Since the entire body of analytic truth (defined below) is established
entirely on the basis of semantic connections between expressions of
language this is the truth predicate that Tarski “proved” cannot exist:

True(x) ↔ (⊨x)

Instead of conventional model theory the body of analytic knowledge is
represented as knowledge ontology (acyclic directed graph) of
connections between expressions of language.

Nodes in this tree of knowledge represent unique individual concepts
roughly equivalent to the individual sense meanings of dictionary
definitions. https://en.wikipedia.org/wiki/Ontology_(computer_science)

*The Tarski Undefinability Proof*
https://liarparadox.org/Tarski_275_276.pdf

Because some of these semantic connections are currently unknown the set
of analytically true expressions of language is a proper superset of the
set of analytic knowledge.

If the Goldbach conjecture requires an infinite proof then it would have
an unknowable truth value, and yet still seem to be a truth bearer.
https://www.britannica.com/science/Goldbach-conjecture

“Analytic” sentences, such as “Pediatricians are doctors,” have
historically been characterized as ones that are true by virtue of the
meanings of their words alone and/or can be known to be so solely by
knowing those meanings.
https://plato.stanford.edu/entries/analytic-synthetic/

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/29/22 12:27 PM, olcott wrote:
> Since the entire body of analytic truth (defined below) is established
> entirely on the basis of semantic connections between expressions of
> language this is the truth predicate that Tarski “proved” cannot exist:
>
> True(x) ↔ (⊨x)

WRONG.

Because Truth can be established by an infinite series of semantic
connections, but a proof requires a finite series.

>
> Instead of conventional model theory the body of analytic knowledge is
> represented as knowledge ontology (acyclic directed graph) of
> connections between expressions of language.

Which becomes infinite when we need to include the fact that a proof
does not exist.

>
> Nodes in this tree of knowledge represent unique individual concepts
> roughly equivalent to the individual sense meanings of dictionary
> definitions. https://en.wikipedia.org/wiki/Ontology_(computer_science)
>
> *The Tarski Undefinability Proof*
> https://liarparadox.org/Tarski_275_276.pdf
>
> Because some of these semantic connections are currently unknown the set
> of analytically true expressions of language is a proper superset of the
> set of analytic knowledge.
Right, and is a proper superset of the ALL POSSIBLE analytic knowledge,
because some Analytic Truths are not Finitely provable.

>
> If the Goldbach conjecture requires an infinite proof then it would have
> an unknowable truth value, and yet still seem to be a truth bearer.
> https://www.britannica.com/science/Goldbach-conjecture

So you admit that unknowable truths exist.

**********************************************************************
* *
* This contradicts your statement above that True requires provable. *
* *
**********************************************************************

>
> “Analytic” sentences, such as “Pediatricians are doctors,” have
> historically been characterized as ones that are true by virtue of the
> meanings of their words alone and/or can be known to be so solely by
> knowing those meanings.
> https://plato.stanford.edu/entries/analytic-synthetic/
>
>

And "Statement x is provable" is known to be an Analytic Truth Bearer,
even if we do not know if it is, or even can be, determined if it is true.

On 12/29/2022 12:34 PM, Richard Damon wrote:
> On 12/29/22 12:27 PM, olcott wrote:
>> Since the entire body of analytic truth (defined below) is established
>> entirely on the basis of semantic connections between expressions of
>> language this is the truth predicate that Tarski “proved” cannot exist:
>>
>> True(x) ↔ (⊨x)
>
> WRONG.
>
> Because Truth can be established by an infinite series of semantic
> connections, but a proof requires a finite series.
>
>>
>> Instead of conventional model theory the body of analytic knowledge is
>> represented as knowledge ontology (acyclic directed graph) of
>> connections between expressions of language.
>
> Which becomes infinite when we need to include the fact that a proof
> does not exist.
>
>>
>> Nodes in this tree of knowledge represent unique individual concepts
>> roughly equivalent to the individual sense meanings of dictionary
>> definitions. https://en.wikipedia.org/wiki/Ontology_(computer_science)
>>
>> *The Tarski Undefinability Proof*
>> https://liarparadox.org/Tarski_275_276.pdf
>>
>> Because some of these semantic connections are currently unknown the set
>> of analytically true expressions of language is a proper superset of the
>> set of analytic knowledge.
> Right, and is a proper superset of the ALL POSSIBLE analytic knowledge,
> because some Analytic Truths are not Finitely provable.
>
>>
>> If the Goldbach conjecture requires an infinite proof then it would have
>> an unknowable truth value, and yet still seem to be a truth bearer.
>> https://www.britannica.com/science/Goldbach-conjecture
>
> So you admit that unknowable truths exist.
>
> **********************************************************************
> *                                                                    *
> * This contradicts your statement above that True requires provable. *
> *                                                                    *
> **********************************************************************
>
>>
>> “Analytic” sentences, such as “Pediatricians are doctors,” have
>> historically been characterized as ones that are true by virtue of the
>> meanings of their words alone and/or can be known to be so solely by
>> knowing those meanings.
>> https://plato.stanford.edu/entries/analytic-synthetic/
>>
>>
>
> And "Statement x is provable" is known to be an Analytic Truth Bearer,
> even if we do not know if it is, or even can be, determined if it is true.

These things are all a work-in-progress as I use the process of
elimination to chop off the imperfections of my proposal.

Expressions of language that cannot be proven or refuted because they
are self-contradictory are not truth bearers.

This tosses the Tarski Undefinability theorem out on its ass because
this theorem has the (self-contradictory) Liar Paradox as its
foundational basis. https://liarparadox.org/Tarski_247_248.pdf

It is more difficult to see that Tarski Undefinability forms an exact
isomorphism to 1931 Gödel Incompleteness. Tarski is derived from Gödel.

Expressions of language that cannot be proven or refuted only because
they require infinite proofs are truth bearers with unknown truth
values. The Goldbach conjecture may or may not require an infinite
proof, none-the-less it seems that it must be true or false, thus a
truth bearer.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/29/2022 12:43 PM, Skep Dick wrote:
> On Thursday, 29 December 2022 at 19:27:44 UTC+2, olcott wrote:
>> Since the entire body of analytic truth (defined below) is established
>> entirely on the basis of semantic connections between expressions of
>> language this is the truth predicate that Tarski “proved” cannot exist:
>>
>> True(x) ↔ (⊨x)
> Idiot.
>
> True(x) ↔ (⊨x)
> False(x) ↔ (⊨x)

Correction: False(x) ↔ (⊨~x)

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/29/22 2:04 PM, olcott wrote:
> On 12/29/2022 12:34 PM, Richard Damon wrote:
>> On 12/29/22 12:27 PM, olcott wrote:
>>> Since the entire body of analytic truth (defined below) is established
>>> entirely on the basis of semantic connections between expressions of
>>> language this is the truth predicate that Tarski “proved” cannot exist:
>>>
>>> True(x) ↔ (⊨x)
>>
>> WRONG.
>>
>> Because Truth can be established by an infinite series of semantic
>> connections, but a proof requires a finite series.
>>
>>>
>>> Instead of conventional model theory the body of analytic knowledge is
>>> represented as knowledge ontology (acyclic directed graph) of
>>> connections between expressions of language.
>>
>> Which becomes infinite when we need to include the fact that a proof
>> does not exist.
>>
>>>
>>> Nodes in this tree of knowledge represent unique individual concepts
>>> roughly equivalent to the individual sense meanings of dictionary
>>> definitions. https://en.wikipedia.org/wiki/Ontology_(computer_science)
>>>
>>> *The Tarski Undefinability Proof*
>>> https://liarparadox.org/Tarski_275_276.pdf
>>>
>>> Because some of these semantic connections are currently unknown the set
>>> of analytically true expressions of language is a proper superset of the
>>> set of analytic knowledge.
>> Right, and is a proper superset of the ALL POSSIBLE analytic
>> knowledge, because some Analytic Truths are not Finitely provable.
>>
>>>
>>> If the Goldbach conjecture requires an infinite proof then it would have
>>> an unknowable truth value, and yet still seem to be a truth bearer.
>>> https://www.britannica.com/science/Goldbach-conjecture
>>
>> So you admit that unknowable truths exist.
>>
>> **********************************************************************
>> *                                                                    *
>> * This contradicts your statement above that True requires provable. *
>> *                                                                    *
>> **********************************************************************
>>
>>>
>>> “Analytic” sentences, such as “Pediatricians are doctors,” have
>>> historically been characterized as ones that are true by virtue of the
>>> meanings of their words alone and/or can be known to be so solely by
>>> knowing those meanings.
>>> https://plato.stanford.edu/entries/analytic-synthetic/
>>>
>>>
>>
>> And "Statement x is provable" is known to be an Analytic Truth Bearer,
>> even if we do not know if it is, or even can be, determined if it is
>> true.
>
> These things are all a work-in-progress as I use the process of
> elimination to chop off the imperfections of my proposal.

So admit to your imperfections so you can see where you need to work.

>
> Expressions of language that cannot be proven or refuted because they
> are self-contradictory are not truth bearers.

But the statements in question are NOT "self-contradictory". You have
AGREED that statements of provability are ALWAYS truth bearers (perhaps
of unknown truth value), so can not be self-contradictory.

>
> This tosses the Tarski Undefinability theorem out on its ass because
> this theorem has the (self-contradictory) Liar Paradox as its
> foundational basis. https://liarparadox.org/Tarski_247_248.pdf

Except that he doesn't actually use the Liar Paradox in its original
form, but the transform that no longer talks about the Truth of the
statement, to the provability of the statement.

You inability to understand the differenceis your undoing here.

>
> It is more difficult to see that Tarski Undefinability forms an exact
> isomorphism to 1931 Gödel Incompleteness. Tarski is derived from Gödel.
>
> Expressions of language that cannot be proven or refuted only because
> they require infinite proofs are truth bearers with unknown truth
> values. The Goldbach conjecture may or may not require an infinite
> proof, none-the-less it seems that it must be true or false, thus a
> truth bearer.
>
>

So you AGREE that there can be statements which are True but Unprovable,
which contradicts your claim that True(x) implies Provable(x).

You are just being too stupid to understand you own words.

A natural consequence of you above statement is a distintion between
True and Knowable, there can be statements (and will be in a complex
enough system) that are True in the system, but can not be proven in
that system.

