A proof of G in F

[PeteOlcott]

"You are confusing the semantics of formal languages with what we call "meaning" in natural languages. They aren't even remotely related."

Every formal/natural language semantics/meaning is nothing more than relations between objects of thought.

I am not confusing anything at all
but, you are never going to get it because your want to make sure that you never get it, rebuttal is your WHOLE point.

[Skepdick]

"You are confusing the semantics of formal languages with what we call "meaning" in natural languages. They aren't even remotely related."

Every formal/natural language semantics/meaning is nothing more than relations between objects of thought.

I am not confusing anything at all
but, you are never going to get it because your want to make sure that you never get it, rebuttal is your WHOLE point.

Well, I guess I can't help you.

Garbage in - Garbage out.

[PeteOlcott]

The foundation of all correct reasoning
My own system of correct reasoning refutes Tarski and Gödel
(by extending the notion of a syllogism)

Semantic Necessity operator: ⊨□

(a) Some expressions of language L are stipulated to have the semantic property of Boolean true.
(b) Some expressions of language L are a semantically necessary consequence of others.

T is a subset of (a)
True(L,X) means X ∈ (a) or T ⊨□ X
False(L,X) means T ⊨□ ~X

[Skepdick]

The foundation of all correct reasoning

THE foundation? Lol.

You still haven't accepted Logical pluralism into your heart?

Shame. Spend some time trying to understand this video.

[Agent Smith]

"In 1930 ... blah, blah, blah, ... and hence, incom ... incon ... Thank you, and now the floor is open for comments/questions/etc. "

"What on earth was all that about?"

"Kurt Gödel's incompleteness theorems. Were you sleeping this whole time?"

(Yawn) "I don't know, was I? Did he say "etc."?"

"No idea, I think he did, why?"

"Feels important somehow."

"Why? What do you mean?"

"Just a feeling. You should know better than to ask silly questions like that."

"What's so silly about it? You made a claim. I want you to back it up! Is it too much to ask to be reasonable?"

"You know how many times I've been wrong, don't you? Silly Billy!"

[PeteOlcott]

The foundation of all correct reasoning

THE foundation? Lol.

You still haven't accepted Logical pluralism into your heart?

Shame. Spend some time trying to understand this video.

There can be many different logics.
There cannot be any principle of explosion.
A consistent and correct True(L,X) can always be defined.
The conventional mathematical notion of Incomplete cannot occur because
Self-contradictory expressions do not evaluate to TRUE or FALSE and are excluded.

[Skepdick]

There can be many different logics.
There cannot be any principle of explosion.
A consistent and correct True(L,X) can always be defined.
The conventional mathematical notion of Incomplete cannot occur because
Self-contradictory expressions do not evaluate to TRUE or FALSE and are excluded.

You seem to be conflating the inconsistency and explosiveness properties of a system for some reason.

A system can be inconsistent AND non-explosive, you know.

https://en.wikipedia.org/wiki/Paraconsistent_logic

The test of a first-rate intelligence is the ability to hold two opposing ideas in mind at the same time and still retain the ability to function -- F. Scott Fitzgerald

[PeteOlcott]

The foundation of all correct reasoning
Gets rid of all of the errors of other logic systems.

[Skepdick]

T̶h̶e̶ A foundation of a̶l̶l̶ ̶c̶o̶r̶r̶e̶c̶t̶ some reasoning
Gets rid of all of the errors of other logic systems.

Got rid of some more errors for you.

[PeteOlcott]

T̶h̶e̶ A foundation of a̶l̶l̶ ̶c̶o̶r̶r̶e̶c̶t̶ some reasoning
Gets rid of all of the errors of other logic systems.

Got rid of some more errors for you.

The architecture of my system is infallible.
Anything that diverges from its foundation is incorrect reasoning.

Self-contradictory expressions are simply rejected as non-truth bearers
instead of establishing that a formal system is incomplete.

Gödel hid the fact that his G is only unprovable in F because it
is self-contradictory in F behind his Gödel numbers.

