G asserts its own unprovability in 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.

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.

None-the-less the proof of G in F does require a sequence of inference steps in F that proves that no such sequence exists in F.

Gödel knew this so he proved G in Meta-F

[Skepdick]

None-the-less the proof of G in F does require a sequence of inference steps in F that proves that no such sequence exists in F.

"The proof of G in F" is a meaningless phrase.

What is it that you are trying to prove about G (in F)?

[PeteOlcott]

None-the-less the proof of G in F does require a sequence of inference steps in F that proves that no such sequence exists in F.

"The proof of G in F" is a meaningless statement.

Which property of G (in F) are you proving?

When G asserts that it is unprovable in F it is asserting
that there is no sequence of inference steps in F that derives G.

The reason why G is unprovable in F is that a proof of G in F:
(1) Requires a sequence of inference steps (as all proof do) in F.
(2) These same inference steps in F must prove that they themselves do not exist in F.

A thing cannot prove that itself doesn't exist.
So Gödel proves G in Meta-F where G is not contradictory.

Tarski made the same mistake:
This sentence is not true: "This sentence is not true"
The inner sentence is in his theory and the outer sentence is in his meta-theory.

He concluded that because he could not prove that the inner sentence is true
in his theory yet could prove that the outer sentence is true in his meta-theory
That some true statements cannot be defined in a single theory and must rely
on an infinite hierarchy of meta-theories.

He never noticed that the inner sentence is simply not a truth bearer.

[Skepdick]

None-the-less the proof of G in F does require a sequence of inference steps in F that proves that no such sequence exists in F.

"The proof of G in F" is a meaningless statement.

Which property of G (in F) are you proving?

<BLAH BLAH BLAH>

Answer the question, [Redacted]

Given the English sentence "I am not provable". What are you trying to prove about that sentence?



[Edited by iMod]

[PeteOlcott]

"The proof of G in F" is a meaningless statement.

Which property of G (in F) are you proving?

<BLAH BLAH BLAH>

Answer the question, [Redacted].

Given the English sentence "I am not provable". What are you trying to prove about that sentence?

I am not going to reply to you ever again until after you apologize.

[Skepdick]

<BLAH BLAH BLAH>

Answer the question, [Redacted]

Given the English sentence "I am not provable". What are you trying to prove about that sentence?

I am not going to reply to you ever again until after you apologize.

Oh no!

So far you've lied every single time you've made that promise.

[Agent Smith]

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.

Awesome!

G isn't what in the lay world is called a "random, isolated, incident". Take it from there. Note here though that I haven't, I can't, unlike you, invent(ed) a formal system that, sensu latissimo, defeats G.

[PeteOlcott]

Awesome!

G isn't what in the lay world is called a "random, isolated, incident". Take it from there. Note here though that I haven't, I can't, unlike you, invent(ed) a formal system that, sensu latissimo, defeats G.

Gödel's proof relies upon a definition of incompleteness that
requires formal systems to be able to prove self-contradictory
expressions of language, as indicated by his statement:

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

The standard definition of incompleteness:
A theory T is incomplete if and only if there is some sentence φ such that (T ⊬ φ) and (T ⊬ ¬φ).

Does it make sense that formal systems are required to prove
epistemological antinomies (AKA self-contradictory expressions)
or should these expressions be rejected as non sequitur?

The valid/sound deductive inference model seems to think that latter:
∀F ∈ Formal_Systems ∀C ∈ WFF(F) ((F ⊢ C) ↔ True(F, C))
∀F ∈ Formal_Systems ∀C ∈ WFF(F) ((F ⊢ ¬C) ↔ False(F, C))
∀F ∈ Formal_Systems ∀C ∈ WFF(F) (((F ⊬ C) ∧ (F ⊬ ¬C)) ↔ NonSequitur(F, C))

Non Sequitur (https://en.wikipedia.org/wiki/Formal_fallacy)
In philosophy, a formal fallacy, deductive fallacy, logical fallacy or non sequitur[1] (Latin for "it does not follow")

By simply disallowing symbolic logic to diverge from the valid/sound deductive
inference model Gödel Incompleteness and Tarski Undefinability cease to exist.

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

[Skepdick]

Gödel's proof relies upon a definition of incompleteness that requires formal systems
to be able to prove self-contradictory expressions of language.