On 12/29/2022 2:14 PM, Richard Damon wrote:
> On 12/29/22 2:04 PM, olcott wrote:
>> On 12/29/2022 12:34 PM, Richard Damon wrote:
>>> On 12/29/22 12:27 PM, olcott wrote:
>>>> Since the entire body of analytic truth (defined below) is established
>>>> entirely on the basis of semantic connections between expressions of
>>>> language this is the truth predicate that Tarski “proved” cannot exist:
>>>>
>>>> True(x) ↔ (⊨x)
>>>
>>> WRONG.
>>>
>>> Because Truth can be established by an infinite series of semantic
>>> connections, but a proof requires a finite series.
>>>
>>>>
>>>> Instead of conventional model theory the body of analytic knowledge is
>>>> represented as knowledge ontology (acyclic directed graph) of
>>>> connections between expressions of language.
>>>
>>> Which becomes infinite when we need to include the fact that a proof
>>> does not exist.
>>>
>>>>
>>>> Nodes in this tree of knowledge represent unique individual concepts
>>>> roughly equivalent to the individual sense meanings of dictionary
>>>> definitions. https://en.wikipedia.org/wiki/Ontology_(computer_science)
>>>>
>>>> *The Tarski Undefinability Proof*
>>>> https://liarparadox.org/Tarski_275_276.pdf
>>>>
>>>> Because some of these semantic connections are currently unknown the
>>>> set
>>>> of analytically true expressions of language is a proper superset of
>>>> the
>>>> set of analytic knowledge.
>>> Right, and is a proper superset of the ALL POSSIBLE analytic
>>> knowledge, because some Analytic Truths are not Finitely provable.
>>>
>>>>
>>>> If the Goldbach conjecture requires an infinite proof then it would
>>>> have
>>>> an unknowable truth value, and yet still seem to be a truth bearer.
>>>> https://www.britannica.com/science/Goldbach-conjecture
>>>
>>> So you admit that unknowable truths exist.
>>>
>>> **********************************************************************
>>> *                                                                    *
>>> * This contradicts your statement above that True requires provable. *
>>> *                                                                    *
>>> **********************************************************************
>>>
>>>>
>>>> “Analytic” sentences, such as “Pediatricians are doctors,” have
>>>> historically been characterized as ones that are true by virtue of the
>>>> meanings of their words alone and/or can be known to be so solely by
>>>> knowing those meanings.
>>>> https://plato.stanford.edu/entries/analytic-synthetic/
>>>>
>>>>
>>>
>>> And "Statement x is provable" is known to be an Analytic Truth
>>> Bearer, even if we do not know if it is, or even can be, determined
>>> if it is true.
>>
>> These things are all a work-in-progress as I use the process of
>> elimination to chop off the imperfections of my proposal.
>
> So admit to your imperfections so you can see where you need to work.
>
>>
>> Expressions of language that cannot be proven or refuted because they
>> are self-contradictory are not truth bearers.
>
> But the statements in question are NOT "self-contradictory". You have
> AGREED that statements of provability are ALWAYS truth bearers (perhaps
> of unknown truth value), so can not be self-contradictory.
>
>>
>> This tosses the Tarski Undefinability theorem out on its ass because
>> this theorem has the (self-contradictory) Liar Paradox as its
>> foundational basis. https://liarparadox.org/Tarski_247_248.pdf
>
> Except that he doesn't actually use the Liar Paradox in its original
> form, but the transform that no longer talks about the Truth of the
> statement, to the provability of the statement.
>

He does use the Lair paradox in its original form:
It would then be possible to reconstruct the antinomy
of the liar in the metalanguage, by forming in the
language itself a sentence x such that the sentence of
the metalanguage which is correlated with x asserts
that x is not a true sentence.
https://liarparadox.org/Tarski_247_248.pdf

> You inability to understand the differenceis your undoing here.
>
>>
>> It is more difficult to see that Tarski Undefinability forms an exact
>> isomorphism to 1931 Gödel Incompleteness. Tarski is derived from Gödel.
>>
>> Expressions of language that cannot be proven or refuted only because
>> they require infinite proofs are truth bearers with unknown truth
>> values. The Goldbach conjecture may or may not require an infinite
>> proof, none-the-less it seems that it must be true or false, thus a
>> truth bearer.
>>
>>
>
> So you AGREE that there can be statements which are True but Unprovable,
> which contradicts your claim that True(x) implies Provable(x).
>

Not quite:
True(x) ↔ (⊨x)
False(x) ↔ (⊨~x)
~True(x) ↔ (~⊨x)

If there are no known or unknown semantic connections that derive the
truth of The Goldbach conjecture then it is not true.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/29/22 3:31 PM, olcott wrote:
> On 12/29/2022 2:14 PM, Richard Damon wrote:
>> On 12/29/22 2:04 PM, olcott wrote:
>>> On 12/29/2022 12:34 PM, Richard Damon wrote:
>> Except that he doesn't actually use the Liar Paradox in its original
>> form, but the transform that no longer talks about the Truth of the
>> statement, to the provability of the statement.
>>
>
> He does use the Lair paradox in its original form:
>    It would then be possible to reconstruct the antinomy
>    of the liar in the metalanguage, by forming in the
>    language itself a sentence x such that the sentence of
>    the metalanguage which is correlated with x asserts
>    that x is not a true sentence.
>    https://liarparadox.org/Tarski_247_248.pdf
>

You are missing the context, he isn't saying that we can just express
the liar's paradox, but that under this set of assumptions, we can PROVE
it true, which shows the system is inconsistent.

It isn't that the Metalanguage has an issue with not a statement not
being a Truth Bearer, but that given a definition of Truth, there will
exist a statement that both it and its antinomy can both be proven true.

>
>> You inability to understand the differenceis your undoing here.
>>
>>>
>>> It is more difficult to see that Tarski Undefinability forms an exact
>>> isomorphism to 1931 Gödel Incompleteness. Tarski is derived from Gödel.
>>>
>>> Expressions of language that cannot be proven or refuted only because
>>> they require infinite proofs are truth bearers with unknown truth
>>> values. The Goldbach conjecture may or may not require an infinite
>>> proof, none-the-less it seems that it must be true or false, thus a
>>> truth bearer.
>>>
>>>
>>
>> So you AGREE that there can be statements which are True but
>> Unprovable, which contradicts your claim that True(x) implies
>> Provable(x).
>>
>
> Not quite:
>  True(x) ↔ (⊨x)
> False(x) ↔ (⊨~x)
> ~True(x) ↔ (~⊨x)

So are you still saying that "x is Provable" will always be True or False?

Are you trying to equivocate and say that "x is Provable" might just be
~True but not False?

>
> If there are no known or unknown semantic connections that derive the
> truth of The Goldbach conjecture then it is not true.
>

But an infinite unknown series of semantic connection means a statement
is True but not Provable (since Provable means showing a finite series
of connections).

You are just showing you don't have any understand of the nature of the
infinte.

You logic just becomes too small to be usable.

On 12/29/2022 2:52 PM, Richard Damon wrote:
> On 12/29/22 3:31 PM, olcott wrote:
>> On 12/29/2022 2:14 PM, Richard Damon wrote:
>>> On 12/29/22 2:04 PM, olcott wrote:
>>>> On 12/29/2022 12:34 PM, Richard Damon wrote:
>>> Except that he doesn't actually use the Liar Paradox in its original
>>> form, but the transform that no longer talks about the Truth of the
>>> statement, to the provability of the statement.
>>>
>>
>> He does use the Lair paradox in its original form:
>>     It would then be possible to reconstruct the antinomy
>>     of the liar in the metalanguage, by forming in the
>>     language itself a sentence x such that the sentence of
>>     the metalanguage which is correlated with x asserts
>>     that x is not a true sentence.
>>     https://liarparadox.org/Tarski_247_248.pdf
>>
>
> You are missing the context,  he isn't saying that we can just express
> the liar's paradox, but that under this set of assumptions, we can PROVE
> it true, which shows the system is inconsistent.
>

The Liar Paradox is not true therefore his proof that it is true is
wrong. Truth bearers must have (semantic connection) truth makers.

?- LP = not(true(LP)).
LP = not(true(LP)).

?- unify_with_occurs_check(LP, not(true(LP))).
false.

Because the Prolog Liar Paradox has an “uninstantiated subterm of
itself” we can know that unification will fail because it specifies
“some kind of infinite structure.” that causes the LP expression to be
rejected by unify_with_occurs_check.

https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence

> It isn't that the Metalanguage has an issue with not a statement not
> being a Truth Bearer, but that given a definition of Truth, there will
> exist a statement  that both it and its antinomy can both be proven true.
>

Only if one does the proof incorrectly.
Prolog detects and rejects the Liar Paradox (as shown above).

>>
>>> You inability to understand the differenceis your undoing here.
>>>
>>>>
>>>> It is more difficult to see that Tarski Undefinability forms an exact
>>>> isomorphism to 1931 Gödel Incompleteness. Tarski is derived from Gödel.
>>>>
>>>> Expressions of language that cannot be proven or refuted only because
>>>> they require infinite proofs are truth bearers with unknown truth
>>>> values. The Goldbach conjecture may or may not require an infinite
>>>> proof, none-the-less it seems that it must be true or false, thus a
>>>> truth bearer.
>>>>
>>>>
>>>
>>> So you AGREE that there can be statements which are True but
>>> Unprovable, which contradicts your claim that True(x) implies
>>> Provable(x).
>>>
>>
>> Not quite:
>>   True(x) ↔ (⊨x)
>> False(x) ↔ (⊨~x)
>> ~True(x) ↔ (~⊨x)
>
> So are you still saying that "x is Provable" will always be True or False?
>
> Are you trying to equivocate and say that "x is Provable" might just be
> ~True but not False?
>

Self contradictory sentences are never true or false.
That Tarski thinks they are is his mistake.

>>
>> If there are no known or unknown semantic connections that derive the
>> truth of The Goldbach conjecture then it is not true.
>>
>
> But an infinite unknown series of semantic connection means a statement
> is True but not Provable (since Provable means showing a finite series
> of connections).

Yes and the lack of an infinite or finite sequence of semantic
connections that makes the sentence true means that it is untrue.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/30/22 10:30 AM, olcott wrote:
> On 12/29/2022 2:52 PM, Richard Damon wrote:
>> On 12/29/22 3:31 PM, olcott wrote:
>>> On 12/29/2022 2:14 PM, Richard Damon wrote:
>>>> On 12/29/22 2:04 PM, olcott wrote:
>>>>> On 12/29/2022 12:34 PM, Richard Damon wrote:
>>>> Except that he doesn't actually use the Liar Paradox in its original
>>>> form, but the transform that no longer talks about the Truth of the
>>>> statement, to the provability of the statement.
>>>>
>>>
>>> He does use the Lair paradox in its original form:
>>>     It would then be possible to reconstruct the antinomy
>>>     of the liar in the metalanguage, by forming in the
>>>     language itself a sentence x such that the sentence of
>>>     the metalanguage which is correlated with x asserts
>>>     that x is not a true sentence.
>>>     https://liarparadox.org/Tarski_247_248.pdf
>>>
>>
>> You are missing the context,  he isn't saying that we can just express
>> the liar's paradox, but that under this set of assumptions, we can
>> PROVE it true, which shows the system is inconsistent.
>>
>
> The Liar Paradox is not true therefore his proof that it is true is
> wrong. Truth bearers must have (semantic connection) truth makers.

