XPost: comp.theory, sci.logic

On 5/10/23 10:27 AM, olcott wrote:

On 5/10/2023 6:24 AM, Richard Damon wrote:

On 5/9/23 10:46 PM, olcott wrote:

On 5/9/2023 8:30 PM, Richard Damon wrote:

On 5/9/23 8:18 PM, olcott wrote:

Gödel intended his actual G to be isomorphic to the above self-
referential expression.

Nope, you are over-simplifying things.

Not at all. I boiled them down to their barest essence. Gödel's G was
intended to be and is isomorphic to a self-contradictory expression.

This is dead obvious in Tarski's comparable proof where he flat out
states that he is anchoring his proof in the actual Liar Paradox.

So, you are just PROVING that you don't understand how logic actually
works and are falling for your own Straw man Error.

No I am proving to have a deeper understanding of these things than most others have.

Nope, just that you are so dumb you don't know what you don't understand.

When we understand that he sums up his own proof as
   ...We are therefore confronted with a proposition which asserts its
   own unprovability. 15 ... (Gödel 1931:39-41)

No, that isn't a "summary" of his proof, but a STEP in the proof.

From G in F, we can prove in Meta-F, that G

Then we can see that he intended his G to be isomorphic to a G that
...which asserts its own unprovability. 15 ... (Gödel 1931:39-41)

Nope, you don't seem to understand what a chain of logic is.

and he intended this be self contradictory
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:39-41)

No, it just shows that you have no idea what he is talking about, or the meaning of the words are that you are using.

YOU are the one guilt of trying to put words in other peoples mouthes,
to then try to disprove those altered words.

In other words, your whole arguement is bassed on asserting a Strawman
Falacy.

Here is how G asserts its own unprovability in F is self-contradictory: Proving G requires a sequence of inference steps in F that prove that
they themselves do not exist.

Except that the ACTUAL statement of G isn't in any way
"Self-Contradictiory", so your "Isomorphism" / "Equivalence" is just
your pathologica lie.

That you continue to fail to understand this is not my mistake it is
your mistake.

Nope, You are the one making the mistake.

It is a demonstarted principle, that if EVERYONE disagrees with you, you
are likely wrong. Even the greatest who came up with new ideas, were
able to get at least a FEW of the smartest to understand what they were
talking about.

You have only gotten agreement from a couple at the bottom, and people
you have "tricked" by the misuse of words, and who don't actually agree
with your ideas.

Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems

https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf

Since Tarski directly stated that he is anchoring his comparable proof
in the actual Liar Paradox I have provided sufficient support for my position.

Nope, In fact, he is using the non-truth bearing of the Liars Paradox
for his proof,

You are again showing your stupiity.

Ever since 1936 the world has been convinced that the notion of Truth
is not formally definable entirely on the basis that Tarski could not
prove that the non-truth bearer of the Liar Paradox is true.

Nope, and you are just proving that YOU have no idea what Truth actually
is, or what Logic actually is.

You are just proving your utter ignorance and stupidity with your
pathological lying about these things.

Your eternal destiny is to be known (for as long as you are remembered)
as the ignorant pathologica liar who totally misunderstands how logic works.

YOU FAIL.

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XPost: comp.theory, sci.logic

On 5/10/2023 6:29 PM, Richard Damon wrote:

On 5/10/23 10:27 AM, olcott wrote:

On 5/10/2023 6:24 AM, Richard Damon wrote:

On 5/9/23 10:46 PM, olcott wrote:

On 5/9/2023 8:30 PM, Richard Damon wrote:

On 5/9/23 8:18 PM, olcott wrote:

Gödel intended his actual G to be isomorphic to the above self-
referential expression.

Nope, you are over-simplifying things.

Not at all. I boiled them down to their barest essence. Gödel's G was >>>> intended to be and is isomorphic to a self-contradictory expression.

This is dead obvious in Tarski's comparable proof where he flat out
states that he is anchoring his proof in the actual Liar Paradox.

So, you are just PROVING that you don't understand how logic actually
works and are falling for your own Straw man Error.

No I am proving to have a deeper understanding of these things than most
others have.

Nope, just that you are so dumb you don't know what you don't understand.

I say that incorrectly. I have a deeper understanding OF THE ESSENCE OF
HIS PROOF. It is commonly understood that Gödel's actual proof is
isomorphic to {a proposition which asserts its own unprovability}. It is
also commonly understood that this is self-contradictory.

