G asserts its own unprovability in F

[Agent Smith]

I spent 10,000 hours on this since 2004, do you think that it enough?

It is clear that the basis of his incompleteness proof
is that formal systems cannot prove self contradictory
expressions. He admits that he does this right here:

14 Every epistemological antinomy can likewise be used for a similar undecidability proof.
END:(Gödel 1931:40)

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

Antinomy
...term often used in logic and epistemology, when describing a paradox or unresolvable contradiction. https://www.newworldencyclopedia.org/entry/Antinomy

First off, I don't get why your thread is not registering more hits than it deserves. Skepdick, the only other guy, seems unimpressed and that's putting it mildly.

Secondum, please read what I wrote closely - my take on Gödel should've crossed over to your side despite my karmic delusions that permits of only vague pics of reality whatever that is.

Thirdum, Gödel, in a manner of speaking, stopped ... eating?

Skepdick chose his name on the basis that obnoxiousness rather than
honest dialogue is his intention.

Secondum I thought that I did read it closely.

Third Yes Gödel was a little nutty towards the end and starved himself to death.

Later in his life, Gödel suffered periods of mental instability and illness. Following the assassination of his close friend Moritz Schlick,[34] Gödel developed an obsessive fear of being poisoned, and would eat only food prepared by his wife Adele. Adele was hospitalized beginning in late 1977, and in her absence Gödel refused to eat;[35] he weighed 29 kilograms (65 lb) when he died of "malnutrition and inanition caused by personality disturbance" in Princeton Hospital on January 14, 1978.[36] He was buried in Princeton Cemetery. Adele died in 1981.[37] https://en.wikipedia.org/wiki/Kurt_G%C3 ... _and_death

His fear of being poisoned was somewhat justified his fear of his own cooking was too nutty.

There's something a certain kinda a personality would love to sink his teeth into.

Anyway, Gödel's theorems were vetted by his peers and they gave Gödel the all clear and the rest is history.

What I find odd is no one as in no mathematician seems interested, even in the slightest way, to pick up as it were where the late Gödel left off. Philosophers (of mathematics), au contraire, are a different story.

[PeteOlcott]

There's something a certain kinda a personality would love to sink his teeth into.

Anyway, Gödel's theorems were vetted by his peers and they gave Gödel the all clear and the rest is history.

What I find odd is no one as in no mathematician seems interested, even in the slightest way, to pick up as it were where the late Gödel left off. Philosophers (of mathematics), au contraire, are a different story.

Math people seem to be computer programmed machines that can't think
outside of the box if their soul depended on it.

Philosophers of math such as Wittgenstein totally agree with me.
https://www.liarparadox.org/Wittgenstein.pdf

[Agent Smith]

There's something a certain kinda a personality would love to sink his teeth into.

Anyway, Gödel's theorems were vetted by his peers and they gave Gödel the all clear and the rest is history.

What I find odd is no one as in no mathematician seems interested, even in the slightest way, to pick up as it were where the late Gödel left off. Philosophers (of mathematics), au contraire, are a different story.

Math people seem to be computer programmed machines that can't think
outside of the box if their soul depended on it.

Philosophers of math such as Wittgenstein totally agree with me.
https://www.liarparadox.org/Wittgenstein.pdf

I'm, alas, too uninformed to sensibly comment further, but I will say this: one, Gödel probably didn't err in his reasoning and two, to resort to formal symbolic logic to prove Gödel wrong is, ex mea (humble) sententia, overkill.

[Skepdick]

Math people seem to be computer programmed machines that can't think
outside of the box if their soul depended on it.

Philosophers of math such as Wittgenstein totally agree with me.
https://www.liarparadox.org/Wittgenstein.pdf

Olcott, y[Redacted]

Wittgenstein is talking about Russel's system which is founded upon excluded middle/Classical logic.

True in Russell's system' means, as was said: proved in Russell's system;
'false in Russell's system' means: the opposite has been proved in Russell's system

Thinking outside the box also requires you to think outside of logic's own dogma/axioms.

Gödel work (together with Brouwer's contributions) was the very thing which gave birth to intuitionistic/constructive logic/mathematics e.g the rejection of excluded middle.

And if you are going to reject excluded middle you ALSO have to reject the axiom of choice, because choice implies excluded middle.

https://en.wikipedia.org/wiki/Diaconescu%27s_theorem


[Edited by iMod]

[Agent Smith]

There's something a certain kinda a personality would love to sink his teeth into.