No it doesn't. Stop lying you [redacted}

The standard definition of incompleteness:
A theory T is incomplete if and only if there is some sentence φ such that (T ⊬ φ) and (T ⊬ ¬φ).

(T ⊬ φ) and (T ⊬ ¬φ) is not a contradiction. Because you can't prove the statement or its negation.
(T ⊢ φ) and (T ⊢ ¬φ) is a contradiction. Because you can prove the statement and its negation.

[redacted}


[Edited by iMod}

[Agent Smith]

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.

Awesome!

G isn't what in the lay world is called a "random, isolated, incident". Take it from there. Note here though that I haven't, I can't, unlike you, invent(ed) a formal system that, sensu latissimo, defeats G.

As I regretfully informed you, the level of discussion - formal symbolic logic - is beyond me ken. Upon reexamining Gödel's argument, I'm forced retract my earlier claim that there's something off about Gödel's argument. What was I thinking? That a genius could make a silly boo boo like the one I thought he made? The audacity!!

Nevertheless, what I do wish to impress upon you and others who're interested is that we may not need to go so far as to reel in symbolic logic to show that Gödel could be wrong.

[PeteOlcott]

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.

Awesome!

G isn't what in the lay world is called a "random, isolated, incident". Take it from there. Note here though that I haven't, I can't, unlike you, invent(ed) a formal system that, sensu latissimo, defeats G.

As I regretfully informed you, the level of discussion - formal symbolic logic - is beyond me ken. Upon reexamining Gödel's argument, I'm forced retract my earlier claim that there's something off about Gödel's argument. What was I thinking? That a genius could make a silly boo boo like the one I thought he made? The audacity!!

Nevertheless, what I do wish to impress upon you and others who're interested is that we may not need to go so far as to reel in symbolic logic to show that Gödel could be wrong.

The key error of his proof is that he assumes the standard definition
of incompleteness that determines that formal systems are required
to prove contradictory statements rather than reject them as erroneous.

You can probably understand that doesn't make sense can't you?

[Agent Smith]

Awesome!

G isn't what in the lay world is called a "random, isolated, incident". Take it from there. Note here though that I haven't, I can't, unlike you, invent(ed) a formal system that, sensu latissimo, defeats G.

As I regretfully informed you, the level of discussion - formal symbolic logic - is beyond me ken. Upon reexamining Gödel's argument, I'm forced retract my earlier claim that there's something off about Gödel's argument. What was I thinking? That a genius could make a silly boo boo like the one I thought he made? The audacity!!

Nevertheless, what I do wish to impress upon you and others who're interested is that we may not need to go so far as to reel in symbolic logic to show that Gödel could be wrong.

The key error of his proof is that he assumes the standard definition
of incompleteness that determines that formal systems are required
to prove contradictory statements rather than reject them as erroneous.

You can probably understand that doesn't make sense can't you?

From what I, as an eternal noob, can gather, Kurt Gödel was a great thinker. Cognition at his level is as natural as breathing. We must think about that before offering any criticism.

[PeteOlcott]

As I regretfully informed you, the level of discussion - formal symbolic logic - is beyond me ken. Upon reexamining Gödel's argument, I'm forced retract my earlier claim that there's something off about Gödel's argument. What was I thinking? That a genius could make a silly boo boo like the one I thought he made? The audacity!!

Nevertheless, what I do wish to impress upon you and others who're interested is that we may not need to go so far as to reel in symbolic logic to show that Gödel could be wrong.

The key error of his proof is that he assumes the standard definition
of incompleteness that determines that formal systems are required
to prove contradictory statements rather than reject them as erroneous.

You can probably understand that doesn't make sense can't you?

From what I, as an eternal noob, can gather, Kurt Gödel was a great thinker. Cognition at his level is as natural as breathing. We must think about that before offering any criticism.

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

[Agent Smith]

The key error of his proof is that he assumes the standard definition
of incompleteness that determines that formal systems are required
to prove contradictory statements rather than reject them as erroneous.

You can probably understand that doesn't make sense can't you?

From what I, as an eternal noob, can gather, Kurt Gödel was a great thinker. Cognition at his level is as natural as breathing. We must think about that before offering any criticism.

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?

[PeteOlcott]

From what I, as an eternal noob, can gather, Kurt Gödel was a great thinker. Cognition at his level is as natural as breathing. We must think about that before offering any criticism.

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.