Skepdick wrote: ↑Sun Aug 25, 2019 10:23 amPerhaps you are referring to Sexpressions?PeteOlcott wrote: ↑Sat Aug 24, 2019 3:28 pmThe 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.
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")
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 truthvalue. It's about operator precedence. Grammar!PeteOlcott wrote: ↑Sat Aug 24, 2019 3:28 pmThe 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.
Which one is the correct Sexpression 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 wellformed formula and it must throw a syntax error.
The Mathematician must either write (8 ÷ 4)(5  3); or 8 ÷ (4(5  3))
Conceptual Truth can be understood as math
Re: Truth can be understood as math

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Re: Truth can be understood as math
Self contradictory sentences such as the liar paradox have no truth value.Skepdick wrote: ↑Sun Aug 25, 2019 10:15 amYou are grasping at straws.PeteOlcott wrote: ↑Sat Aug 24, 2019 3:29 pmWhen Quine handles the Liar Paradox without selfreference he does
so incorrectly because the Liar Paradox specifies SelfReference.
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 selfcontradictory.
LP ↔ ¬True(LP)
TFF
FFT
The Liar's paradox demonstrates the difficulty in assigning a truthvalue to a selfreferential sentence.
Quine's paradox demonstrates the difficulty in assigning a truthvalue to a NONselfreferential sentence.
In both cases the paradoxes demonstrate the difficulty in assigning truthvalues to sentences.
It's natural that you disagree with its "correctness", because it shits all over your theory.
Quine's paradox is merely indirect selfreference which is logically equivalent
to actual selfreference. 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:
Falsewhentruthconditionismet ∧ Truthconditionismet
Since the actual proposition includes both pieces its was only subterfuge
that made it superficially appear to be not a case of selfreference.
Last edited by PeteOlcott on Mon Aug 26, 2019 6:15 pm, edited 2 times in total.

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Re: Truth can be understood as math
Leaving precedence unspecified either creates the error of ambiguitySkepdick wrote: ↑Sun Aug 25, 2019 10:23 amPerhaps you are referring to Sexpressions?PeteOlcott wrote: ↑Sat Aug 24, 2019 3:28 pmThe 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.
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")
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 truthvalue. It's about operator precedence. Grammar!PeteOlcott wrote: ↑Sat Aug 24, 2019 3:28 pmThe 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.
Which one is the correct Sexpression 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 wellformed formula and it must throw a syntax error.
The Mathematician must either write (8 ÷ 4)(5  3); or 8 ÷ (4(5  3))
or creates two different correct answers depending on the premise of
how the ambiguity is resolved.
Re: Truth can be understood as math
Only two? It creates as many correct answers as the number of interpretations available! It leads to a combinatorial explosionPeteOlcott wrote: ↑Mon Aug 26, 2019 6:04 pmLeaving precedence unspecified either creates the error of ambiguity
or creates two different correct answers depending on the premise of
how the ambiguity is resolved.
It also leads to the most important question in tour design: How do you resolve ambiguity?
Re: Truth can be understood as math
It's not selfreference, Pete. It's a directed graph. A>B>C....Z. The truthvalue of A depends on Z. And so you have to perform full depth traversal, before you assign it a truthvalue.PeteOlcott wrote: ↑Mon Aug 26, 2019 5:59 pmSelf contradictory sentences such as the liar paradox have no truth value.
Quine's paradox is merely indirect selfreference which is logically equivalent
to actual selfreference. 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:
Falsewhentruthconditionismet ∧ Truthconditionismet
Since the actual proposition includes both pieces its was only subterfuge
that made it superficially appear to be not a case of selfreference.
What Quine is effectively doing is expanding the recursion into a graph. Which is exactly what you have proposed to do.

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Re: Truth can be understood as math
With conventional order of operations and operator precedence it specifies only one correct interpretation.Skepdick wrote: ↑Mon Aug 26, 2019 6:44 pmOnly two? It creates as many correct answers as the number of interpretations available! It leads to a combinatorial explosionPeteOlcott wrote: ↑Mon Aug 26, 2019 6:04 pmLeaving precedence unspecified either creates the error of ambiguity
or creates two different correct answers depending on the premise of
how the ambiguity is resolved.
It also leads to the most important question in tour design: How do you resolve ambiguity?