Anyway, Gödel's theorems were vetted by his peers and they gave Gödel the all clear and the rest is history.

What I find odd is no one as in no mathematician seems interested, even in the slightest way, to pick up as it were where the late Gödel left off. Philosophers (of mathematics), au contraire, are a different story.

Math people seem to be computer programmed machines that can't think
outside of the box if their soul depended on it.

Philosophers of math such as Wittgenstein totally agree with me.
https://www.liarparadox.org/Wittgenstein.pdf

Thank you for the linked pdf.

[PeteOlcott]

There's something a certain kinda a personality would love to sink his teeth into.

Anyway, Gödel's theorems were vetted by his peers and they gave Gödel the all clear and the rest is history.

What I find odd is no one as in no mathematician seems interested, even in the slightest way, to pick up as it were where the late Gödel left off. Philosophers (of mathematics), au contraire, are a different story.

Math people seem to be computer programmed machines that can't think
outside of the box if their soul depended on it.

Philosophers of math such as Wittgenstein totally agree with me.
https://www.liarparadox.org/Wittgenstein.pdf

I'm, alas, too uninformed to sensibly comment further, but I will say this: one, Gödel probably didn't err in his reasoning and two, to resort to formal symbolic logic to prove Gödel wrong is, ex mea (humble) sententia, overkill.

In other words you are simply guessing that he is right on the basis that no one proved he is wrong since 1931.

Within Gödel's assumption of the standard definition of incompleteness he is not wrong:
The conventional definition of incompleteness: Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))

The problem is that the standard definition of incompleteness construes a formal system
as "incomplete" on the basis that it cannot prove a contradiction.

...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...
(Gödel 1931:40)

Antinomy
...term often used in logic and epistemology, when describing a paradox or unresolvable contradiction. https://www.newworldencyclopedia.org/entry/Antinomy

Thus showing that Gödel's proof relies on a contradictory expression of language.

Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And Related Systems
https://mavdisk.mnsu.edu/pj2943kt/Fall% ... l-1931.pdf

Contradictions are not truth bearers thus have no Boolean value.
https://en.wikipedia.org/wiki/Truth-bearer

It is obvious to all that the sentence: "What time is it?" is neither true nor false.
It is not so obvious that the sentence: "This sentence is not true" is not a truth bearer.

[Agent Smith]

Math people seem to be computer programmed machines that can't think
outside of the box if their soul depended on it.

Philosophers of math such as Wittgenstein totally agree with me.
https://www.liarparadox.org/Wittgenstein.pdf

I'm, alas, too uninformed to sensibly comment further, but I will say this: one, Gödel probably didn't err in his reasoning and two, to resort to formal symbolic logic to prove Gödel wrong is, ex mea (humble) sententia, overkill.

In other words you are simply guessing that he is right on the basis that no one proved he is wrong since 1931.

Within Gödel's assumption of the standard definition of incompleteness he is not wrong:
The conventional definition of incompleteness: Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))

The problem is that the standard definition of incompleteness construes a formal system
as "incomplete" on the basis that it cannot prove a contradiction.

...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...
(Gödel 1931:40)

Antinomy
...term often used in logic and epistemology, when describing a paradox or unresolvable contradiction. https://www.newworldencyclopedia.org/entry/Antinomy

Thus showing that Gödel's proof relies on a contradictory expression of language.

Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And Related Systems
https://mavdisk.mnsu.edu/pj2943kt/Fall% ... l-1931.pdf

Contradictions are not truth bearers thus have no Boolean value.
https://en.wikipedia.org/wiki/Truth-bearer

It is obvious to all that the sentence: "What time is it?" is neither true nor false.
It is not so obvious that the sentence: "This sentence is not true" is not a truth bearer.

All I'm saying is Gödel's theorems have been examined and reexamined by his equals and his superiors and they've not found any mistakes in the proofs.

Gödel was, the great logician that he was, very clear, like you are too, with regard to the wording of his claims. At his level even commas bear specific logical meaning.

[PeteOlcott]

I'm, alas, too uninformed to sensibly comment further, but I will say this: one, Gödel probably didn't err in his reasoning and two, to resort to formal symbolic logic to prove Gödel wrong is, ex mea (humble) sententia, overkill.

In other words you are simply guessing that he is right on the basis that no one proved he is wrong since 1931.

Within Gödel's assumption of the standard definition of incompleteness he is not wrong:
The conventional definition of incompleteness: Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))

The problem is that the standard definition of incompleteness construes a formal system
as "incomplete" on the basis that it cannot prove a contradiction.