What is not commonly understood is that formal systems that cannot prove self-contradictory expressions are not in any way deficient.



--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

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XPost: comp.theory, sci.logic

On 5/10/2023 6:29 PM, Richard Damon wrote:

On 5/10/23 10:27 AM, olcott wrote:

On 5/10/2023 6:24 AM, Richard Damon wrote:

On 5/9/23 10:46 PM, olcott wrote:

On 5/9/2023 8:30 PM, Richard Damon wrote:

On 5/9/23 8:18 PM, olcott wrote:

Gödel intended his actual G to be isomorphic to the above self-
referential expression.

Nope, you are over-simplifying things.

Not at all. I boiled them down to their barest essence. Gödel's G was >>>> intended to be and is isomorphic to a self-contradictory expression.

This is dead obvious in Tarski's comparable proof where he flat out
states that he is anchoring his proof in the actual Liar Paradox.

So, you are just PROVING that you don't understand how logic actually
works and are falling for your own Straw man Error.

No I am proving to have a deeper understanding of these things than most
others have.

Nope, just that you are so dumb you don't know what you don't understand.

When we understand that he sums up his own proof as
    ...We are therefore confronted with a proposition which asserts its >>     own unprovability. 15 ... (Gödel 1931:39-41)

No, that isn't a "summary" of his proof, but a STEP in the proof.

From G in F, we can prove in Meta-F, that G

Then we can see that he intended his G to be isomorphic to a G that
...which asserts its own unprovability. 15 ... (Gödel 1931:39-41)

Nope, you don't seem to understand what a chain of logic is.

and he intended this be self contradictory
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:39-41)

No, it just shows that you have no idea what he is talking about, or the meaning of the words are that you are using.

YOU are the one guilt of trying to put words in other peoples mouthes,
to then try to disprove those altered words.

In other words, your whole arguement is bassed on asserting a Strawman Falacy.

Here is how G asserts its own unprovability in F is self-contradictory:
Proving G requires a sequence of inference steps in F that prove that
they themselves do not exist.

Except that the ACTUAL statement of G isn't in any way
"Self-Contradictiory", so your "Isomorphism" / "Equivalence" is just
your pathologica lie.

That you continue to fail to understand this is not my mistake it is
your mistake.

Nope, You are the one making the mistake.

It is a demonstarted principle, that if EVERYONE disagrees with you, you
are likely wrong. Even the greatest who came up with new ideas, were
able to get at least a FEW of the smartest to understand what they were talking about.

You have only gotten agreement from a couple at the bottom, and people
you have "tricked" by the misuse of words, and who don't actually agree
with your ideas.

Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems

https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf

Since Tarski directly stated that he is anchoring his comparable proof
in the actual Liar Paradox I have provided sufficient support for my
position.

Nope, In fact, he is using the non-truth bearing of the Liars Paradox
for his proof,

I say that Tarski is using the Liar Paradox as the basis of his proof
and you say no I am wrong the truth is that Tarski is using the Liar
Paradox as the basis of his proof?




--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

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XPost: comp.theory, sci.logic

On 5/10/23 11:08 PM, olcott wrote:

On 5/10/2023 6:29 PM, Richard Damon wrote:

On 5/10/23 10:27 AM, olcott wrote:

On 5/10/2023 6:24 AM, Richard Damon wrote:

On 5/9/23 10:46 PM, olcott wrote:

On 5/9/2023 8:30 PM, Richard Damon wrote:

On 5/9/23 8:18 PM, olcott wrote:

Gödel intended his actual G to be isomorphic to the above self- >>>>>>> referential expression.

Nope, you are over-simplifying things.

Not at all. I boiled them down to their barest essence. Gödel's G was >>>>> intended to be and is isomorphic to a self-contradictory expression. >>>>>
This is dead obvious in Tarski's comparable proof where he flat out
states that he is anchoring his proof in the actual Liar Paradox.

So, you are just PROVING that you don't understand how logic
actually works and are falling for your own Straw man Error.

No I am proving to have a deeper understanding of these things than most >>> others have.

Nope, just that you are so dumb you don't know what you don't understand.

I say that incorrectly. I have a deeper understanding OF THE ESSENCE OF
HIS PROOF. It is commonly understood that Gödel's actual proof is
isomorphic to {a proposition which asserts its own unprovability}. It is
also commonly understood that this is self-contradictory.

