A junior high school level of understanding of logic

[PeteOlcott]

It only takes a junior high school level of understanding of this:
Validity and Soundness https://www.iep.utm.edu/val-snd/
A deductive argument is said to be valid if and only if it takes a form that makes it
impossible for the premises to be true and the conclusion nevertheless to be false.
Otherwise, a deductive argument is said to be invalid.

A deductive argument is sound if and only if it is both valid, and all of its premises
are actually true. Otherwise, a deductive argument is unsound.

To verify that this refutes Tarski undefinability by correctly defining
what Tarski "proved" impossible to define:
When we specify that True(x) is the consequences of the subset
of the of conventional formal proofs of mathematical logic having
true premises then True(x) is always defined and never undefinable.

To understand that I am correct one need only know this:
Whenever every element of the set of premises to a formal proof of mathematical
logic is true then provability derives necessarily true consequences.

[Speakpigeon]

It only takes a junior high school level of understanding of this:
Validity and Soundness https://www.iep.utm.edu/val-snd/
A deductive argument is said to be valid if and only if it takes a form that makes it
impossible for the premises to be true and the conclusion nevertheless to be false.
Otherwise, a deductive argument is said to be invalid.

A deductive argument is sound if and only if it is both valid, and all of its premises
are actually true. Otherwise, a deductive argument is unsound.

To verify that this refutes Tarski undefinability by correctly defining
what Tarski "proved" impossible to define:
When we specify that True(x) is the consequences of the subset
of the of conventional formal proofs of mathematical logic having
true premises then True(x) is always defined and never undefinable.

Your definition seems circular. Could you give an example?

To understand that I am correct one need only know this:
Whenever every element of the set of premises to a formal proof of mathematical
logic is true then provability derives necessarily true consequences.

I don't understand how "provability" could "derive" anything.
I think you need to look at the way you express your ideas.

[PeteOlcott]

It only takes a junior high school level of understanding of this:
Validity and Soundness https://www.iep.utm.edu/val-snd/
A deductive argument is said to be valid if and only if it takes a form that makes it
impossible for the premises to be true and the conclusion nevertheless to be false.
Otherwise, a deductive argument is said to be invalid.

A deductive argument is sound if and only if it is both valid, and all of its premises
are actually true. Otherwise, a deductive argument is unsound.

To verify that this refutes Tarski undefinability by correctly defining
what Tarski "proved" impossible to define:
When we specify that True(x) is the consequences of the subset
of the of conventional formal proofs of mathematical logic having
true premises then True(x) is always defined and never undefinable.

Your definition seems circular. Could you give an example?

To understand that I am correct one need only know this:
Whenever every element of the set of premises to a formal proof of mathematical
logic is true then provability derives necessarily true consequences.

I don't understand how "provability" could "derive" anything.
I think you need to look at the way you express your ideas.

Premise(A) All dogs are mammals.
Premise(B) All mammals breathe.
Conclusion(C) All dogs breathe.

A
B
{A, B} ⊢ C
-------------
∴ C

[Speakpigeon]

It only takes a junior high school level of understanding of this:
Validity and Soundness https://www.iep.utm.edu/val-snd/
A deductive argument is said to be valid if and only if it takes a form that makes it
impossible for the premises to be true and the conclusion nevertheless to be false.
Otherwise, a deductive argument is said to be invalid.

A deductive argument is sound if and only if it is both valid, and all of its premises
are actually true. Otherwise, a deductive argument is unsound.

To verify that this refutes Tarski undefinability by correctly defining
what Tarski "proved" impossible to define:
When we specify that True(x) is the consequences of the subset
of the of conventional formal proofs of mathematical logic having
true premises then True(x) is always defined and never undefinable.

Your definition seems circular. Could you give an example?

To understand that I am correct one need only know this:
Whenever every element of the set of premises to a formal proof of mathematical
logic is true then provability derives necessarily true consequences.

I don't understand how "provability" could "derive" anything.
I think you need to look at the way you express your ideas.

Premise(A) All dogs are mammals.
Premise(B) All mammals breathe.
Conclusion(C) All dogs breathe.

A
B
{A, B} ⊢ C
-------------
∴ C

So, what is "true" and what is "True(x)" in your example?
EB

[PeteOlcott]

Your definition seems circular. Could you give an example?


I don't understand how "provability" could "derive" anything.
I think you need to look at the way you express your ideas.

Premise(A) All dogs are mammals.
Premise(B) All mammals breathe.
Conclusion(C) All dogs breathe.

A
B
{A, B} ⊢ C
-------------
∴ C

So, what is "true" and what is "True(x)" in your example?
EB

To keep it as simple as possible we can assume the propositional logic notion of true.
Every propositional variable without a negation symbol asserts its own truth.

[Speakpigeon]

Premise(A) All dogs are mammals.
Premise(B) All mammals breathe.
Conclusion(C) All dogs breathe.

A
B
{A, B} ⊢ C
-------------
∴ C

So, what is "true" and what is "True(x)" in your example?
EB

To keep it as simple as possible we can assume the propositional logic notion of true.
Every propositional variable without a negation symbol asserts its own truth.