F ⊢ GF ↔ ¬ProvF (┌GF┐).
https://plato.stanford.edu/entries/goed ... rIncTheCom

When we simply strip away the reference to Gödel numbers thus requiring
F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).

When we convert to more standard notational conventions an add an
existential quantifier: ∃G ∈ F (G ↔ ¬(F ⊢ G))
There exists a G in F such that G is logically equivalent to its own unprovability in F.

∃G ∈ F (G ↔ ¬(F ⊢ G))
F---------T--F--F---T
F---------F--F--T---F
There exists no such G in F.

[Skepdick]

T̶h̶e̶ A foundation of a̶l̶l̶ ̶c̶o̶r̶r̶e̶c̶t̶ some reasoning
Gets rid of all of the errors of other logic systems.

Got rid of some more errors for you.

The architecture of my system is infallible.
Anything that diverges from its foundation is incorrect reasoning.

Self-contradictory expressions are simply rejected as non-truth bearers
instead of establishing that a formal system is incomplete.

Gödel hid the fact that his G is only unprovable in F because it
is self-contradictory in F behind his Gödel numbers.

F ⊢ GF ↔ ¬ProvF (┌GF┐).
https://plato.stanford.edu/entries/goed ... rIncTheCom

When we simply strip away the reference to Gödel numbers thus requiring
F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).

When we convert to more standard notational conventions an add an
existential quantifier: ∃G ∈ F (G ↔ ¬(F ⊢ G))
There exists a G in F such that G is logically equivalent to its own unprovability in F.

∃G ∈ F (G ↔ ¬(F ⊢ G))
F---------T--F--F---T
F---------F--F--T---F
There exists no such G in F.

I reject your system.

[PeteOlcott]

"I reject your system."

I soundly reject your rejection as baseless dogma.
The fact that you did not and cannot show any error
because there is no error rejects every rejection in advance.

My own system of correct reasoning refutes Tarski and Gödel
(by extending the notion of a syllogism)

Semantic Necessity operator: ⊨□
(a) Some expressions of language L are stipulated to have the semantic property of Boolean true.
(b) Some expressions of language L are a semantically necessary consequence of others.

T is a subset of (a)
True(L,X) means X ∈ (a) or T ⊨□ X
False(L,X) means T ⊨□ ~X

This is simply the way that analytic truth really works.

[Skepdick]

"I reject your system."

I soundly reject your rejection as baseless dogma.
The fact that you did not and cannot show any error
because there is no error rejects every rejection in advance.

My own system of correct reasoning refutes Tarski and Gödel
(by extending the notion of a syllogism)

Semantic Necessity operator: ⊨□
(a) Some expressions of language L are stipulated to have the semantic property of Boolean true.
(b) Some expressions of language L are a semantically necessary consequence of others.

T is a subset of (a)
True(L,X) means X ∈ (a) or T ⊨□ X
False(L,X) means T ⊨□ ~X

This is simply the way that analytic truth really works.

I reject your rejection of my rejection.

Your "foundation" is unfounded and lacks a community of people interested in developing it.
You are the only one who uses it and your thinking it still in contest with people who mattered a century ago, so I'd rather stick with something more contemporary and well developed

Good luck to you.

[PeteOlcott]

"I reject your rejection of my rejection."
Since you reject it on the basis that this brand new system is
not currently very popular your basis is void.

To reject it on a legitimate basis requires finding an actual error
and no one can do that because there is no error.

[Skepdick]

"I reject your rejection of my rejection."
Since you reject it on the basis that this brand new system is
not currently very popular your basis is void.

To reject it on a legitimate basis requires finding an actual error
and no one can do that because there is no error.

Which part of this English sentence went over your head?

Your "foundation" is unfounded

I reject your system on the basis that it has no basis.

If you want me, or anyone to find an "error" in your system then you have to define the semantics of the Error() predicate.
How else could I possibly check that Error ∈ (a) ?!?

Otherwise ... what the hell do you mean by "error" ?!?