...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...
(Gödel 1931:40)

Antinomy
...term often used in logic and epistemology, when describing a paradox or unresolvable contradiction. https://www.newworldencyclopedia.org/entry/Antinomy

Thus showing that Gödel's proof relies on a contradictory expression of language.

Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And Related Systems
https://mavdisk.mnsu.edu/pj2943kt/Fall% ... l-1931.pdf

Contradictions are not truth bearers thus have no Boolean value.
https://en.wikipedia.org/wiki/Truth-bearer

It is obvious to all that the sentence: "What time is it?" is neither true nor false.
It is not so obvious that the sentence: "This sentence is not true" is not a truth bearer.

All I'm saying is Gödel's theorems have been examined and reexamined by his equals and his superiors and they've not found any mistakes in the proofs.

Gödel was, the great logician that he was, very clear, like you are too, with regard to the wording of his claims. At his level even commas bear specific logical meaning.

There are no mistakes in his proof or in his conclusion within
The conventional definition of incompleteness:
Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))

The entire issue is that the above definition requires formal systems
to do the logically impossible: To prove self-contradictory expressions.

By analogous reasoning one could say that a baker has insufficient
baking skill if they are unable to bake an angel food cake using
conventional red house bricks as the only ingredient.

Mathematicians don't care about whether or not the foundations of
mathematics are coherent or incoherent they only go by the book
and follow the rules.

[Agent Smith]

In other words you are simply guessing that he is right on the basis that no one proved he is wrong since 1931.

Within Gödel's assumption of the standard definition of incompleteness he is not wrong:
The conventional definition of incompleteness: Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))

The problem is that the standard definition of incompleteness construes a formal system
as "incomplete" on the basis that it cannot prove a contradiction.

...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...
(Gödel 1931:40)

Antinomy
...term often used in logic and epistemology, when describing a paradox or unresolvable contradiction. https://www.newworldencyclopedia.org/entry/Antinomy

Thus showing that Gödel's proof relies on a contradictory expression of language.

Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And Related Systems
https://mavdisk.mnsu.edu/pj2943kt/Fall% ... l-1931.pdf

Contradictions are not truth bearers thus have no Boolean value.
https://en.wikipedia.org/wiki/Truth-bearer

It is obvious to all that the sentence: "What time is it?" is neither true nor false.
It is not so obvious that the sentence: "This sentence is not true" is not a truth bearer.

All I'm saying is Gödel's theorems have been examined and reexamined by his equals and his superiors and they've not found any mistakes in the proofs.

Gödel was, the great logician that he was, very clear, like you are too, with regard to the wording of his claims. At his level even commas bear specific logical meaning.

There are no mistakes in his proof or in his conclusion within
The conventional definition of incompleteness:
Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))

The entire issue is that the above definition requires formal systems
to do the logically impossible: To prove self-contradictory expressions.

By analogous reasoning one could say that a baker has insufficient
baking skill if they are unable to bake an angel food cake using
conventional red house bricks as the only ingredient.

Mathematicians don't care about whether or not the foundations of
mathematics are coherent or incoherent they only go by the book
and follow the rules.

I can see where you're coming from. I guess we should dive deeper into formal systems.

My own stance on the topic is that the Gödelian idea has precedents, implicit and vague though that may be, in the 50 - 70 years before him.

[PeteOlcott]

All I'm saying is Gödel's theorems have been examined and reexamined by his equals and his superiors and they've not found any mistakes in the proofs.

Gödel was, the great logician that he was, very clear, like you are too, with regard to the wording of his claims. At his level even commas bear specific logical meaning.

There are no mistakes in his proof or in his conclusion within
The conventional definition of incompleteness:
Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))

The entire issue is that the above definition requires formal systems
to do the logically impossible: To prove self-contradictory expressions.

By analogous reasoning one could say that a baker has insufficient
baking skill if they are unable to bake an angel food cake using
conventional red house bricks as the only ingredient.

Mathematicians don't care about whether or not the foundations of
mathematics are coherent or incoherent they only go by the book
and follow the rules.

I can see where you're coming from. I guess we should dive deeper into formal systems.

My own stance on the topic is that the Gödelian idea has precedents, implicit and vague though that may be, in the 50 - 70 years before him.

I am glad that you can see where I am coming from. This is the
point where math guys resort to ad hominem and start throwing
insults. That is why I quit talking to Skepdick.

Gödel is correct within his false assumptions.
I already defined the foundational architecture of a formal system
that cannot possibly suffer from Gödel incompleteness or Tarski
Undefinability.

