## Conceptual Truth can be understood as math

What is the basis for reason? And mathematics?

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Eodnhoj7
Posts: 5039
Joined: Mon Mar 13, 2017 3:18 am

### Re: Truth can be understood as math

Skepdick wrote:
Sun Aug 25, 2019 10:23 am
PeteOlcott wrote:
Sat Aug 24, 2019 3:28 pm
The relation of words to each other is handled by predicates, which is merely
another name for Relations:
"="("2 + 3", "5") has its Boolean property assigned the value of TRUE.
Perhaps you are referring to S-expressions?

It's like this: (= (+ 2 3) 5)

But lets stick to your proposed convention for this single example. Which one is "true"?

A: "="("8 ÷ 4(5 - 3)", "1")
B: "="("8 ÷ 4(5 - 3)", "4")
PeteOlcott wrote:
Sat Aug 24, 2019 3:28 pm
The above is merely a single example to show the gist of what stipulated
relations between finite strings are. Arithmetic would actually be handled
by an algorithm.
Arithmetic IS just an algorithm. Everybody knows that! The problem Quine's paradox demonstrates is that in practice ambiguity in the evaluation order fucks your truth-value. It's about operator precedence. Grammar!

Which one is the correct S-expression for 8 ÷ 4(5 - 3): A or B?
A: (÷ 8 (* 4 (- 5 3))
B: (* ( ÷ 8 4) (- 5 3))

Under this premise

⊙(2,3)○○ (▪8,▪6,▪4,▪1. 5,▪1,▪2/3, •2/3,•1,•1.5,•2,•3,•4,•5,•6,•8,•9,****)
****Respective roots.

Is correct.

There is no "correct" answer. It's just an ARBITRARY CHOICE.

If your system is to work, then the Mathematical sentence 8 ÷ 4(5 - 3) is not a well-formed formula and it must throw a syntax error.
The Mathematician must either write (8 ÷ 4)(5 - 3); or 8 ÷ (4(5 - 3))

PeteOlcott
Posts: 730
Joined: Mon Jul 25, 2016 6:55 pm

### Re: Truth can be understood as math

Skepdick wrote:
Sun Aug 25, 2019 10:15 am
PeteOlcott wrote:
Sat Aug 24, 2019 3:29 pm
When Quine handles the Liar Paradox without self-reference he does
so incorrectly because the Liar Paradox specifies Self-Reference.

The ONLY way to fully understand things as difficult as the Liar Paradox
is to boil them down to their barest essence, Quine does the opposite of this.

LP := ~True(LP) This one is logically equivalent LP ↔ ~True(LP).
The second one essentially says that it is logically equivalent to not being logically equivalent.

The Formalized Liar Paradox says that LP is materially equivalent to Not True.
The truth table shows that this is self-contradictory.
LP ↔ ¬True(LP)
T---F------F
F---F------T
You are grasping at straws.

The Liar's paradox demonstrates the difficulty in assigning a truth-value to a self-referential sentence.
Quine's paradox demonstrates the difficulty in assigning a truth-value to a NON-self-referential sentence.

In both cases the paradoxes demonstrate the difficulty in assigning truth-values to sentences.

It's natural that you disagree with its "correctness", because it shits all over your theory.
Self contradictory sentences such as the liar paradox have no truth value.
Quine's paradox is merely indirect self-reference which is logically equivalent
to actual self-reference. All that Quine's paradox does is add totally extraneous
complexity.

"yields falsehood when preceded by its quotation" yields falsehood when preceded by its quotation.
Is merely a more convoluted form of this sentence:
False-when-truth-condition-is-met ∧ Truth-condition-is-met

Since the actual proposition includes both pieces its was only subterfuge
that made it superficially appear to be not a case of self-reference.
Last edited by PeteOlcott on Mon Aug 26, 2019 6:15 pm, edited 2 times in total.

PeteOlcott
Posts: 730
Joined: Mon Jul 25, 2016 6:55 pm

### Re: Truth can be understood as math

Skepdick wrote:
Sun Aug 25, 2019 10:23 am
PeteOlcott wrote:
Sat Aug 24, 2019 3:28 pm
The relation of words to each other is handled by predicates, which is merely
another name for Relations:
"="("2 + 3", "5") has its Boolean property assigned the value of TRUE.
Perhaps you are referring to S-expressions?

It's like this: (= (+ 2 3) 5)

But lets stick to your proposed convention for this single example. Which one is "true"?

A: "="("8 ÷ 4(5 - 3)", "1")
B: "="("8 ÷ 4(5 - 3)", "4")
PeteOlcott wrote:
Sat Aug 24, 2019 3:28 pm
The above is merely a single example to show the gist of what stipulated
relations between finite strings are. Arithmetic would actually be handled
by an algorithm.
Arithmetic IS just an algorithm. Everybody knows that! The problem Quine's paradox demonstrates is that in practice ambiguity in the evaluation order fucks your truth-value. It's about operator precedence. Grammar!

