALLY True or NOT.

Also, what you CLAIM is 'tiny little insight' looks, at first appearances anyway, like a Truly ABSURD view and perspective to have and maintain. BUT, we do AWAIT CLARITY, FIRST.

Major premise: All X are Y. // X ⊆ Y
Minor premise: All Z are X. // Z ⊆ X
Conclusion: All Z are Y. // ∴ Z ⊆ X

Gödel sums up his own G as:
...a proposition which asserts its own unprovability. 15 (Gödel 1931:39-41)

G is an expression of language that asserts there are no inference steps that derive G.
To prove G requires a sequence of inference steps that prove that there is no such sequence of steps.

That this is absurd is the whole point. No one ever noticed this before because
Gödel hid this absurdity behind a bunch of enormously complicated math steps
called arithmetization and diagonalization.

But I NOTICED and could SEE that 'it' WAS Truly ABSURD, on FIRST SiGHT of 'it'.

Gödel's proof was supposed to show that every system used to perform this proof
had something missing so he called this his incompleteness theorem, as if formal
systems are supposed to be able to prove gibberish.

There was a fair bit of 'GIBBERISH' spoken, and written, back in the days when this was being written, in relation to 'gibberish', itself.

So it seems that you agree with me.
It seems that many people had an intuition that Gödel was wrong.

The problem with math people is that they truly believe that rote
memorization of a complex bunch of details provides actual understanding.

Philosophy of math requires understanding how things fit together coherently.
Math people make sure to always ignore this, they take the gospel of math as
a given and anything that goes against it as nonsense.

[Age]

Major premise: All X are Y. // X ⊆ Y
Minor premise: All Z are X. // Z ⊆ X
Conclusion: All Z are Y. // ∴ Z ⊆ X

Gödel sums up his own G as:
...a proposition which asserts its own unprovability. 15 (Gödel 1931:39-41)

G is an expression of language that asserts there are no inference steps that derive G.
To prove G requires a sequence of inference steps that prove that there is no such sequence of steps.

That this is absurd is the whole point. No one ever noticed this before because
Gödel hid this absurdity behind a bunch of enormously complicated math steps
called arithmetization and diagonalization.

But I NOTICED and could SEE that 'it' WAS Truly ABSURD, on FIRST SiGHT of 'it'.

Gödel's proof was supposed to show that every system used to perform this proof
had something missing so he called this his incompleteness theorem, as if formal
systems are supposed to be able to prove gibberish.

There was a fair bit of 'GIBBERISH' spoken, and written, back in the days when this was being written, in relation to 'gibberish', itself.

So it seems that you agree with me.
It seems that many people had an intuition that Gödel was wrong.

The problem with math people is that they truly believe that rote
memorization of a complex bunch of details provides actual understanding.

'Maths' it could be said and argued is just the use of, memories, 'symbols' that, literally, do NOT spell out what is being referred to, EXACTLY.

'Actual understanding' only arises, comes about, obtained, and/or gained, WHEN one KNOWS, absolutely or fully, WHAT EXACTLY is being talked ABOUT, or REFERRENCED.

For example, '1 + 1 = 2', is NOT 'actually NOR fully understood'. If I was to put those symbols to ANY one who han NOT seen them before, then they, literally, mean absolutely NOTHING AT ALL.

Now for those who have somewhat LEARNED the "english" language those 'symbols' 'actual mean', and thus understood as, ' one 'thing' plus one more 'thing' or another 'thing' equalls two 'things' '.

BUT, to FULLY or ABSOLUTELY UNDERSTAND one has to FIRST LEAEN or KNOW WHAT the 'things' ARE, EXACTLY.

And, to do this PROPERLY and ACCURATELY is through CLARIFICATION and by obtaining CLARITY. As I have SHOWN examples of HOW TO DO throughout this forum.

Philosophy of math requires understanding how things fit together coherently.

But ONLY through the ACTUAL UNDERSTANDING OF 'things' can we FINALLY SEE HOW ALL 'things' FIT TOGETHER, PERFECTLY, and this is done by FINDING OUT what 'it' IS, EXACTLY, which is being talked ABOUT and/or REFERRED TO, FIRSTLY. Or, in other words, literally 'fit together', COHERENTLY.

Math people make sure to always ignore this, they take the gospel of math as
a given and anything that goes against it as nonsense.

WHAT (math) 'symbols' are REFERRING TO, EXACTLY, HAS TO BE KNOWN FIRST, to ASCERTAIN NONSENSE or NOT. For example, one (orange) plus one (apple) does NOT equal two (potatoes). Although a so-called "mathematician" might 'try' and tell you otherwise, BECAUSE 1 + 1 (does) = 2. Right?

