Philosophy Now Forum

PeteOlcott wrote: ↑Thu May 23, 2019 7:59 pm

Univalence wrote: ↑Thu May 23, 2019 7:38 pm

PeteOlcott wrote: ↑Thu May 23, 2019 7:20 pm 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.

Univalence wrote: ↑Thu May 23, 2019 8:02 pm

PeteOlcott wrote: ↑Thu May 23, 2019 7:59 pm

Univalence wrote: ↑Thu May 23, 2019 7:38 pm
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.

You are building a classifier.

Input: String
Output: {A,B,C,D}

You can have 4 buckets or 4 million. It doesn't matter. The hard part (and the algorithm I want to see) is the detection of the 'semantic error'.
So let me help you get started.
https://repl.it/repls/GiftedLastingTrials

Please fill in the blanks in the parser() function and make it raise(SemanticError) when appropriate.
I gave you a unit test and everything.

PeteOlcott wrote: ↑Thu May 23, 2019 9:07 pm The fully operational parser spec, it took me 18 months to create this and the parser.
https://www.researchgate.net/publicatio ... y_YACC_BNF

Univalence wrote: ↑Thu May 23, 2019 10:06 pm

PeteOlcott wrote: ↑Thu May 23, 2019 9:07 pm The fully operational parser spec, it took me 18 months to create this and the parser.
https://www.researchgate.net/publicatio ... y_YACC_BNF

What parser syntax is that? yacc ?

PeteOlcott wrote:...

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

A
B
{A, B} ⊢ C
-------------
∴ C

Arising_uk wrote: ↑Fri May 24, 2019 10:38 am Just being picky but if we are using a junior school level of understanding logic then why are you using propostional logic and not predicate logic to represent an argument that uses universal quantifiers, can this even be done?

Arising_uk wrote: ↑Fri May 24, 2019 10:38 am

PeteOlcott wrote:...

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

A
B
{A, B} ⊢ C
-------------
∴ C

Just being picky but if we are using a junior school level of understanding logic then why are you using propostional logic and not predicate logic to represent an argument that uses universal quantifiers, can this even be done?

Univalence wrote: ↑Fri May 24, 2019 12:28 pm

Arising_uk wrote: ↑Fri May 24, 2019 10:38 am Just being picky but if we are using a junior school level of understanding logic then why are you using propostional logic and not predicate logic to represent an argument that uses universal quantifiers, can this even be done?

I think all predicate logic is 2-valued. P(X) -> {0,1} ?

What he is doing is; P(X) -> {0,1, 2 ,3}

PeteOlcott wrote:
This is the junior high school level
That the sound deductive inference model necessitates true
conclusions is known on the basis of the definition of the sound
deductive inference model, thus impossibly false.

It divides every expression of language into True and ¬True such that
we end up with an exhaustive list of all true sentences.

Arising_uk wrote: ↑Fri May 24, 2019 7:10 pm

PeteOlcott wrote:
This is the junior high school level
That the sound deductive inference model necessitates true
conclusions is known on the basis of the definition of the sound
deductive inference model, thus impossibly false.

It divides every expression of language into True and ¬True such that
we end up with an exhaustive list of all true sentences.

I'm a touched confused here as apart from the contradictions and tautologies how can logic tell us which sentences are true or false? Also "every expression"? "Time flies furiously."?

PeteOlcott wrote: ↑Fri May 24, 2019 8:32 pm You have it exactly right, apart from contradictions (false) and tautologies (true) there is no true and false.

Univalence wrote: ↑Sat May 25, 2019 10:52 am

PeteOlcott wrote: ↑Fri May 24, 2019 8:32 pm You have it exactly right, apart from contradictions (false) and tautologies (true) there is no true and false.

Linguistically - true.
Conceptually - false.

The symbols contain no semantics.
The sentences contain no grammar.