Right, so unles you can point to an actual ERROR he makes in his proof,
the fact that it proves a statement that can't be true says one of the
input hypothesis is wrong, in this case, the hypothesis that Truth has a
defintion.

>
> ?- LP = not(true(LP)).
> LP = not(true(LP)).
>
> ?- unify_with_occurs_check(LP, not(true(LP))).
> false.
>
> Because the Prolog Liar Paradox has an “uninstantiated subterm of
> itself” we can know that unification will fail because it specifies
> “some kind of infinite structure.” that causes the LP expression to be
> rejected by unify_with_occurs_check.
>
> https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence

You DO understand that Prolog can't handle all logic system?

You reliance on it seems to demostrate your lack of understanding of
what you are claiming.

>
>> It isn't that the Metalanguage has an issue with not a statement not
>> being a Truth Bearer, but that given a definition of Truth, there will
>> exist a statement  that both it and its antinomy can both be proven true.
>>
>
> Only if one does the proof incorrectly.
> Prolog detects and rejects the Liar Paradox (as shown above).

Right, and since the steps of the proof ARE correct, it means one of the
premises is false, namely that we can form a correct defintion of Truth.

The fact that your brain can't handle how (dis)proof by contradiction
works, shows you to be incapable of actually handling logic.

>
>>>
>>>> You inability to understand the differenceis your undoing here.
>>>>
>>>>>
>>>>> It is more difficult to see that Tarski Undefinability forms an exact
>>>>> isomorphism to 1931 Gödel Incompleteness. Tarski is derived from
>>>>> Gödel.
>>>>>
>>>>> Expressions of language that cannot be proven or refuted only because
>>>>> they require infinite proofs are truth bearers with unknown truth
>>>>> values. The Goldbach conjecture may or may not require an infinite
>>>>> proof, none-the-less it seems that it must be true or false, thus a
>>>>> truth bearer.
>>>>>
>>>>>
>>>>
>>>> So you AGREE that there can be statements which are True but
>>>> Unprovable, which contradicts your claim that True(x) implies
>>>> Provable(x).
>>>>
>>>
>>> Not quite:
>>>   True(x) ↔ (⊨x)
>>> False(x) ↔ (⊨~x)
>>> ~True(x) ↔ (~⊨x)
>>
>> So are you still saying that "x is Provable" will always be True or
>> False?
>>
>> Are you trying to equivocate and say that "x is Provable" might just
>> be ~True but not False?
>>
>
> Self contradictory sentences are never true or false.
> That Tarski thinks they are is his mistake.
>

No, that isn't what he claims. He KNOWS the Self Contradictoy sentences
are never true, so a system that can PROVE such a statement has an error.

>>>
>>> If there are no known or unknown semantic connections that derive the
>>> truth of The Goldbach conjecture then it is not true.
>>>
>>
>> But an infinite unknown series of semantic connection means a
>> statement is True but not Provable (since Provable means showing a
>> finite series of connections).
>
> Yes and the lack of an infinite or finite sequence of semantic
> connections that makes the sentence true means that it is untrue.
>

But the existance of ONLY an infinite sequence of semantic connections
for a sentence make it True but Unprovable.

Thus your idea that all Truth is Provable is debunked, and you are shown
to be an idiot.

On 12/30/2022 10:15 AM, Richard Damon wrote:
> On 12/30/22 10:30 AM, olcott wrote:
>> On 12/29/2022 2:52 PM, Richard Damon wrote:
>>> On 12/29/22 3:31 PM, olcott wrote:
>>>> On 12/29/2022 2:14 PM, Richard Damon wrote:
>>>>> On 12/29/22 2:04 PM, olcott wrote:
>>>>>> On 12/29/2022 12:34 PM, Richard Damon wrote:
>>>>> Except that he doesn't actually use the Liar Paradox in its
>>>>> original form, but the transform that no longer talks about the
>>>>> Truth of the statement, to the provability of the statement.
>>>>>
>>>>
>>>> He does use the Lair paradox in its original form:
>>>>     It would then be possible to reconstruct the antinomy
>>>>     of the liar in the metalanguage, by forming in the
>>>>     language itself a sentence x such that the sentence of
>>>>     the metalanguage which is correlated with x asserts
>>>>     that x is not a true sentence.
>>>>     https://liarparadox.org/Tarski_247_248.pdf
>>>>
>>>
>>> You are missing the context,  he isn't saying that we can just
>>> express the liar's paradox, but that under this set of assumptions,
>>> we can PROVE it true, which shows the system is inconsistent.
>>>
>>
>> The Liar Paradox is not true therefore his proof that it is true is
>> wrong. Truth bearers must have (semantic connection) truth makers.
>
> Right, so unles you can point to an actual ERROR he makes in his proof,
> the fact that it proves a statement that can't be true says one of the
> input hypothesis is wrong, in this case, the hypothesis that Truth has a
> defintion.
>
>>
>> ?- LP = not(true(LP)).
>> LP = not(true(LP)).
>>
>> ?- unify_with_occurs_check(LP, not(true(LP))).
>> false.
>>
>> Because the Prolog Liar Paradox has an “uninstantiated subterm of
>> itself” we can know that unification will fail because it specifies
>> “some kind of infinite structure.” that causes the LP expression to be
>> rejected by unify_with_occurs_check.
>>
>> https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
>
> You DO understand that Prolog can't handle all logic system?
>

Red Herring because it does handle the Liar Paradox.

A red herring is something that misleads or distracts from a relevant or
important question. https://en.wikipedia.org/wiki/Red_herring

> You reliance on it seems to demostrate your lack of understanding of
> what you are claiming.
>
>>
>>> It isn't that the Metalanguage has an issue with not a statement not
>>> being a Truth Bearer, but that given a definition of Truth, there
>>> will exist a statement  that both it and its antinomy can both be
>>> proven true.
>>>
>>
>> Only if one does the proof incorrectly.
>> Prolog detects and rejects the Liar Paradox (as shown above).
>
> Right, and since the steps of the proof ARE correct, it means one of the
> premises is false, namely that we can form a correct defintion of Truth.
>

Prolog detects and rejects the Liar Paradox (as shown above).
This means that the semantically incoherent expression of language that
forms the foundation of the Tarski proof is rejected and thus Tarski's
proof loses its entire basis.

> The fact that your brain can't handle how (dis)proof by contradiction
> works, shows you to be incapable of actually handling logic.
>
>>
>>>>
>>>>> You inability to understand the differenceis your undoing here.
>>>>>
>>>>>>
>>>>>> It is more difficult to see that Tarski Undefinability forms an exact
>>>>>> isomorphism to 1931 Gödel Incompleteness. Tarski is derived from
>>>>>> Gödel.
>>>>>>
>>>>>> Expressions of language that cannot be proven or refuted only because
>>>>>> they require infinite proofs are truth bearers with unknown truth
>>>>>> values. The Goldbach conjecture may or may not require an infinite
>>>>>> proof, none-the-less it seems that it must be true or false, thus a
>>>>>> truth bearer.
>>>>>>
>>>>>>
>>>>>
>>>>> So you AGREE that there can be statements which are True but
>>>>> Unprovable, which contradicts your claim that True(x) implies
>>>>> Provable(x).
>>>>>
>>>>
>>>> Not quite:
>>>>   True(x) ↔ (⊨x)
>>>> False(x) ↔ (⊨~x)
>>>> ~True(x) ↔ (~⊨x)
>>>
>>> So are you still saying that "x is Provable" will always be True or
>>> False?
>>>
>>> Are you trying to equivocate and say that "x is Provable" might just
>>> be ~True but not False?
>>>
>>
>> Self contradictory sentences are never true or false.
>> That Tarski thinks they are is his mistake.
>>
>
> No, that isn't what he claims. He KNOWS the Self Contradictoy sentences
> are never true, so a system that can PROVE such a statement has an error.
>
>>>>
>>>> If there are no known or unknown semantic connections that derive
>>>> the truth of The Goldbach conjecture then it is not true.
>>>>
>>>
>>> But an infinite unknown series of semantic connection means a
>>> statement is True but not Provable (since Provable means showing a
>>> finite series of connections).
>>
>> Yes and the lack of an infinite or finite sequence of semantic
>> connections that makes the sentence true means that it is untrue.
>>
>
> But the existance of ONLY an infinite sequence of semantic connections
> for a sentence make it True but Unprovable.
>
> Thus your idea that all Truth is Provable is debunked, and you are shown
> to be an idiot.
>

My prior claim that every true statement must be provable is either
qualified to allow infinite proofs or changed to refer to semantic
connections that may be finite or infinite.

Thus an expression of language is never true unless it is connected to
its truth maker.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/30/22 11:30 AM, olcott wrote:
> On 12/30/2022 10:15 AM, Richard Damon wrote:

>> But the existance of ONLY an infinite sequence of semantic connections
>> for a sentence make it True but Unprovable.
>>
>> Thus your idea that all Truth is Provable is debunked, and you are
>> shown to be an idiot.
>>
>
> My prior claim that every true statement must be provable is either
> qualified to allow infinite proofs or changed to refer to semantic
> connections that may be finite or infinite.

If you allow your "Proof" to be infinite, then you have broken the link
between provable and knowable, and have left the language that everyone
else is talking.

Since some Semantic Statement DO require an infinite set of semantic
connections, but knowable requries a finite set of semantic connections,
we have that there exsits some statements that are True but not
knowable, and thus not Provable by the classical definition.

>
> Thus an expression of language is never true unless it is connected to
> its truth maker.
>

Right, but that connection might not be knowable, because it is
infinite, and thus not provable by the classical meaning.

If you redefine your idea of "Proof" to include "infinite proofs" you
have just made you logic system incompatible with ALL standard logic
that requires it to be finite, so you need to restart at the begining.