What is not commonly understood is that formal systems that cannot prove self-contradictory expressions are not in any way deficient.

But that isn't what his proof is about,

You just have a deeper MISunderstanding of what he is saying because you
don't understand what he is saying at all, but are just trying to
understand the altered strawman arguement that you think you can understand,

YOU FAIL.

None of thes proofs are about a system being deficient for not being
able to resolve a self-contradictory statement or a non-truth-bearer.
The fact you think they are just shows that you are misunderstanding the proofs.

Godel shows a statement, THAT IS TRUE, (and thus CAN'T be
self-contradictory) that can not be proven in that system. This meets
the DEFINTION of "Incompleteness" in Logic.

Tarski shows that there are some statements, that have a truth value,
that we can not know that truth value, because the mere existance of a "Definition" (deterministic method) to test them with leads to the contradiction that the Liar's Paradox must be True..

The problem isn't that he expects that a system should be able to
resolve the Liar's Paradox, but that a "Definition of Truth" leads to a
claimed resolution, namely that the Liar's Paradox IS True (which means
it also must be False). He shows that a "Definition of Truth" turns the
Liar's Paradox from a non-truth-bearer into a Truth Bearer that is True
(and thus also False).

Your failure to understand this just shows your stupidity.

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XPost: comp.theory, sci.logic

On 5/11/2023 6:37 AM, Richard Damon wrote:

On 5/10/23 11:01 PM, olcott wrote:

On 5/10/2023 6:29 PM, Richard Damon wrote:

Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems

https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf

Since Tarski directly stated that he is anchoring his comparable proof >>>> in the actual Liar Paradox I have provided sufficient support for my
position.

Nope, In fact, he is using the non-truth bearing of the Liars Paradox
for his proof,

I say that Tarski is using the Liar Paradox as the basis of his proof
and you say no I am wrong the truth is that Tarski is using the Liar
Paradox as the basis of his proof?

YOU have been saying that because Tarski, erroneosly, finds that logic
can't prove the liar's paradox, his proof must be wrong, i.e  there is
no definition of Truth.

I say that his proof shows that if a Definition of Truth (meaning a determinate procedure to determine if any statement is true or false) existed, then it would be possible to prove that the liar's paradox is a
true statement,

Where did you get that nutty idea?

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

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XPost: comp.theory, sci.logic

On 5/11/2023 6:37 AM, Richard Damon wrote:

On 5/10/23 11:08 PM, olcott wrote:

On 5/10/2023 6:29 PM, Richard Damon wrote:

On 5/10/23 10:27 AM, olcott wrote:

On 5/10/2023 6:24 AM, Richard Damon wrote:

On 5/9/23 10:46 PM, olcott wrote:

On 5/9/2023 8:30 PM, Richard Damon wrote:

On 5/9/23 8:18 PM, olcott wrote:

Gödel intended his actual G to be isomorphic to the above self- >>>>>>>> referential expression.

Nope, you are over-simplifying things.

Not at all. I boiled them down to their barest essence. Gödel's G was >>>>>> intended to be and is isomorphic to a self-contradictory expression. >>>>>>
This is dead obvious in Tarski's comparable proof where he flat out >>>>>> states that he is anchoring his proof in the actual Liar Paradox.

So, you are just PROVING that you don't understand how logic
actually works and are falling for your own Straw man Error.

No I am proving to have a deeper understanding of these things than
most
others have.

Nope, just that you are so dumb you don't know what you don't
understand.

I say that incorrectly. I have a deeper understanding OF THE ESSENCE OF
HIS PROOF. It is commonly understood that Gödel's actual proof is
isomorphic to {a proposition which asserts its own unprovability}. It is
also commonly understood that this is self-contradictory.

What is not commonly understood is that formal systems that cannot prove
self-contradictory expressions are not in any way deficient.

But that isn't what his proof is about,

You just have a deeper MISunderstanding of what he is saying because you don't understand what he is saying at all, but are just trying to
understand the altered strawman arguement that you think you can
understand,

YOU FAIL.

None of thes proofs are about a system being deficient for not being
able to resolve a self-contradictory statement or a non-truth-bearer.
The fact you think they are just shows that you are misunderstanding the proofs.

