Tarski Undefinability Theorem proof’s Error

[PeteOlcott]

The choice of your username seems to indicate the latter.

being a dick
conducting oneself in an inappropriate manner to the annoyance of others.
https://www.urbandictionary.com/define. ... 20a%20Dick

My conduct has nothing to do with the fact that you are wrong, but it sure gives you a convenient excuse to change the subject without acknowledging your error.

Your conduct and choice of user name both indicate that do not want an honest dialogue.
In any case there cannot possibly be any mistake in the way that analytical truth really works:

Introducing the foundation of correct reasoning

Just like with syllogisms conclusions are a semantically necessary consequence of their premises

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.
P is a subset of expressions of language L
T is a subset of (a)

Provable(P,X) means P ⊨□ X // This is the conventional provable not Tarski's that has axioms as premises
True(T,X) means X ∈ (a) or T ⊨□ X // True(X) means X is an axiom or X is derived from axioms
False(T,X) means T ⊨□ ~X // False(X) means ~X is derived from axioms

Copyright 2018-2023 PL Olcott

[Skepdick]

Your conduct and choice of user name both indicate that do not want an honest dialogue.

It was proven otherwise. Why do you keep lying?

I want an honest dialogue ⊨□ I want an honest dialogue.

Q.E.D

[Skepdick]

In any case there cannot possibly be any mistake in the way that analytical truth really works:

The error is right here:

Provable(P,X) means P ⊨□ X // This is the conventional provable not Tarski's that has axioms as premises
True(T,X) means X ∈ (a) or T ⊨□ X // True(X) means X is an axiom or X is derived from axioms

If Provable(P,X) means P ⊨□ X then Provable(X,X) means X ⊨□ X

And True(T,X) T ⊨□ X, then True(X,X) means X ⊨□ X

∀X: True(X,X) ↔ Provable(X,X)

∀X: True(X,X)

[PeteOlcott]

In any case there cannot possibly be any mistake in the way that analytical truth really works:

The error is right here:

Provable(P,X) means P ⊨□ X // This is the conventional provable not Tarski's that has axioms as premises
True(T,X) means X ∈ (a) or T ⊨□ X // True(X) means X is an axiom or X is derived from axioms

If Provable(P,X) means P ⊨□ X then Provable(X,X) means X ⊨□ X

And True(T,X) T ⊨□ X, then True(X,X) means X ⊨□ X

∀X: True(X,X) ↔ Provable(X,X)

∀X: True(X)

"If Provable(P,X) means P ⊨□ X then Provable(X,X) means X ⊨□ X"
P is a class of expressions of language X is a single instance of this class a single
instance of a class is not identical to the whole class.

"And True(T,X) T ⊨□ X, then True(X,X) means X ⊨□ X"
Every element of T is TRUE, X need not be true, yet still derives itself.

The first argument to True must be a set of axioms. Maybe it would be
more clear if I disallowed this first argument:
True(X) means X ∈ (a) or T ⊨□ X // True(X) means X is an axiom or X is derived from axioms

[Skepdick]

"If Provable(P,X) means P ⊨□ X then Provable(X,X) means X ⊨□ X"
P is a class of expressions of language X is a single instance of this class a single
instance of a class is not identical to the whole class.

Why do you need a whole class when X is a member of this class and X ⊨□ X?

"And True(T,X) T ⊨□ X, then True(X,X) means X ⊨□ X"
Every element of T is TRUE, X need not be true, yet still derives itself.

The first argument to True must be a set of axioms. Maybe it would be
more clear if I disallowed this first argument:
True(X) means X ∈ (a) or T ⊨□ X // True(X) means X is an axiom or X is derived from axioms

Why do you need a set of axioms when the set of X all by itself is sufficient for X ⊨□ X ?

Just make everything an axiom!

[PeteOlcott]

"If Provable(P,X) means P ⊨□ X then Provable(X,X) means X ⊨□ X"
P is a class of expressions of language X is a single instance of this class a single
instance of a class is not identical to the whole class.

Why do you need a whole class when X is a member of this class and X ⊨□ X?

"And True(T,X) T ⊨□ X, then True(X,X) means X ⊨□ X"
Every element of T is TRUE, X need not be true, yet still derives itself.

The first argument to True must be a set of axioms. Maybe it would be
more clear if I disallowed this first argument:
True(X) means X ∈ (a) or T ⊨□ X // True(X) means X is an axiom or X is derived from axioms

Why do you need a set of axioms when the set of X all by itself is sufficient for X ⊨□ X ?

Just make everything an axiom!

"Just make everything an axiom!"
That is not the way that analytical truth really works.
My system models the way that analytical truth really works.

[Skepdick]

"Just make everything an axiom!"
That is not the way that analytical truth really works.
My system models the way that analytical truth really works.

Of course it is the way it works!

What makes an axiom true?
Why can't an axiom be false?

[PeteOlcott]

"Just make everything an axiom!"
That is not the way that analytical truth really works.
My system models the way that analytical truth really works.

Of course it is the way it works!

What makes an axiom true?
Why can't an axiom be false?

"What makes an axiom true?"
"Why can't an axiom be false?"
Axioms / theorems are stipulated to be true (shown below) Same idea as Prolog Facts.
Axioms are elements of the set of analytical truth, they cannot be false for the same
reason that a dog cannot be a cat.

Introducing the foundation of correct reasoning
(the actual way that analytical truth really works)
Just like with syllogisms conclusions are a semantically necessary consequence of their premises
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.
P is a subset of expressions of language L
T is a subset of (a)

Provable(P,X) means P ⊨□ X
True(X) means X ∈ (a) or T ⊨□ X
False(X) means T ⊨□ ~X

[Skepdick]

"What makes an axiom true?"
"Why can't an axiom be false?"
Axioms / theorems are stipulated to be true (shown below) Same idea as Prolog Facts.
Axioms are elements of the set of analytical truth, they cannot be false for the same
reason that a dog cannot be a cat.

That's nonsense.

A statement can be true.
The negation of a statement can be true.
Therefore the negation of a Boolean:True statement (e.g a statement which evaluates to Boolean:False) can also be true.

The statement "I have 7 fingers on my left hand" evaluates to false.
It's true that it's false that I have 7 fingers on my left hand.

Introducing the foundation of correct reasoning
(the actual way that analytical truth really works)

And he continues with the false advertising.

[PeteOlcott]

"Just make everything an axiom!"
That is not the way that analytical truth really works.
My system models the way that analytical truth really works.

Of course it is the way it works!

What makes an axiom true?
Why can't an axiom be false?

Axioms are expressions of language that have been stipulated to be true, thus cannot be false.
{Cats} <are> {Animals} is an axiom of natural language.