Which one is the correct S-expression for 8 ÷ 4(5 - 3): A or B?
A: (÷ 8 (* 4 (- 5 3))
B: (* ( ÷ 8 4) (- 5 3))

There is no "correct" answer. It's just an ARBITRARY CHOICE.

If your system is to work, then the Mathematical sentence 8 ÷ 4(5 - 3) is not a well-formed formula and it must throw a syntax error.
The Mathematician must either write (8 ÷ 4)(5 - 3); or 8 ÷ (4(5 - 3))
Leaving precedence unspecified either creates the error of ambiguity
or creates two different correct answers depending on the premise of
how the ambiguity is resolved.

Skepdick
Posts: 1846
Joined: Fri Jun 14, 2019 11:16 am

### Re: Truth can be understood as math

PeteOlcott wrote:
Mon Aug 26, 2019 6:04 pm
Leaving precedence unspecified either creates the error of ambiguity
or creates two different correct answers depending on the premise of
how the ambiguity is resolved.
Only two? It creates as many correct answers as the number of interpretations available! It leads to a combinatorial explosion

It also leads to the most important question in tour design: How do you resolve ambiguity?

Skepdick
Posts: 1846
Joined: Fri Jun 14, 2019 11:16 am

### Re: Truth can be understood as math

PeteOlcott wrote:
Mon Aug 26, 2019 5:59 pm
Self contradictory sentences such as the liar paradox have no truth value.
Quine's paradox is merely indirect self-reference which is logically equivalent
to actual self-reference. All that Quine's paradox does is add totally extraneous
complexity.

"yields falsehood when preceded by its quotation" yields falsehood when preceded by its quotation.
Is merely a more convoluted form of this sentence:
False-when-truth-condition-is-met ∧ Truth-condition-is-met

Since the actual proposition includes both pieces its was only subterfuge
that made it superficially appear to be not a case of self-reference.
It's not self-reference, Pete. It's a directed graph. A->B->C....Z. The truth-value of A depends on Z. And so you have to perform full depth traversal, before you assign it a truth-value.

What Quine is effectively doing is expanding the recursion into a graph. Which is exactly what you have proposed to do.

PeteOlcott
Posts: 730
Joined: Mon Jul 25, 2016 6:55 pm

### Re: Truth can be understood as math

Skepdick wrote:
Mon Aug 26, 2019 6:44 pm
PeteOlcott wrote:
Mon Aug 26, 2019 6:04 pm
Leaving precedence unspecified either creates the error of ambiguity
or creates two different correct answers depending on the premise of
how the ambiguity is resolved.
Only two? It creates as many correct answers as the number of interpretations available! It leads to a combinatorial explosion

It also leads to the most important question in tour design: How do you resolve ambiguity?
With conventional order of operations and operator precedence it specifies only one correct interpretation.

PeteOlcott
Posts: 730
Joined: Mon Jul 25, 2016 6:55 pm

### Re: Truth can be understood as math

Skepdick wrote:
Mon Aug 26, 2019 6:50 pm
PeteOlcott wrote:
Mon Aug 26, 2019 5:59 pm
Self contradictory sentences such as the liar paradox have no truth value.
Quine's paradox is merely indirect self-reference which is logically equivalent
to actual self-reference. All that Quine's paradox does is add totally extraneous
complexity.

"yields falsehood when preceded by its quotation" yields falsehood when preceded by its quotation.
Is merely a more convoluted form of this sentence:
False-when-truth-condition-is-met ∧ Truth-condition-is-met

Since the actual proposition includes both pieces its was only subterfuge
that made it superficially appear to be not a case of self-reference.
It's not self-reference, Pete. It's a directed graph. A->B->C....Z. The truth-value of A depends on Z. And so you have to perform full depth traversal, before you assign it a truth-value.

What Quine is effectively doing is expanding the recursion into a graph. Which is exactly what you have proposed to do.
"yields falsehood when preceded by its quotation" yields falsehood when preceded by its quotation.
MEANS THIS:
False-when-truth-condition-is-met ∧ Truth-condition-is-met
WHICH SPECIFIES SELF-REFERENCE.

It was intentionally made too difficult to untangle by almost everyone including you and its author but not including me.

Skepdick
Posts: 1846
Joined: Fri Jun 14, 2019 11:16 am

### Re: Truth can be understood as math

PeteOlcott wrote:
Mon Aug 26, 2019 7:30 pm
With conventional order of operations and operator precedence it specifies only one correct interpretation.
'correct' interpretation

Skepdick
Posts: 1846
Joined: Fri Jun 14, 2019 11:16 am

### Re: Truth can be understood as math

PeteOlcott wrote:
Mon Aug 26, 2019 7:34 pm
"yields falsehood when preceded by its quotation" yields falsehood when preceded by its quotation.
MEANS THIS:
False-when-truth-condition-is-met ∧ Truth-condition-is-met
WHICH SPECIFIES SELF-REFERENCE.