As can be SEEN here, what 'symbols' are REFERRING TO HAS TO BE KNOWN, FIRST, for ACTUAL UNDERSTANDING to be ASCERTAINED, OBTAINED, GAINED. And, even the 'symbols' of 'letters' HAVE TO BE UNDERSTOOD, FULLY, to WORK OUT the ABSURD from the SENSIBLE. And the ONLY WAY to do this PROPERLY and FULLY is to FIRST OBTAIN and GAIN ACTUAL CLARITY, BEFOREHAND. Which is, AGAIN, done by JUST SEEKING OUT and OBTAINING CLARIFICATION, and UNDERSTANDING, of what 'it' IS, EXACTLY, one is talking ABOUT or REFERREING TO.

[Agent Smith]

People on Stack Exchange seem to think that you are capable of more than this nonsense.

You'll havta cut me some slack. Not exactly my best day or month or year. G (the Gödel sentence, the main protagonist in this tale of twisted logic) is an assertion. What does it assert?

G asserts that it cannot be proven.
This is analogous to the Liar Paradox.

A formal proof is simply a set of inference steps. (the simplest kind of formal proof)
https://en.wikipedia.org/wiki/Syllogism#Basic_structure

Major premise: All humans are mortal.
Minor premise: All Greeks are humans.
Conclusion: All Greeks are mortal.
The first two steps prove that the conclusion is true.

G asserts that there is a sequence of steps that proves
that there is no such sequence of steps. (a contradiction)
This tiny little insight overturns 92 years of math.
It has taken me 19 years to boil it down to that.

Thanks for the logic lesson.

E = God exists
The Gödel sentence G = ?

[Skepdick]

If we take the simplest possible essence of Gödel's logic sentence we have:
G asserts its own unprovability in F. This means that G is asserting
that there is no sequence of inference steps in F that derives G [something's missing here]

Yes, that's what it means. But you are missing somethign at the end.

Your statement (and understanding) is incomplete! And Gödel sure understood incompleteness.

The part that's mising is: "from other elements in F".

e.g G exists in F, but it is not connected to anything else in F.
G exists and G is not provable in F are both true.

For G to be proved in F requires a sequence of
inference steps in F that proves there is no such
sequence of inference steps in F.

This is like René Descartes saying: “I think therefore thoughts do not exist”

Why are you conflating Provable(G) with Exists(G) ?

Time to learn the difference between connected and disconnected spaces.

https://en.wikipedia.org/wiki/Totally_d ... cted_space

[PeteOlcott]

You'll havta cut me some slack. Not exactly my best day or month or year. G (the Gödel sentence, the main protagonist in this tale of twisted logic) is an assertion. What does it assert?

G asserts that it cannot be proven.
This is analogous to the Liar Paradox.

A formal proof is simply a set of inference steps. (the simplest kind of formal proof)
https://en.wikipedia.org/wiki/Syllogism#Basic_structure

Major premise: All humans are mortal.
Minor premise: All Greeks are humans.
Conclusion: All Greeks are mortal.
The first two steps prove that the conclusion is true.

G asserts that there is a sequence of steps that proves
that there is no such sequence of steps. (a contradiction)
This tiny little insight overturns 92 years of math.
It has taken me 19 years to boil it down to that.

Thanks for the logic lesson.

E = God exists
The Gödel sentence G = ?

Although this seems difficult
G = There is no sequence of inference steps in F that proves there is no such sequence of inference steps in F.

Compared to Gödel's arithmetization and diagonalization (that takes dozens of pages) the above expression is simple.

[Skepdick]

Although this seems difficult
G = There is no sequence of inference steps in F that proves there is no such sequence of inference steps in F.

Compared to Gödel's arithmetization and diagonalization (that takes dozens of pages) the above expression is simple.

What sequence of steps do you expect to prove that no paths lead to G when it's true that no paths lead to G?

A->B->C->D G

[Agent Smith]

G asserts that it cannot be proven.
This is analogous to the Liar Paradox.

A formal proof is simply a set of inference steps. (the simplest kind of formal proof)
https://en.wikipedia.org/wiki/Syllogism#Basic_structure

Major premise: All humans are mortal.
Minor premise: All Greeks are humans.
Conclusion: All Greeks are mortal.
The first two steps prove that the conclusion is true.

G asserts that there is a sequence of steps that proves
that there is no such sequence of steps. (a contradiction)
This tiny little insight overturns 92 years of math.
It has taken me 19 years to boil it down to that.

Thanks for the logic lesson.

E = God exists
The Gödel sentence G = ?

Although this seems difficult
G = There is no sequence of inference steps in F that proves there is no such sequence of inference steps in F.

Compared to Gödel's arithmetization and diagonalization (that takes dozens of pages) the above expression is simple.

Ok!