You are going to need to define SOMETHING, to indicate actually knowable
due to having a finite proof. Knowable isn't actually a good word for
this, as we often want to include in knowable not just things proven
with a finite analytical proof, but also things knowable by direct
sensation.

Thus, if you redefine "Provable" to include an infinite sequence of
steps, it becomes just a synonym for True, and we have lost the use of
it for its normal use, and need to replace it with something more
clumbsy like Analytically Knowable.

The claim you seem to want to make is that all Analytically True
statements are Anayltically Knowable, but that is a false statement.

You try to hide the error by redefining the words and saying that all
Analytical True statements are Provable, and implying that this means
Analytically Knowable, but that is wrong because you are using
incompatible meanings of Provable.

You need to actually DEFINE what you mean by your terms, and any term
that doesn't mean what it means what it actually means in classical
logic can not use any of the results from classical logic.

You seem to want to change the foundation, but then expect that the
whole structure built on it will stay mostly the same. That is a false
assumption. If you change the base, you need to work up from that base
and see what changes above it, but going through ALL the steps,
especially those that depend on the things you have changed, to see what
actually changes.

Many of your ideas you think of as "New" are not really new, just you
have failed to see their use in the past. They might not have used your
names, but they did use the same base ideas. The limitations of these
ideas have been long established.

On 12/30/2022 11:56 AM, Richard Damon wrote:
> On 12/30/22 11:30 AM, olcott wrote:
>> On 12/30/2022 10:15 AM, Richard Damon wrote:
>
>>> But the existance of ONLY an infinite sequence of semantic
>>> connections for a sentence make it True but Unprovable.
>>>
>>> Thus your idea that all Truth is Provable is debunked, and you are
>>> shown to be an idiot.
>>>
>>
>> My prior claim that every true statement must be provable is either
>> qualified to allow infinite proofs or changed to refer to semantic
>> connections that may be finite or infinite.
>
> If you allow your "Proof" to be infinite, then you have broken the link
> between provable and knowable, and have left the language that everyone
> else is talking.
>

You and I already know that the possibility that an expression of
language can only be confirmed as true by an infinite proof then the
link between true and knowable was already broken.

> Since some Semantic Statement DO require an infinite set of semantic
> connections, but knowable requries a finite set of semantic connections,
> we have that there exsits some statements that are True but not
> knowable, and thus not Provable by the classical definition.
>

When infinite proofs are required to verify the truth of an expression
of language and formal systems are not allowed to have infinite proofs
then unprovable in no way means that the formal system is in any way
incomplete.

>>
>> Thus an expression of language is never true unless it is connected to
>> its truth maker.
>>
>
> Right, but that connection might not be knowable, because it is
> infinite, and thus not provable by the classical meaning.
>

Yet formal systems that are not allowed to have infinite proofs cannot
be called "incomplete" because they lack an infinite proof.

> If you redefine your idea of "Proof" to include "infinite proofs" you
> have just made you logic system incompatible with ALL standard logic
> that requires it to be finite, so you need to restart at the begining.
>

We can simply use my semantic version instead: True(x) ↔ (⊨x).

> You are going to need to define SOMETHING, to indicate actually knowable
> due to having a finite proof. Knowable isn't actually a good word for
> this, as we often want to include in knowable not just things proven
> with a finite analytical proof, but also things knowable by direct
> sensation.
>
> Thus, if you redefine "Provable" to include an infinite sequence of
> steps, it becomes just a synonym for True, and we have lost the use of
> it for its normal use, and need to replace it with something more
> clumbsy like Analytically Knowable.
>
>
> The claim you seem to want to make is that all Analytically True
> statements are Anayltically Knowable, but that is a false statement.
>
> You try to hide the error by redefining the words and saying that all
> Analytical True statements are Provable, and implying that this means
> Analytically Knowable, but that is wrong because you are using
> incompatible meanings of Provable.

All analytically true statements have a semantic connection to their
truth maker.

>
> You need to actually DEFINE what you mean by your terms, and any term
> that doesn't mean what it means what it actually means in classical
> logic can not use any of the results from classical logic.
>

Hence my new idea of semantic connections using a knowledge ontology
instead of model theory.

> You seem to want to change the foundation, but then expect that the
> whole structure built on it will stay mostly the same. That is a false
> assumption. If you change the base, you need to work up from that base
> and see what changes above it, but going through ALL the steps,
> especially those that depend on the things you have changed, to see what
> actually changes.
>

True(x) requires semantic connections to its truth maker, else we have
~True(x) or False(x). Semantically incoherent expressions of language
(such as the Liar Paradox) are neither true nor false.

> Many of your ideas you think of as "New" are not really new, just you
> have failed to see their use in the past. They might not have used your
> names, but they did use the same base ideas. The limitations of these
> ideas have been long established.

I have shown that Tarski Undefinability and Gödel Incompleteness are
incorrect. Tarski "proved" that the Liar Paradox is true and we both
know that it is not true so Tarski goofed.

Because Gödel Incompleteness is an exact isomorphism to Tarski
Undefinability the refutation of one is a refutation of both.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/30/22 6:04 PM, olcott wrote:
> On 12/30/2022 11:56 AM, Richard Damon wrote:
>> On 12/30/22 11:30 AM, olcott wrote:
>>> On 12/30/2022 10:15 AM, Richard Damon wrote:
>>
>>>> But the existance of ONLY an infinite sequence of semantic
>>>> connections for a sentence make it True but Unprovable.
>>>>
>>>> Thus your idea that all Truth is Provable is debunked, and you are
>>>> shown to be an idiot.
>>>>
>>>
>>> My prior claim that every true statement must be provable is either
>>> qualified to allow infinite proofs or changed to refer to semantic
>>> connections that may be finite or infinite.
>>
>> If you allow your "Proof" to be infinite, then you have broken the
>> link between provable and knowable, and have left the language that
>> everyone else is talking.
>>
>
> You and I already know that the possibility that an expression of
> language can only be confirmed as true by an infinite proof then the
> link between true and knowable was already broken.

Right, which means that there are some things that are True that are
unknowable.

>
>> Since some Semantic Statement DO require an infinite set of semantic
>> connections, but knowable requries a finite set of semantic
>> connections, we have that there exsits some statements that are True
>> but not knowable, and thus not Provable by the classical definition.
>>
>
> When infinite proofs are required to verify the truth of an expression
> of language and formal systems are not allowed to have infinite proofs
> then unprovable in no way means that the formal system is in any way
> incomplete.

WRONG. The DEFINITION of "Incomplete" is that there exist statements
that are True that can not be Prove, with the definition of Provable
being a Finite Proof.

In your modified terminology, Incompletenesss is DEFINED as the
existance of statements that are Analytically True but are Unknowable.

THAT IS DEFINITION.

>
>>>
>>> Thus an expression of language is never true unless it is connected to
>>> its truth maker.
>>>
>>
>> Right, but that connection might not be knowable, because it is
>> infinite, and thus not provable by the classical meaning.
>>
>
> Yet formal systems that are not allowed to have infinite proofs cannot
> be called "incomplete" because they lack an infinite proof.

But that is the DEFINTION of the Term.

>
>> If you redefine your idea of "Proof" to include "infinite proofs" you
>> have just made you logic system incompatible with ALL standard logic
>> that requires it to be finite, so you need to restart at the begining.
>>
>
> We can simply use my semantic version instead: True(x) ↔ (⊨x).

So, start with your restart and see what you get. Make sure you fully
document you other definitions and axioms as you go.

In particular, do you plan to redefine the implication operator?

Note currently A -> B means that for every model where A is true, B is
also true, even if that truth of B is not directly connected to the
Truth of A.

Note, PROVING a statement like A -> B, without knowing the actual truth
of A or B, will require building such a direct connection.

>
>> You are going to need to define SOMETHING, to indicate actually
>> knowable due to having a finite proof. Knowable isn't actually a good
>> word for this, as we often want to include in knowable not just things
>> proven with a finite analytical proof, but also things knowable by
>> direct sensation.
>>
>> Thus, if you redefine "Provable" to include an infinite sequence of
>> steps, it becomes just a synonym for True, and we have lost the use of
>> it for its normal use, and need to replace it with something more
>> clumbsy like Analytically Knowable.
>>
>>
>> The claim you seem to want to make is that all Analytically True
>> statements are Anayltically Knowable, but that is a false statement.
>>
>> You try to hide the error by redefining the words and saying that all
>> Analytical True statements are Provable, and implying that this means
>> Analytically Knowable, but that is wrong because you are using
>> incompatible meanings of Provable.
>
> All analytically true statements have a semantic connection to their
> truth maker.

Ok. But I don't think that actually establishs what you are trying to
make it establish.

>
>>
>> You need to actually DEFINE what you mean by your terms, and any term
>> that doesn't mean what it means what it actually means in classical
>> logic can not use any of the results from classical logic.
>>
>
> Hence my new idea of semantic connections using a knowledge ontology
> instead of model theory.

So DO IT. Of course, changing the base means you have to redo EVERYTHING
to see what survives.

Ultimately, my guess is you will find that with the restrictions you are
talking about, you are going to find that you logic system is not able
to handle much of the current logic families, but you system is just
going to put them outside what it can show.

That, or you system is going to fall into a massive mess of
inconsistencies because you fail to guard against it, and you ego is
unable to see these problems.

>
>> You seem to want to change the foundation, but then expect that the
>> whole structure built on it will stay mostly the same. That is a false
>> assumption. If you change the base, you need to work up from that base
>> and see what changes above it, but going through ALL the steps,
>> especially those that depend on the things you have changed, to see
>> what actually changes.
>>
>
> True(x) requires semantic connections to its truth maker, else we have
> ~True(x) or False(x). Semantically incoherent expressions of language
> (such as the Liar Paradox) are neither true nor false.

Ok, so what.

It is accept that statements like the Liar's paradox are not truth holders.

The problem is that it is absolutely TRUE that Some True Statements are
Unknowable in a sufficently powerful logic system (and that sufficently
powerful is a fairly low hurdle).

You can't just try to make that statems be just the same as the Liar's
Paradox, because they aren't.

It is a fundamental property of Knowable/Provable for systems of any
reasonable power.

>
>> Many of your ideas you think of as "New" are not really new, just you
>> have failed to see their use in the past. They might not have used
>> your names, but they did use the same base ideas. The limitations of
>> these ideas have been long established.
>
> I have shown that Tarski Undefinability and Gödel Incompleteness are
> incorrect. Tarski "proved" that the Liar Paradox is true and we both
> know that it is not true so Tarski goofed.

No, you haven't.

You just don't understand his proof.