It's only when you combine the symbols with the parser/interpreter do the concepts of "true", "false", GrammaticalError and SyntaxError appear.

Since you really are going out of your way to eliminate undecidability (e.g Turing completeness), I can't see how you are going to end up at anything other than total functions.

PeteOlcott wrote: ↑Sat May 25, 2019 2:42 pm

Univalence wrote: ↑Sat May 25, 2019 10:52 am

PeteOlcott wrote: ↑Fri May 24, 2019 8:32 pm You have it exactly right, apart from contradictions (false) and tautologies (true) there is no true and false.

Linguistically - true.
Conceptually - false.

The symbols contain no semantics.
The sentences contain no grammar.

It's only when you combine the symbols with the parser/interpreter do the concepts of "true", "false", GrammaticalError and SyntaxError appear.

Since you really are going out of your way to eliminate undecidability (e.g Turing completeness), I can't see how you are going to end up at anything other than total functions.

http://mathworld.wolfram.com/TotalFunction.html
A function defined for all possible input values.

My system takes an infinite set of finite strings and selects the true
sentences of formal system F from these input strings.

This is to understand the gist of my idea so some of the ideas a simplistic to make them
easier to understand.

const int EMPTY = -1;
const int FALSE = 0;
const int TRUE = 1;

class Expression
{
std::string expression;
int Truth_Value = EMPTY;
};

std:vector<Expression> Axioms; // e.True_Value set to TRUE

bool Provable(Expression Consequence)
{
if (Formal_Proof(Axioms, Consequence))
{
Consequence.Truth_Value = TRUE;
return true;
}
return false;
}

Univalence wrote: ↑Sat May 25, 2019 2:49 pm

PeteOlcott wrote: ↑Sat May 25, 2019 2:42 pm

Univalence wrote: ↑Sat May 25, 2019 10:52 am
Linguistically - true.
Conceptually - false.

The symbols contain no semantics.
The sentences contain no grammar.

It's only when you combine the symbols with the parser/interpreter do the concepts of "true", "false", GrammaticalError and SyntaxError appear.

Since you really are going out of your way to eliminate undecidability (e.g Turing completeness), I can't see how you are going to end up at anything other than total functions.

http://mathworld.wolfram.com/TotalFunction.html
A function defined for all possible input values.

My system takes an infinite set of finite strings and selects the true
sentences of formal system F from these input strings.

This is to understand the gist of my idea so some of the ideas a simplistic to make them
easier to understand.

const int EMPTY = -1;
const int FALSE = 0;
const int TRUE = 1;

class Expression
{
std::string expression;
int Truth_Value = EMPTY;
};

std:vector<Expression> Axioms; // e.True_Value set to TRUE

bool Provable(Expression Consequence)
{
if (Formal_Proof(Axioms, Consequence))
{
Consequence.Truth_Value = TRUE;
return true;
}
return false;
}

Infinities..... OK.

How do you parse an infinitely-long string?

PeteOlcott wrote: ↑Sat May 25, 2019 4:06 pm

Univalence wrote: ↑Sat May 25, 2019 2:49 pm

PeteOlcott wrote: ↑Sat May 25, 2019 2:42 pm

http://mathworld.wolfram.com/TotalFunction.html
A function defined for all possible input values.

My system takes an infinite set of finite strings and selects the true
sentences of formal system F from these input strings.

This is to understand the gist of my idea so some of the ideas a simplistic to make them
easier to understand.

const int EMPTY = -1;
const int FALSE = 0;
const int TRUE = 1;

class Expression
{
std::string expression;
int Truth_Value = EMPTY;
};

std:vector<Expression> Axioms; // e.True_Value set to TRUE

bool Provable(Expression Consequence)
{
if (Formal_Proof(Axioms, Consequence))
{
Consequence.Truth_Value = TRUE;
return true;
}
return false;
}

Infinities..... OK.

How do you parse an infinitely-long string?

They are excluded from consideration.