It was intentionally made too difficult to untangle by almost everyone including you and its author but not including me.
Precisely, you dimwit!

It was made in such a way as to demonstrate to you the very notion of dependency/coupling!

https://en.wikipedia.org/wiki/Coupling_ ... ogramming)

The very notion that the truth-value on a sentence could depend on something external to the sentence itself.
The truth-value of the sentence depends on something OTHER than the meaning of its words.

Which is a long way of saying that English sentences are not in closed form.
Which is the same as saying 'additional information is required for Interpret a sentence and assign it a truth-value' .
Which is the same thing Model theory says!

PeteOlcott
Posts: 730
Joined: Mon Jul 25, 2016 6:55 pm

### Re: Truth can be understood as math

Skepdick wrote:
Mon Aug 26, 2019 7:35 pm
PeteOlcott wrote:
Mon Aug 26, 2019 7:30 pm
With conventional order of operations and operator precedence it specifies only one correct interpretation.
'correct' interpretation

According to your reasoning there is not such thing as the logical tautology defining
what is correct and incorrect arithmetic, there are only the popular ideas of correct
arithmetic and incorrect arithmetic is merely an unpopular correct idea.

Skepdick
Posts: 1846
Joined: Fri Jun 14, 2019 11:16 am

### Re: Truth can be understood as math

PeteOlcott wrote:
Mon Aug 26, 2019 8:09 pm
According to your reasoning there is not such thing as the logical tautology defining
what is correct and incorrect arithmetic, there are only the popular ideas of correct
arithmetic and incorrect arithmetic is merely an unpopular correct idea.
That's right!

How do you choose between the BODMAS or the BOMDAS convention?

Unless you answer that question you can't tell me the correct answer to 8 ÷ 4 * 2
Last edited by Skepdick on Mon Aug 26, 2019 8:17 pm, edited 2 times in total.

PeteOlcott
Posts: 730
Joined: Mon Jul 25, 2016 6:55 pm

### Re: Truth can be understood as math

Skepdick wrote:
Mon Aug 26, 2019 7:39 pm
PeteOlcott wrote:
Mon Aug 26, 2019 7:34 pm
"yields falsehood when preceded by its quotation" yields falsehood when preceded by its quotation.
MEANS THIS:
False-when-truth-condition-is-met ∧ Truth-condition-is-met
WHICH SPECIFIES SELF-REFERENCE.

It was intentionally made too difficult to untangle by almost everyone including you and its author but not including me.
Precisely, you dimwit!

It was made in such a way as to demonstrate to you the very notion of dependency/coupling!

https://en.wikipedia.org/wiki/Coupling_ ... ogramming)

The very notion that the truth-value on a sentence could depend on something external to the sentence itself.
The truth-value of the sentence depends on something OTHER than the meaning of its words.

Which is a long way of saying that English sentences are not in closed form.
Which is the same as saying 'additional information is required for Interpret a sentence and assign it a truth-value' .
Which is the same thing Model theory says!
Yes of course everyone knows that it is totally impossible to specify any
statement of fact unambiguously without an additional layer of extraneous
specification. In fact if the truth be truly known anything less than an infinite
number of totally extraneous layers of specification is always necessarily
insufficient to say anything at all.

Skepdick
Posts: 1846
Joined: Fri Jun 14, 2019 11:16 am

### Re: Truth can be understood as math

PeteOlcott wrote:
Mon Aug 26, 2019 8:15 pm
Yes of course everyone knows that it is totally impossible to specify any
statement of fact unambiguously without an additional layer of extraneous
specification. In fact if the truth be truly known anything less than an infinite
number of totally extraneous layers of specification is always necessarily
insufficient to say anything at all.
Then.... I don't understand what kind of knowledge-database you are trying to build.

PeteOlcott
Posts: 730
Joined: Mon Jul 25, 2016 6:55 pm

### Re: Truth can be understood as math

Skepdick wrote:
Mon Aug 26, 2019 8:18 pm
PeteOlcott wrote:
Mon Aug 26, 2019 8:15 pm
Yes of course everyone knows that it is totally impossible to specify any
statement of fact unambiguously without an additional layer of extraneous
specification. In fact if the truth be truly known anything less than an infinite
number of totally extraneous layers of specification is always necessarily
insufficient to say anything at all.
Then.... I don't understand what kind of knowledge-database you are trying to build.
I was being sarcastic about the actual need for model theory.

Skepdick
Posts: 1846
Joined: Fri Jun 14, 2019 11:16 am

### Re: Truth can be understood as math

PeteOlcott wrote:
Mon Aug 26, 2019 8:30 pm
I was being sarcastic about the actual need for model theory.
Well, that's ironic since in Tarski's universe English is the metalanguage and formalisms are the object language.

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