The fact is that Tarski PROVED (not in quotes) that the Liar's Paradox
is True IF A DEFINITION OF TRUTH EXISTS, this is actually proof that no
such definitio of truth can exist.

Unless you find an actual ERROR in his proof, you haven't established
anything but to confirm his proof.

Note, you probably need to look at the AcTUAL PROOF he gives, not just
the short summary you quote. Yes, that summary is not in itself a proof,
but references that actual proof that has been firmly established.

This seems to be a common error of yours, you don't read the actual
proof (probalby because it is too complicated for you since you admit
you have avoid formal study of the field) so you can't actually come up
with a refutatioh of the proof, so you just say it must be wrong.

In actuality YOU must certainly be wrong, since you are the one claiming
something without proof that is contradicted by an actual vetted proof.

>
> Because Gödel Incompleteness is an exact isomorphism to Tarski
> Undefinability the refutation of one is a refutation of both.
>
>

Which you haven't done, because it seems you don't understand what
either one is doing, in part because it seems you don't actually
understand how logic works.

Note, one error in your logic is that if we have a statement A which we
have proven true by some finite series of connections, then we can, by
the definition of the terms, state that

B -> A is True.

Note, even though B doesn't have a semantic connection to A, the
implication operator is always correct here, as A has been proven to be
True.

Simerly, if B has been proven to never be true, then the statement

B -> C is also True

On 12/30/2022 7:09 PM, Richard Damon wrote:
> On 12/30/22 6:04 PM, olcott wrote:
>> On 12/30/2022 11:56 AM, Richard Damon wrote:
>>> On 12/30/22 11:30 AM, olcott wrote:
>>>> On 12/30/2022 10:15 AM, Richard Damon wrote:
>>>
>>>>> But the existance of ONLY an infinite sequence of semantic
>>>>> connections for a sentence make it True but Unprovable.
>>>>>
>>>>> Thus your idea that all Truth is Provable is debunked, and you are
>>>>> shown to be an idiot.
>>>>>
>>>>
>>>> My prior claim that every true statement must be provable is either
>>>> qualified to allow infinite proofs or changed to refer to semantic
>>>> connections that may be finite or infinite.
>>>
>>> If you allow your "Proof" to be infinite, then you have broken the
>>> link between provable and knowable, and have left the language that
>>> everyone else is talking.
>>>
>>
>> You and I already know that the possibility that an expression of
>> language can only be confirmed as true by an infinite proof then the
>> link between true and knowable was already broken.
>
> Right, which means that there are some things that are True that are
> unknowable.
>
>>
>>> Since some Semantic Statement DO require an infinite set of semantic
>>> connections, but knowable requries a finite set of semantic
>>> connections, we have that there exsits some statements that are True
>>> but not knowable, and thus not Provable by the classical definition.
>>>
>>
>> When infinite proofs are required to verify the truth of an expression
>> of language and formal systems are not allowed to have infinite proofs
>> then unprovable in no way means that the formal system is in any way
>> incomplete.
>
> WRONG. The DEFINITION of "Incomplete" is that there exist statements
> that are True that can not be Prove, with the definition of Provable
> being a Finite Proof.
>
> In your modified terminology, Incompletenesss is DEFINED as the
> existance of statements that are Analytically True but are Unknowable.
>
> THAT IS DEFINITION.

In other words you are saying that unless a formal system violates its
own definition and performs an infinite proof then the formal system is
incomplete.

>
>>
>>>>
>>>> Thus an expression of language is never true unless it is connected to
>>>> its truth maker.
>>>>
>>>
>>> Right, but that connection might not be knowable, because it is
>>> infinite, and thus not provable by the classical meaning.
>>>
>>
>> Yet formal systems that are not allowed to have infinite proofs cannot
>> be called "incomplete" because they lack an infinite proof.
>
> But that is the DEFINTION of the Term.

That definition is incoherent. It is like saying that apples are
incomplete because they are not oranges.

>>
>>> If you redefine your idea of "Proof" to include "infinite proofs" you
>>> have just made you logic system incompatible with ALL standard logic
>>> that requires it to be finite, so you need to restart at the begining.
>>>
>>
>> We can simply use my semantic version instead: True(x) ↔ (⊨x).
>
> So, start with your restart and see what you get. Make sure you fully
> document you other definitions and axioms as you go.
>
> In particular, do you plan to redefine the implication operator?

I am only specifying the natural preexisting way that analytical truth
really works.

>
> Note currently A -> B means that for every model where A is true, B is
> also true, even if that truth of B is not directly connected to the
> Truth of A.
>

That is an error. To say that
cows give milk implies the grass is purple
is false at the semantic level, thus not a truth preserving operation.

> Note, PROVING a statement like A -> B, without knowing the actual truth
> of A or B, will require building such a direct connection.
>
>>
>>> You are going to need to define SOMETHING, to indicate actually
>>> knowable due to having a finite proof. Knowable isn't actually a good
>>> word for this, as we often want to include in knowable not just
>>> things proven with a finite analytical proof, but also things
>>> knowable by direct sensation.
>>>
>>> Thus, if you redefine "Provable" to include an infinite sequence of
>>> steps, it becomes just a synonym for True, and we have lost the use
>>> of it for its normal use, and need to replace it with something more
>>> clumbsy like Analytically Knowable.
>>>
>>>
>>> The claim you seem to want to make is that all Analytically True
>>> statements are Anayltically Knowable, but that is a false statement.
>>>
>>> You try to hide the error by redefining the words and saying that all
>>> Analytical True statements are Provable, and implying that this means
>>> Analytically Knowable, but that is wrong because you are using
>>> incompatible meanings of Provable.
>>
>> All analytically true statements have a semantic connection to their
>> truth maker.
>
> Ok. But I don't think that actually establishs what you are trying to
> make it establish.
>

It does, I spent 25 years on this and can finally say it succinctly.

>>
>>>
>>> You need to actually DEFINE what you mean by your terms, and any term
>>> that doesn't mean what it means what it actually means in classical
>>> logic can not use any of the results from classical logic.
>>>
>>
>> Hence my new idea of semantic connections using a knowledge ontology
>> instead of model theory.
>
> So DO IT. Of course, changing the base means you have to redo EVERYTHING
> to see what survives.
>

I am not going to write down every element of the set of all analytic
knowledge. True(x) ↔ (⊨x) has the set of all known and unknown analytic
truth as its formal system.

> Ultimately, my guess is you will find that with the restrictions you are
> talking about, you are going to find that you logic system is not able
> to handle much of the current logic families, but you system is just
> going to put them outside what it can show.
>

The set of analytic knowledge can show everything that is analytically
known.

> That, or you system is going to fall into a massive mess of
> inconsistencies because you fail to guard against it, and you ego is
> unable to see these problems.
>

Expressions of language that are not coherently linked to the set of
analytic knowledge are not members of this set.

>>
>>> You seem to want to change the foundation, but then expect that the
>>> whole structure built on it will stay mostly the same. That is a
>>> false assumption. If you change the base, you need to work up from
>>> that base and see what changes above it, but going through ALL the
>>> steps, especially those that depend on the things you have changed,
>>> to see what actually changes.
>>>
>>
>> True(x) requires semantic connections to its truth maker, else we have
>> ~True(x) or False(x). Semantically incoherent expressions of language
>> (such as the Liar Paradox) are neither true nor false.
>
> Ok, so what.
>

Tarski's undefinability theorem fails. He claimed to have proved an
incoherent expression of language is true, that is ridiculous.

> It is accept that statements like the Liar's paradox are not truth holders.
>

Tarski claimed to have proved that it is true, what a nut.

> The problem is that it is absolutely TRUE that Some True Statements are
> Unknowable in a sufficently powerful logic system (and that sufficently
> powerful is a fairly low hurdle).
>

We cannot possibly correctly say that some statements are unknowable
until we can prove that no finite proofs exist. Until then they are
simply unknown.

> You can't just try to make that statems be just the same as the Liar's
> Paradox, because they aren't.
>

Gödel himself implied that his logic sentence is isomorphic to the liar
paradox.

> It is a fundamental property of Knowable/Provable for systems of any
> reasonable power.
>

Gödel said that any epistemological antinomy will do, thus he limited
his proof to be based only on self-contradictory expressions of
language.

On 12/30/22 11:06 PM, olcott wrote:
> On 12/30/2022 7:09 PM, Richard Damon wrote:
>> On 12/30/22 6:04 PM, olcott wrote:
>>> On 12/30/2022 11:56 AM, Richard Damon wrote:
>>>> On 12/30/22 11:30 AM, olcott wrote:
>>>>> On 12/30/2022 10:15 AM, Richard Damon wrote:
>>>>
>>>>>> But the existance of ONLY an infinite sequence of semantic
>>>>>> connections for a sentence make it True but Unprovable.
>>>>>>
>>>>>> Thus your idea that all Truth is Provable is debunked, and you are
>>>>>> shown to be an idiot.
>>>>>>
>>>>>
>>>>> My prior claim that every true statement must be provable is either
>>>>> qualified to allow infinite proofs or changed to refer to semantic
>>>>> connections that may be finite or infinite.
>>>>
>>>> If you allow your "Proof" to be infinite, then you have broken the
>>>> link between provable and knowable, and have left the language that
>>>> everyone else is talking.
>>>>
>>>
>>> You and I already know that the possibility that an expression of
>>> language can only be confirmed as true by an infinite proof then the
>>> link between true and knowable was already broken.
>>
>> Right, which means that there are some things that are True that are
>> unknowable.
>>
>>>
>>>> Since some Semantic Statement DO require an infinite set of semantic
>>>> connections, but knowable requries a finite set of semantic
>>>> connections, we have that there exsits some statements that are True
>>>> but not knowable, and thus not Provable by the classical definition.
>>>>
>>>
>>> When infinite proofs are required to verify the truth of an expression
>>> of language and formal systems are not allowed to have infinite proofs
>>> then unprovable in no way means that the formal system is in any way
>>> incomplete.
>>
>> WRONG. The DEFINITION of "Incomplete" is that there exist statements
>> that are True that can not be Prove, with the definition of Provable
>> being a Finite Proof.
>>
>> In your modified terminology, Incompletenesss is DEFINED as the
>> existance of statements that are Analytically True but are Unknowable.
>>
>> THAT IS DEFINITION.
>
> In other words you are saying that unless a formal system violates its
> own definition and performs an infinite proof then the formal system is
> incomplete.
>

No, a formal system simple enough to be able to prove all true
statements in it is what is defined as "Complete".

It just turns out that most usable systems are incomplete, because it
turns out they are expressive enough to create Truth that can't be proven.