If an expression of language of any formal system cannot possibly
resolve to true or false it is rejected as non-sequitur.

[Agent Smith]

There are no mistakes in his proof or in his conclusion within
The conventional definition of incompleteness:
Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))

The entire issue is that the above definition requires formal systems
to do the logically impossible: To prove self-contradictory expressions.

By analogous reasoning one could say that a baker has insufficient
baking skill if they are unable to bake an angel food cake using
conventional red house bricks as the only ingredient.

Mathematicians don't care about whether or not the foundations of
mathematics are coherent or incoherent they only go by the book
and follow the rules.

I can see where you're coming from. I guess we should dive deeper into formal systems.

My own stance on the topic is that the Gödelian idea has precedents, implicit and vague though that may be, in the 50 - 70 years before him.

I am glad that you can see where I am coming from. This is the
point where math guys resort to ad hominem and start throwing
insults. That is why I quit talking to Skepdick.

Gödel is correct within his false assumptions.
I already defined the foundational architecture of a formal system
that cannot possibly suffer from Gödel incompleteness or Tarski
Undefinability.

If an expression of language of any formal system cannot possibly
resolve to true or false it is rejected as non-sequitur.

Gödel's theorems come up a lot in philosophy fora and almost never in math fora.


I'd focus on axiomatic systems and G (the Gödel sentence) and its relation to L (the liar sentence), proofs, the scope of G, ganatishastra (aka math).

[Skepdick]

If an expression of language of any formal system cannot possibly
resolve to true or false it is rejected as non-sequitur.

[Redacted]

G is true.
G is not provable.

[Redacted]


[Edited by iMod]

[PeteOlcott]

I can see where you're coming from. I guess we should dive deeper into formal systems.

My own stance on the topic is that the Gödelian idea has precedents, implicit and vague though that may be, in the 50 - 70 years before him.

I am glad that you can see where I am coming from. This is the
point where math guys resort to ad hominem and start throwing
insults. That is why I quit talking to Skepdick.

Gödel is correct within his false assumptions.
I already defined the foundational architecture of a formal system
that cannot possibly suffer from Gödel incompleteness or Tarski
Undefinability.

If an expression of language of any formal system cannot possibly
resolve to true or false it is rejected as non-sequitur.

Gödel's theorems come up a lot in philosophy fora and almost never in math fora.


I'd focus on axiomatic systems and G (the Gödel sentence) and its relation to L (the liar sentence), proofs, the scope of G, ganatishastra (aka math).

I have written about 18 papers on that.
https://www.researchgate.net/profile/Pl-Olcott/research

Here are the five most recent.
https://www.researchgate.net/publicatio ... l_sentence
https://www.researchgate.net/publicatio ... _Formalism
https://www.researchgate.net/publicatio ... bout_Godel
https://www.researchgate.net/publicatio ... mal_Proofs
https://www.researchgate.net/publicatio ... Refutation

[Agent Smith]

I am glad that you can see where I am coming from. This is the
point where math guys resort to ad hominem and start throwing
insults. That is why I quit talking to Skepdick.

Gödel is correct within his false assumptions.
I already defined the foundational architecture of a formal system
that cannot possibly suffer from Gödel incompleteness or Tarski
Undefinability.

If an expression of language of any formal system cannot possibly
resolve to true or false it is rejected as non-sequitur.

Gödel's theorems come up a lot in philosophy fora and almost never in math fora.


I'd focus on axiomatic systems and G (the Gödel sentence) and its relation to L (the liar sentence), proofs, the scope of G, ganatishastra (aka math).

I have written about 18 papers on that.
https://www.researchgate.net/profile/Pl-Olcott/research

Here are the five most recent.
https://www.researchgate.net/publicatio ... l_sentence
https://www.researchgate.net/publicatio ... _Formalism
https://www.researchgate.net/publicatio ... bout_Godel
https://www.researchgate.net/publicatio ... mal_Proofs
https://www.researchgate.net/publicatio ... Refutation

That's good to hear. It looks like the Gödelian problem is bigger than it's thought to be. There are also specific cases in math (heard it/read it) that kinda clinch the (Gödel's) diagnosis.

From a novice's point of view, there appears to be quite a number of actors in this mathematical play so to speak.

[Skepdick]

I have written about 18 papers on that.
https://www.researchgate.net/profile/Pl-Olcott/research

Write a million - it doesn't matter.

if you keep ignoring all the feedback telling you that you are wrong, your papers are worth less than toilet paper.