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Re: Truth can be understood as math
"yields falsehood when preceded by its quotation" yields falsehood when preceded by its quotation.Skepdick wrote: ↑Mon Aug 26, 2019 6:50 pmIt's not selfreference, Pete. It's a directed graph. A>B>C....Z. The truthvalue of A depends on Z. And so you have to perform full depth traversal, before you assign it a truthvalue.PeteOlcott wrote: ↑Mon Aug 26, 2019 5:59 pmSelf contradictory sentences such as the liar paradox have no truth value.
Quine's paradox is merely indirect selfreference which is logically equivalent
to actual selfreference. 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:
Falsewhentruthconditionismet ∧ Truthconditionismet
Since the actual proposition includes both pieces its was only subterfuge
that made it superficially appear to be not a case of selfreference.
What Quine is effectively doing is expanding the recursion into a graph. Which is exactly what you have proposed to do.
MEANS THIS:
Falsewhentruthconditionismet ∧ Truthconditionismet
WHICH SPECIFIES SELFREFERENCE.
It was intentionally made too difficult to untangle by almost everyone including you and its author but not including me.
Re: Truth can be understood as math
'correct' interpretationPeteOlcott wrote: ↑Mon Aug 26, 2019 7:30 pmWith conventional order of operations and operator precedence it specifies only one correct interpretation.
https://en.wikipedia.org/wiki/Argumentum_ad_populum
Re: Truth can be understood as math
Precisely, you dimwit!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:
Falsewhentruthconditionismet ∧ Truthconditionismet
WHICH SPECIFIES SELFREFERENCE.
It was intentionally made too difficult to untangle by almost everyone including you and its author but not including me.
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 truthvalue on a sentence could depend on something external to the sentence itself.
The truthvalue 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 truthvalue' .
Which is the same thing Model theory says!

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Re: Truth can be understood as math
According to your reasoning there is not such thing as the logical tautology definingSkepdick wrote: ↑Mon Aug 26, 2019 7:35 pm'correct' interpretationPeteOlcott wrote: ↑Mon Aug 26, 2019 7:30 pmWith conventional order of operations and operator precedence it specifies only one correct interpretation.
https://en.wikipedia.org/wiki/Argumentum_ad_populum
what is correct and incorrect arithmetic, there are only the popular ideas of correct
arithmetic and incorrect arithmetic is merely an unpopular correct idea.
Re: Truth can be understood as math
That's right!PeteOlcott wrote: ↑Mon Aug 26, 2019 8:09 pmAccording 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.
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.

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Re: Truth can be understood as math
Yes of course everyone knows that it is totally impossible to specify anySkepdick wrote: ↑Mon Aug 26, 2019 7:39 pmPrecisely, you dimwit!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:
Falsewhentruthconditionismet ∧ Truthconditionismet
WHICH SPECIFIES SELFREFERENCE.
It was intentionally made too difficult to untangle by almost everyone including you and its author but not including me.
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 truthvalue on a sentence could depend on something external to the sentence itself.
The truthvalue 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 truthvalue' .
Which is the same thing Model theory says!
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.
Re: Truth can be understood as math
Then.... I don't understand what kind of knowledgedatabase you are trying to build.PeteOlcott wrote: ↑Mon Aug 26, 2019 8:15 pmYes 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.

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Re: Truth can be understood as math
I was being sarcastic about the actual need for model theory.Skepdick wrote: ↑Mon Aug 26, 2019 8:18 pmThen.... I don't understand what kind of knowledgedatabase you are trying to build.PeteOlcott wrote: ↑Mon Aug 26, 2019 8:15 pmYes 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.
Re: Truth can be understood as math
Well, that's ironic since in Tarski's universe English is the metalanguage and formalisms are the object language.PeteOlcott wrote: ↑Mon Aug 26, 2019 8:30 pmI was being sarcastic about the actual need for model theory.
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