Nothing wrong with being "Incomplete" by this definition,

What the systems lack, is the ability to prove every true statement.

What is wrong with that?

Somehow you seem to not understand the meaning of that statement.

>>
>>>
>>>>>
>>>>> Thus an expression of language is never true unless it is connected to
>>>>> its truth maker.
>>>>>
>>>>
>>>> Right, but that connection might not be knowable, because it is
>>>> infinite, and thus not provable by the classical meaning.
>>>>
>>>
>>> Yet formal systems that are not allowed to have infinite proofs
>>> cannot be called "incomplete" because they lack an infinite proof.
>>
>> But that is the DEFINTION of the Term.
>
> That definition is incoherent. It is like saying that apples are
> incomplete because they are not oranges.

Nope, just means you don't understand the concept that it is talking about.

I suspect the issue is you are trying to use a colloqual English meaning
for the word in your mind instead of its actual Technical Meaning in the
Field.

Apples are logic systems, so this definition doesn't apply to them.

Maybe a better analogy would be that a grape that grew without seeds in
it could be considered incomplete because it is missing something that
was expected, and needed for the fruit to reproduce itself.

It just turns out that for grapes, this can be a FEATURE, not a defect.

In the same way, logic systems that are incomplete, are lacking a useful
feature, the ability to prove all truth statements in them, but come
with the advantage of being able to express concepts that can't be done
when you limit yourself to logic that allows all truths to be proven.

>
>>>
>>>> If you redefine your idea of "Proof" to include "infinite proofs"
>>>> you have just made you logic system incompatible with ALL standard
>>>> logic that requires it to be finite, so you need to restart at the
>>>> begining.
>>>>
>>>
>>> We can simply use my semantic version instead: True(x) ↔ (⊨x).
>>
>> So, start with your restart and see what you get. Make sure you fully
>> document you other definitions and axioms as you go.
>>
>> In particular, do you plan to redefine the implication operator?
>
> I am only specifying the natural preexisting way that analytical truth
> really works.

So you accept that it is a True Statement that "Unicorns being purple
implies that the world is flat".

>
>>
>> Note currently A -> B means that for every model where A is true, B is
>> also true, even if that truth of B is not directly connected to the
>> Truth of A.
>>
>
> That is an error. To say that
> cows give milk implies the grass is purple
> is false at the semantic level, thus not a truth preserving operation.

How is your example a proper counter to my statement?

Since it is not true that in every model where "Cows give milk" is true
that "Grass is purple" is true, that statement fails the definition of a
valid implication.

You are just showing you don't understand what you are talking about.

Are you saying that you are BANNING the implication operator because all
of the following are valid implications?

True -> True
False -> False
False -> True

and only if there is a case of

True -> False

is the implication invalid?

Good luck trying to develop your logic system if you remove the
implication operator from your system.

>
>> Note, PROVING a statement like A -> B, without knowing the actual
>> truth of A or B, will require building such a direct connection.
>>
>>>
>>>> You are going to need to define SOMETHING, to indicate actually
>>>> knowable due to having a finite proof. Knowable isn't actually a
>>>> good word for this, as we often want to include in knowable not just
>>>> things proven with a finite analytical proof, but also things
>>>> knowable by direct sensation.
>>>>
>>>> Thus, if you redefine "Provable" to include an infinite sequence of
>>>> steps, it becomes just a synonym for True, and we have lost the use
>>>> of it for its normal use, and need to replace it with something more
>>>> clumbsy like Analytically Knowable.
>>>>
>>>>
>>>> The claim you seem to want to make is that all Analytically True
>>>> statements are Anayltically Knowable, but that is a false statement.
>>>>
>>>> You try to hide the error by redefining the words and saying that
>>>> all Analytical True statements are Provable, and implying that this
>>>> means Analytically Knowable, but that is wrong because you are using
>>>> incompatible meanings of Provable.
>>>
>>> All analytically true statements have a semantic connection to their
>>> truth maker.
>>
>> Ok. But I don't think that actually establishs what you are trying to
>> make it establish.
>>
>
> It does, I spent 25 years on this and can finally say it succinctly.

Then do so.

>
>>>
>>>>
>>>> You need to actually DEFINE what you mean by your terms, and any
>>>> term that doesn't mean what it means what it actually means in
>>>> classical logic can not use any of the results from classical logic.
>>>>
>>>
>>> Hence my new idea of semantic connections using a knowledge ontology
>>> instead of model theory.
>>
>> So DO IT. Of course, changing the base means you have to redo
>> EVERYTHING to see what survives.
>>
>
> I am not going to write down every element of the set of all analytic
> knowledge. True(x) ↔ (⊨x) has the set of all known and unknown analytic
> truth as its formal system.

On 12/30/2022 11:05 PM, Richard Damon wrote:
> On 12/30/22 11:06 PM, olcott wrote:
>> On 12/30/2022 7:09 PM, Richard Damon wrote:
>>> On 12/30/22 6:04 PM, olcott wrote:
>>>> On 12/30/2022 11:56 AM, Richard Damon wrote:
>>>>> On 12/30/22 11:30 AM, olcott wrote:
>>>>>> On 12/30/2022 10:15 AM, Richard Damon wrote:
>>>>>
>>>>>>> But the existance of ONLY an infinite sequence of semantic
>>>>>>> connections for a sentence make it True but Unprovable.
>>>>>>>
>>>>>>> Thus your idea that all Truth is Provable is debunked, and you
>>>>>>> are shown to be an idiot.
>>>>>>>
>>>>>>
>>>>>> My prior claim that every true statement must be provable is either
>>>>>> qualified to allow infinite proofs or changed to refer to semantic
>>>>>> connections that may be finite or infinite.
>>>>>
>>>>> If you allow your "Proof" to be infinite, then you have broken the
>>>>> link between provable and knowable, and have left the language that
>>>>> everyone else is talking.
>>>>>
>>>>
>>>> You and I already know that the possibility that an expression of
>>>> language can only be confirmed as true by an infinite proof then the
>>>> link between true and knowable was already broken.
>>>
>>> Right, which means that there are some things that are True that are
>>> unknowable.
>>>
>>>>
>>>>> Since some Semantic Statement DO require an infinite set of
>>>>> semantic connections, but knowable requries a finite set of
>>>>> semantic connections, we have that there exsits some statements
>>>>> that are True but not knowable, and thus not Provable by the
>>>>> classical definition.
>>>>>
>>>>
>>>> When infinite proofs are required to verify the truth of an expression
>>>> of language and formal systems are not allowed to have infinite proofs
>>>> then unprovable in no way means that the formal system is in any way
>>>> incomplete.
>>>
>>> WRONG. The DEFINITION of "Incomplete" is that there exist statements
>>> that are True that can not be Prove, with the definition of Provable
>>> being a Finite Proof.
>>>
>>> In your modified terminology, Incompletenesss is DEFINED as the
>>> existance of statements that are Analytically True but are Unknowable.
>>>
>>> THAT IS DEFINITION.
>>
>> In other words you are saying that unless a formal system violates its
>> own definition and performs an infinite proof then the formal system
>> is incomplete.
>>
>
> No, a formal system simple enough to be able to prove all true
> statements in it is what is defined as "Complete".

Gödel said this in his footnote 14
14 Every epistemological antinomy can likewise be used for a similar
undecidability proof

Every Epistemological antinomy is untrue thus when Gödel and Tarski
proved that they are true they both erred.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/31/22 9:19 AM, olcott wrote:
> On 12/30/2022 11:05 PM, Richard Damon wrote:
>> On 12/30/22 11:06 PM, olcott wrote:
>>> On 12/30/2022 7:09 PM, Richard Damon wrote:
>>>> On 12/30/22 6:04 PM, olcott wrote:
>>>>> On 12/30/2022 11:56 AM, Richard Damon wrote:
>>>>>> On 12/30/22 11:30 AM, olcott wrote:
>>>>>>> On 12/30/2022 10:15 AM, Richard Damon wrote:
>>>>>>
>>>>>>>> But the existance of ONLY an infinite sequence of semantic
>>>>>>>> connections for a sentence make it True but Unprovable.
>>>>>>>>
>>>>>>>> Thus your idea that all Truth is Provable is debunked, and you
>>>>>>>> are shown to be an idiot.
>>>>>>>>
>>>>>>>
>>>>>>> My prior claim that every true statement must be provable is either
>>>>>>> qualified to allow infinite proofs or changed to refer to semantic
>>>>>>> connections that may be finite or infinite.
>>>>>>
>>>>>> If you allow your "Proof" to be infinite, then you have broken the
>>>>>> link between provable and knowable, and have left the language
>>>>>> that everyone else is talking.
>>>>>>
>>>>>
>>>>> You and I already know that the possibility that an expression of
>>>>> language can only be confirmed as true by an infinite proof then the
>>>>> link between true and knowable was already broken.
>>>>
>>>> Right, which means that there are some things that are True that are
>>>> unknowable.
>>>>
>>>>>
>>>>>> Since some Semantic Statement DO require an infinite set of
>>>>>> semantic connections, but knowable requries a finite set of
>>>>>> semantic connections, we have that there exsits some statements
>>>>>> that are True but not knowable, and thus not Provable by the
>>>>>> classical definition.
>>>>>>
>>>>>
>>>>> When infinite proofs are required to verify the truth of an expression
>>>>> of language and formal systems are not allowed to have infinite proofs
>>>>> then unprovable in no way means that the formal system is in any way
>>>>> incomplete.
>>>>
>>>> WRONG. The DEFINITION of "Incomplete" is that there exist statements
>>>> that are True that can not be Prove, with the definition of Provable
>>>> being a Finite Proof.
>>>>
>>>> In your modified terminology, Incompletenesss is DEFINED as the
>>>> existance of statements that are Analytically True but are Unknowable.
>>>>
>>>> THAT IS DEFINITION.
>>>
>>> In other words you are saying that unless a formal system violates
>>> its own definition and performs an infinite proof then the formal
>>> system is incomplete.
>>>
>>
>> No, a formal system simple enough to be able to prove all true
>> statements in it is what is defined as "Complete".
>
> Gödel said this in his footnote 14
> 14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof
>
> Every Epistemological antinomy is untrue thus when Gödel and Tarski
> proved that they are true they both erred.
>

And you still show that you do not understand that Godel didn't use the
Liar's Paradox in its Paradoxial form in his proof, but transformed it
from a statement about Truth to a statement about Provability.