Sure. And?
EB

[Univalence]

To keep it as simple as possible we can assume the propositional logic notion of true.
Every propositional variable without a negation symbol asserts its own truth.

That's not simple. That's ambiguous. You clearly stated that Untrue(x) does NOT mean Boolean False.

So any particular proposition in your grammar could be True, False or Untrue.
Why not Unfalse also?

[PeteOlcott]

Your definition seems circular. Could you give an example?


I don't understand how "provability" could "derive" anything.
I think you need to look at the way you express your ideas.

Premise(A) All dogs are mammals.
Premise(B) All mammals breathe.
Conclusion(C) All dogs breathe.

A
B
{A, B} ⊢ C
-------------
∴ C

So, what is "true" and what is "True(x)" in your example?
EB

I am trying to simplify what I am saying enough so that someone that does not totally
understand formal proofs of mathematical logic can get the gist of what I am saying.
To really fully understand what I am requires totally understanding formal proofs
of mathematical logic as operations on finite strings.

https://en.wikipedia.org/wiki/Formalism ... thematics)
In foundations of mathematics, philosophy of mathematics, and philosophy of logic,
formalism is a theory that holds that statements of mathematics and logic can be
considered to be statements about the consequences of the manipulation of strings
(alphanumeric sequences of symbols, usually as equations) using established manipulation
rules.

[PeteOlcott]

To keep it as simple as possible we can assume the propositional logic notion of true.
Every propositional variable without a negation symbol asserts its own truth.

That's not simple. That's ambiguous. You clearly stated that Untrue(x) does NOT mean Boolean False.

So any particular proposition in your grammar could be True, False or Untrue.
Why not Unfalse also?

In other words it is a tautology that sound deduction would
partition the exhaustively complete set of finite strings
(or expressions of language) into True(x) and ¬True(x).

[Univalence]

In other words it is a tautology that sound deduction would
partition the exhaustively complete set of finite strings
(or expressions of language) into True(x) and ¬True(x).

OK so, two categories?

Is there any particular reason you are using the syntax ¬True(x) instead of False(x)?
(I have to check with you after you defined 'truth' as an integer and then you initialized it as -1)

[PeteOlcott]

In other words it is a tautology that sound deduction would
partition the exhaustively complete set of finite strings
(or expressions of language) into True(x) and ¬True(x).

OK so, two categories?

Is there any particular reason you are using the syntax ¬True(x) instead of False(x)?

True(x) selects the consequences of the subset of the of conventional formal proofs
of mathematical logic having true premises.

When operating on the infinite set of finite strings everything else is (exactly one of)
(a) False
(b) Syntactically ill-formed
(c) Semantically ill-formed

[Univalence]

True(x) selects the consequences of the subset of the of conventional formal proofs
of mathematical logic having true premises.

When operating on the infinite set of finite strings everything else is (exactly one of)
(a) False
(b) Syntactically ill-formed
(c) Semantically ill-formed

*SIGH*

So any particular string can be classified into 4 separate categories then?
I was joking when I said True, False, Untrue and Unfalse. But you were serious.

Still. Your decision-space is 2 bits. 4 categories.

[PeteOlcott]

True(x) selects the consequences of the subset of the of conventional formal proofs
of mathematical logic having true premises.

When operating on the infinite set of finite strings everything else is (exactly one of)
(a) False
(b) Syntactically ill-formed
(c) Semantically ill-formed

*SIGH*

So any particular string can be classified into 4 separate categories then?
I was joking when I said True, False, Untrue and Unfalse. But you were serious.

Still. Your decision-space is 2 bits. 4 categories.

What can I say, that is the way that truth really works and only truth itself has the authority to specify how itself works.

w8094t24589y is (b)
"This sentence is not true" is self-contradictory thus (c)
"2 + 3 = 7" is (a)

This is two actual pages from Tarski's actual proof that says the inability to prove the Liar Paradox proves that True(x) is incomplete:
http://liarparadox.org/247_248.pdf

[Univalence]

This is two actual pages from Tarski's actual proof that says the inability to prove the Liar Paradox proves that True(x) is incomplete:
http://liarparadox.org/247_248.pdf

Tarski doesn't use a 4-value logic.

[PeteOlcott]

This is two actual pages from Tarski's actual proof that says the inability to prove the Liar Paradox proves that True(x) is incomplete:
http://liarparadox.org/247_248.pdf

Tarski doesn't use a 4-value logic.

I know hardly anyone does. 4-value logic assumes the mathematical formalist approach
of considering everything a finite string instead of a WFF. If we assume that everything
has already been vetted as a WFF conventionally this is only two values of True and False
because everyone totally ignores the case of semantically incorrect WFF.

When we feed a self-contradictory WFF to Tarski's True(x), it cannot "decide" whether
or not the self-contradictory WFF is true or false. No one ever bothered to consider that
a self-contradictory expressions would be neither true nor false because they totally
ignore semantic error.