Such Transforms converts a statement that is self-contradictory into a
statement that must be a Truth Bearer, BECAUSE all statements, whether
Truth Bearers or Not either Have a Proof, and thus is Provable, or do
not have a Proof, and thus Not Provable, and thus a statement about the
Provability of a Statement is ALWAYS a Truth Bearer.

You mind just seems too small to understand this.

On 12/31/2022 9:33 AM, Richard Damon wrote:
> On 12/31/22 9:19 AM, olcott wrote:
>> On 12/30/2022 11:05 PM, Richard Damon wrote:
>>> On 12/30/22 11:06 PM, olcott wrote:
>>>> On 12/30/2022 7:09 PM, Richard Damon wrote:
>>>>> On 12/30/22 6:04 PM, olcott wrote:
>>>>>> On 12/30/2022 11:56 AM, Richard Damon wrote:
>>>>>>> On 12/30/22 11:30 AM, olcott wrote:
>>>>>>>> On 12/30/2022 10:15 AM, Richard Damon wrote:
>>>>>>>
>>>>>>>>> But the existance of ONLY an infinite sequence of semantic
>>>>>>>>> connections for a sentence make it True but Unprovable.
>>>>>>>>>
>>>>>>>>> Thus your idea that all Truth is Provable is debunked, and you
>>>>>>>>> are shown to be an idiot.
>>>>>>>>>
>>>>>>>>
>>>>>>>> My prior claim that every true statement must be provable is either
>>>>>>>> qualified to allow infinite proofs or changed to refer to semantic
>>>>>>>> connections that may be finite or infinite.
>>>>>>>
>>>>>>> If you allow your "Proof" to be infinite, then you have broken
>>>>>>> the link between provable and knowable, and have left the
>>>>>>> language that everyone else is talking.
>>>>>>>
>>>>>>
>>>>>> You and I already know that the possibility that an expression of
>>>>>> language can only be confirmed as true by an infinite proof then the
>>>>>> link between true and knowable was already broken.
>>>>>
>>>>> Right, which means that there are some things that are True that
>>>>> are unknowable.
>>>>>
>>>>>>
>>>>>>> Since some Semantic Statement DO require an infinite set of
>>>>>>> semantic connections, but knowable requries a finite set of
>>>>>>> semantic connections, we have that there exsits some statements
>>>>>>> that are True but not knowable, and thus not Provable by the
>>>>>>> classical definition.
>>>>>>>
>>>>>>
>>>>>> When infinite proofs are required to verify the truth of an
>>>>>> expression
>>>>>> of language and formal systems are not allowed to have infinite
>>>>>> proofs
>>>>>> then unprovable in no way means that the formal system is in any way
>>>>>> incomplete.
>>>>>
>>>>> WRONG. The DEFINITION of "Incomplete" is that there exist
>>>>> statements that are True that can not be Prove, with the definition
>>>>> of Provable being a Finite Proof.
>>>>>
>>>>> In your modified terminology, Incompletenesss is DEFINED as the
>>>>> existance of statements that are Analytically True but are Unknowable.
>>>>>
>>>>> THAT IS DEFINITION.
>>>>
>>>> In other words you are saying that unless a formal system violates
>>>> its own definition and performs an infinite proof then the formal
>>>> system is incomplete.
>>>>
>>>
>>> No, a formal system simple enough to be able to prove all true
>>> statements in it is what is defined as "Complete".
>>
>> Gödel said this in his footnote 14
>> 14 Every epistemological antinomy can likewise be used for a similar
>> undecidability proof
>>
>> Every Epistemological antinomy is untrue thus when Gödel and Tarski
>> proved that they are true they both erred.
>>
>
> And you still show that you do not understand that Godel didn't use the
> Liar's Paradox in its Paradoxial form in his proof, but transformed it
> from a statement about Truth to a statement about Provability.
>

He claimed that he could have used any Epistemological antinomy such as
the Liar Paradox that Tarski used, thus the two-page Tarski proof forms
and isomorphism to his proof.

> Such Transforms converts a statement that is self-contradictory into a
> statement that must be a Truth Bearer,

The Liar Paradox basis of the Tarski Undefinability Theorem
https://liarparadox.org/Tarski_247_248.pdf

The Tarski Undefinability Theorem
https://liarparadox.org/Tarski_275_276.pdf

這句話不是真的: "This sentence is not true."
The Chinese says "This sentence is not true:" referring to the English.
The Chinese sentence is true, The English sentence remains neither true
nor false because it is self-contradictory.

No need for Tarski's theory and metatheory the English/Chinese serve the
same function in a way that is much easier to understand.

The only reason that the Chinese sentence is true is because
pathological self-reference(Olcott 2004) has been removed. The only
reason why the English sentence is neither true nor false is because it
has pathological self-reference(Olcott 2004) (it is self-contradictory).

Tarski only proved that it is true that self-contradictory sentences are
not true. This is not at all the same thing as proving that truth is
undefinable.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/31/22 11:26 AM, olcott wrote:
> On 12/31/2022 9:33 AM, Richard Damon wrote:

>> And you still show that you do not understand that Godel didn't use
>> the Liar's Paradox in its Paradoxial form in his proof, but
>> transformed it from a statement about Truth to a statement about
>> Provability.
>>
>
> He claimed that he could have used any Epistemological antinomy such as
> the Liar Paradox that Tarski used, thus the two-page Tarski proof forms
> and isomorphism to his proof.

Which shows you still don't undertand what he did.

Yes, ANY Epistemolgical antimomy can be CONVERTED from a statement about
Truth, which makes it a non-truth bearer, into a similar statement about
provability, which MUST be a Truth Bearer, and forces the conclusion
that the statement must be True and Unprovable, because the opposite
condition, Provable but False is definitionally impossible.

>
>> Such Transforms converts a statement that is self-contradictory into a
>> statement that must be a Truth Bearer,
>
> The Liar Paradox basis of the Tarski Undefinability Theorem
> https://liarparadox.org/Tarski_247_248.pdf
>
> The Tarski Undefinability Theorem
> https://liarparadox.org/Tarski_275_276.pdf
>
> 這句話不是真的: "This sentence is not true."
> The Chinese says "This sentence is not true:" referring to the English.
> The Chinese sentence is true, The English sentence remains neither true
> nor false because it is self-contradictory.
>
> No need for Tarski's theory and metatheory the English/Chinese serve the
> same function in a way that is much easier to understand.
>
> The only reason that the Chinese sentence is true is because
> pathological self-reference(Olcott 2004) has been removed. The only
> reason why the English sentence is neither true nor false is because it
> has pathological self-reference(Olcott 2004) (it is self-contradictory).
>
> Tarski only proved that it is true that self-contradictory sentences are
> not true. This is not at all the same thing as proving that truth is
> undefinable.
>
>

Nope, you don't understand what he is doing.

You are just showing yourself to be incapable of understanding the logic.

Unless you point out an ACTAUL ERROR in a specific step of the ACTUAL
PROOF (not just the "Sketch" provided on that page) you are just showing
you don't know anything about what is being talked about,

All you have proved is that the logic system that you seem to be using
is broken, becaue you don't understand how logic actually works.

The fact that you say these pages show "The Proof" shows that you don't
actually understand what a proof is in a formal system. Those pages give
OUTLINE or SKETCHES of the proof, not the proof itself.

On 12/31/2022 10:42 AM, Richard Damon wrote:
> On 12/31/22 11:26 AM, olcott wrote:
>> On 12/31/2022 9:33 AM, Richard Damon wrote:
>
>>> And you still show that you do not understand that Godel didn't use
>>> the Liar's Paradox in its Paradoxial form in his proof, but
>>> transformed it from a statement about Truth to a statement about
>>> Provability.
>>>
>>
>> He claimed that he could have used any Epistemological antinomy such as
>> the Liar Paradox that Tarski used, thus the two-page Tarski proof forms
>> and isomorphism to his proof.
>
> Which shows you still don't undertand what he did.
>
> Yes, ANY Epistemolgical antimomy can be CONVERTED from a statement about
> Truth, which makes it a non-truth bearer, into a similar statement about
> provability, which MUST be a Truth Bearer, and forces the conclusion
> that the statement must be True and Unprovable, because the opposite
> condition, Provable but False is definitionally impossible.
>
>>
>>> Such Transforms converts a statement that is self-contradictory into
>>> a statement that must be a Truth Bearer,
>>
>> The Liar Paradox basis of the Tarski Undefinability Theorem
>> https://liarparadox.org/Tarski_247_248.pdf
>>
>> The Tarski Undefinability Theorem
>> https://liarparadox.org/Tarski_275_276.pdf
>>
>> 這句話不是真的: "This sentence is not true."
>> The Chinese says "This sentence is not true:" referring to the English.
>> The Chinese sentence is true, The English sentence remains neither
>> true nor false because it is self-contradictory.
>>
>> No need for Tarski's theory and metatheory the English/Chinese serve
>> the same function in a way that is much easier to understand.
>>
>> The only reason that the Chinese sentence is true is because
>> pathological self-reference(Olcott 2004) has been removed. The only
>> reason why the English sentence is neither true nor false is because it
>> has pathological self-reference(Olcott 2004) (it is self-contradictory).
>>
>> Tarski only proved that it is true that self-contradictory sentences
>> are not true. This is not at all the same thing as proving that truth
>> is undefinable.
>>
>>
>
> Nope, you don't understand what he is doing.
>
> You are just showing yourself to be incapable of understanding the logic.
>

It is not that I do not understand the logic it is that I understand it
so well that I can boil it down to its essence.

Tarski only proved that it is true that self-contradictory expressions
of language are not true.

This sentence is not true.
is not true because it is self-contradictory.

This sentence is not true: "This sentence is not true."
is true because it is not self-contradictory.

Tarski did not prove that some true expressions cannot be defined.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/31/22 12:10 PM, olcott wrote:
> On 12/31/2022 10:42 AM, Richard Damon wrote:
>> On 12/31/22 11:26 AM, olcott wrote:
>>> On 12/31/2022 9:33 AM, Richard Damon wrote:
>>
>>>> And you still show that you do not understand that Godel didn't use
>>>> the Liar's Paradox in its Paradoxial form in his proof, but
>>>> transformed it from a statement about Truth to a statement about
>>>> Provability.
>>>>
>>>
>>> He claimed that he could have used any Epistemological antinomy such as
>>> the Liar Paradox that Tarski used, thus the two-page Tarski proof forms
>>> and isomorphism to his proof.
>>
>> Which shows you still don't undertand what he did.
>>
>> Yes, ANY Epistemolgical antimomy can be CONVERTED from a statement
>> about Truth, which makes it a non-truth bearer, into a similar
>> statement about provability, which MUST be a Truth Bearer, and forces
>> the conclusion that the statement must be True and Unprovable, because
>> the opposite condition, Provable but False is definitionally impossible.
>>
>>>
>>>> Such Transforms converts a statement that is self-contradictory into
>>>> a statement that must be a Truth Bearer,
>>>
>>> The Liar Paradox basis of the Tarski Undefinability Theorem
>>> https://liarparadox.org/Tarski_247_248.pdf
>>>
>>> The Tarski Undefinability Theorem
>>> https://liarparadox.org/Tarski_275_276.pdf
>>>
>>> 這句話不是真的: "This sentence is not true."
>>> The Chinese says "This sentence is not true:" referring to the English.
>>> The Chinese sentence is true, The English sentence remains neither
>>> true nor false because it is self-contradictory.
>>>
>>> No need for Tarski's theory and metatheory the English/Chinese serve
>>> the same function in a way that is much easier to understand.
>>>
>>> The only reason that the Chinese sentence is true is because
>>> pathological self-reference(Olcott 2004) has been removed. The only
>>> reason why the English sentence is neither true nor false is because it
>>> has pathological self-reference(Olcott 2004) (it is self-contradictory).
>>>
>>> Tarski only proved that it is true that self-contradictory sentences
>>> are not true. This is not at all the same thing as proving that truth
>>> is undefinable.
>>>
>>>
>>
>> Nope, you don't understand what he is doing.
>>
>> You are just showing yourself to be incapable of understanding the logic.
>>
>
> It is not that I do not understand the logic it is that I understand it
> so well that I can boil it down to its essence.

But you understand it wrong. Your "Essence" isn't what it is saying,
because you just don't understand that meaning of the actual words being
used because your own vocabulary is incorrect when used in the system.

This is the flaw of the incorrect application of "First Principles"

>
> Tarski only proved that it is true that self-contradictory expressions
> of language are not true.
>

No, he proved that a definition of Truth can not exist in a system,
because if one did exist, then a self-contradictory expression (that
can't have a truth value) is True.

> This sentence is not true.
> is not true because it is self-contradictory.

Right, and thus there can not be a Definition of Truth in the system
because if there was, you could show that statement True.

>
> This sentence is not true: "This sentence is not true."
> is true because it is not self-contradictory.
>
> Tarski did not prove that some true expressions cannot be defined.
>
>

That wasn't what he was showing, he was showing that a definition of
Truth can not exist, that is, there can not be a test that lets us know
if any arbitrary sentence is true or false.

You are just showing you don't understand the very basics of the field
you claim to have working in for decades.

That shows your stupidity.

On 12/31/2022 12:16 PM, Richard Damon wrote:
> On 12/31/22 12:10 PM, olcott wrote:
>> On 12/31/2022 10:42 AM, Richard Damon wrote:
>>> On 12/31/22 11:26 AM, olcott wrote:
>>>> On 12/31/2022 9:33 AM, Richard Damon wrote:
>>>
>>>>> And you still show that you do not understand that Godel didn't use
>>>>> the Liar's Paradox in its Paradoxial form in his proof, but
>>>>> transformed it from a statement about Truth to a statement about
>>>>> Provability.
>>>>>
>>>>
>>>> He claimed that he could have used any Epistemological antinomy such as
>>>> the Liar Paradox that Tarski used, thus the two-page Tarski proof forms
>>>> and isomorphism to his proof.
>>>
>>> Which shows you still don't undertand what he did.
>>>
>>> Yes, ANY Epistemolgical antimomy can be CONVERTED from a statement
>>> about Truth, which makes it a non-truth bearer, into a similar
>>> statement about provability, which MUST be a Truth Bearer, and forces
>>> the conclusion that the statement must be True and Unprovable,
>>> because the opposite condition, Provable but False is definitionally
>>> impossible.
>>>
>>>>
>>>>> Such Transforms converts a statement that is self-contradictory
>>>>> into a statement that must be a Truth Bearer,
>>>>
>>>> The Liar Paradox basis of the Tarski Undefinability Theorem
>>>> https://liarparadox.org/Tarski_247_248.pdf
>>>>
>>>> The Tarski Undefinability Theorem
>>>> https://liarparadox.org/Tarski_275_276.pdf
>>>>
>>>> 這句話不是真的: "This sentence is not true."
>>>> The Chinese says "This sentence is not true:" referring to the English.
>>>> The Chinese sentence is true, The English sentence remains neither
>>>> true nor false because it is self-contradictory.
>>>>
>>>> No need for Tarski's theory and metatheory the English/Chinese serve
>>>> the same function in a way that is much easier to understand.
>>>>
>>>> The only reason that the Chinese sentence is true is because
>>>> pathological self-reference(Olcott 2004) has been removed. The only
>>>> reason why the English sentence is neither true nor false is because it
>>>> has pathological self-reference(Olcott 2004) (it is
>>>> self-contradictory).
>>>>
>>>> Tarski only proved that it is true that self-contradictory sentences
>>>> are not true. This is not at all the same thing as proving that
>>>> truth is undefinable.
>>>>
>>>>
>>>
>>> Nope, you don't understand what he is doing.
>>>
>>> You are just showing yourself to be incapable of understanding the
>>> logic.
>>>
>>
>> It is not that I do not understand the logic it is that I understand it
>> so well that I can boil it down to its essence.
>
> But you understand it wrong. Your "Essence" isn't what it is saying,
> because you just don't understand that meaning of the actual words being
> used because your own vocabulary is incorrect when used in the system.
>
> This is the flaw of the incorrect application of "First Principles"
>
>>
>> Tarski only proved that it is true that self-contradictory expressions
>> of language are not true.
>>
>
> No, he proved that a definition of Truth can not exist in a system,
> because if one did exist, then a self-contradictory expression (that
> can't have a truth value) is True.
>
>> This sentence is not true.
>> is not true because it is self-contradictory.
>
> Right, and thus there can not be a Definition of Truth in the system
> because if there was, you could show that statement True.

這句話不是真的: "This sentence is not true."
The Chinese says "This sentence is not true:" referring to the English.

The Chinese sentence is true because the English sentence is
self-contradictory. This is an exact isomorphism to:

"sentence x which is undecidable in the original theory [my English]
becomes a decidable sentence in the enriched theory [my Chinese]."

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/31/22 1:34 PM, olcott wrote:
> On 12/31/2022 12:16 PM, Richard Damon wrote:
>> On 12/31/22 12:10 PM, olcott wrote:
>>
>>> This sentence is not true.
>>> is not true because it is self-contradictory.
>>
>> Right, and thus there can not be a Definition of Truth in the system
>> because if there was, you could show that statement True.
>
> 這句話不是真的: "This sentence is not true."
> The Chinese says "This sentence is not true:" referring to the English.
>
> The Chinese sentence is true because the English sentence is
> self-contradictory. This is an exact isomorphism to:
>
>   "sentence x which is undecidable in the original theory [my English]
>    becomes a decidable sentence in the enriched theory [my Chinese]."
>

Which is a non-sequitor, showing you don't understand what you are
talking about.

You are just proving your Stupidity.

I don't think you even actually understand any of the basics of logic.

You can parrot words, but you show an utter lack of knowledge about how
any of it works.

On 12/31/2022 1:07 PM, Richard Damon wrote:
> On 12/31/22 1:34 PM, olcott wrote:
>> On 12/31/2022 12:16 PM, Richard Damon wrote:
>>> On 12/31/22 12:10 PM, olcott wrote:
>>>
>>>> This sentence is not true.
>>>> is not true because it is self-contradictory.
>>>
>>> Right, and thus there can not be a Definition of Truth in the system
>>> because if there was, you could show that statement True.
>>
>> 這句話不是真的: "This sentence is not true."
>> The Chinese says "This sentence is not true:" referring to the English.
>>
>> The Chinese sentence is true because the English sentence is
>> self-contradictory. This is an exact isomorphism to:
>>
>>    "sentence x which is undecidable in the original theory [my English]
>>     becomes a decidable sentence in the enriched theory [my Chinese]."
>>
>
> Which is a non-sequitor, showing you don't understand what you are
> talking about.
>
> You are just proving your Stupidity.
>
> I don't think you even actually understand any of the basics of logic.
>
> You can parrot words, but you show an utter lack of knowledge about how
> any of it works.

Try and paraphrase 100% perfectly exactly what you think that Tarski is
saying. Any idiot (even a bot) can claim that someone is wrong.

It takes actual understanding to point out the exact error and the
reason that it is an error.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/31/22 2:34 PM, olcott wrote:
> On 12/31/2022 1:07 PM, Richard Damon wrote:
>> On 12/31/22 1:34 PM, olcott wrote:
>>> On 12/31/2022 12:16 PM, Richard Damon wrote:
>>>> On 12/31/22 12:10 PM, olcott wrote:
>>>>
>>>>> This sentence is not true.
>>>>> is not true because it is self-contradictory.
>>>>
>>>> Right, and thus there can not be a Definition of Truth in the system
>>>> because if there was, you could show that statement True.
>>>
>>> 這句話不是真的: "This sentence is not true."
>>> The Chinese says "This sentence is not true:" referring to the English.
>>>
>>> The Chinese sentence is true because the English sentence is
>>> self-contradictory. This is an exact isomorphism to:
>>>
>>>    "sentence x which is undecidable in the original theory [my English]
>>>     becomes a decidable sentence in the enriched theory [my Chinese]."
>>>
>>
>> Which is a non-sequitor, showing you don't understand what you are
>> talking about.
>>
>> You are just proving your Stupidity.
>>
>> I don't think you even actually understand any of the basics of logic.
>>
>> You can parrot words, but you show an utter lack of knowledge about
>> how any of it works.
>
> Try and paraphrase 100% perfectly exactly what you think that Tarski is
> saying. Any idiot (even a bot) can claim that someone is wrong.

**Like you are doing**

>
> It takes actual understanding to point out the exact error and the
> reason that it is an error.
>
>

Why do we need to paraphrase?

He says that a "Definition" of Truth, by which he means a way to
determine if a given arbitrary sentence expressed in the Theory is True
or False (or not a Truth Bearer) because, if such a definition existed,
then from that definition you could prove in the defined Meta-Theory
that a Statement like the Liar's Paradox was actually True.

Thus, since we know that can't be, there must not be an ability to
define in a system of logic, a "Definition of Truth" that allows you to
determine (i.e. Proof) every True Statement, Disprove every false
statement, and determine that every non-truthbearer was a non-truthbearer.

What else do you think he is saying?