Godel shows a statement, THAT IS TRUE, (and thus CAN'T be
self-contradictory) that can not be proven in that system. This meets
the DEFINTION of "Incompleteness" in Logic.

He does this in the same way that this Liar Paradox is true:
This sentence is not true: "This sentence is not true"

It is not that the actual Liar Paradox is true it is only when the Liar
Paradox is applied to itself that it becomes true.

G states that it is unprovable in F and is unprovable in F because it is self-contradictory in F.

When we test the same statement in metamathematics then it becomes true
because it escapes the self-contradiction the same way that the above
Liar Paradox escaped the self-contradiction.

The prerequisite to attaining this much deeper understanding of the
essence of Gödel's proof is
(1) Understanding that Gödel's G was intended to be and is isomorphic to
{a proposition which asserts its own unprovability [in PM]}

(2) Thus making Gödel's G isomorphic to a self-contradictory expression.

Tarski shows that there are some statements, that have a truth value,
that we can not know that truth value, because the mere existance of a "Definition" (deterministic method) to test them with leads to the contradiction that the Liar's Paradox must be True..

When you understand the essence of his proof you will understand that
Tarski's metatheory is merely applying the Liar Paradox to itself
outside of the scope of self-contradiction.

"This sentence is not true" is not a truth bearer.
This sentence is not true: "This sentence is not true" is true because
the inner sentence is not a truth bearer.

The problem isn't that he expects that a system should be able to
resolve the Liar's Paradox, but that a "Definition of Truth" leads to a claimed resolution, namely that the Liar's Paradox IS True (which means
it also must be False). He shows that a "Definition of Truth" turns the Liar's Paradox from a non-truth-bearer into a Truth Bearer that is True
(and thus also False).

Your failure to understand this just shows your stupidity.

In this case it was Tarski's failure to understand.
Only when we boil things down to their barest essence (as I have had to
do as a software engineer for almost four decades) do we see these
things in their true light.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

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XPost: comp.theory, sci.logic

On 5/11/23 10:12 AM, olcott wrote:

On 5/11/2023 6:37 AM, Richard Damon wrote:

On 5/10/23 11:01 PM, olcott wrote:

On 5/10/2023 6:29 PM, Richard Damon wrote:

Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems

https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf

Since Tarski directly stated that he is anchoring his comparable proof >>>>> in the actual Liar Paradox I have provided sufficient support for my >>>>> position.

Nope, In fact, he is using the non-truth bearing of the Liars
Paradox for his proof,

I say that Tarski is using the Liar Paradox as the basis of his proof
and you say no I am wrong the truth is that Tarski is using the Liar
Paradox as the basis of his proof?

YOU have been saying that because Tarski, erroneosly, finds that logic
can't prove the liar's paradox, his proof must be wrong, i.e  there is
no definition of Truth.


I say that his proof shows that if a Definition of Truth (meaning a
determinate procedure to determine if any statement is true or false)
existed, then it would be possible to prove that the liar's paradox is
a true statement,

Where did you get that nutty idea?

FROM HIS PROOF!

He first does a lot of work to establish a number of properties.

He then makes a trial assumption that there could be a "Definition of
Truth" per his meaning.

He then goes through a few logical steps, and comes out with a proof
that the Liar's Paradox is True, given the assumption of a Definition of
Truth.

Since he knows this is impossible, he concludes that there can not be a "Defintion of Truth".


You can't see that in his proof?

of course, your "reducing things to there essentials" which requires you changing the meaning of things problably obliterates that part of the logic.

I can't help that you are too ignorant and stupid to understand what he
is saying.

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XPost: comp.theory, sci.logic

On 5/11/2023 9:27 PM, Richard Damon wrote:

On 5/11/23 10:12 AM, olcott wrote:

On 5/11/2023 6:37 AM, Richard Damon wrote:

On 5/10/23 11:01 PM, olcott wrote:

On 5/10/2023 6:29 PM, Richard Damon wrote:

Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems

https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf

Since Tarski directly stated that he is anchoring his comparable
proof
in the actual Liar Paradox I have provided sufficient support for my >>>>>> position.

Nope, In fact, he is using the non-truth bearing of the Liars
Paradox for his proof,

I say that Tarski is using the Liar Paradox as the basis of his
proof and you say no I am wrong the truth is that Tarski is using
the Liar Paradox as the basis of his proof?

YOU have been saying that because Tarski, erroneosly, finds that
logic can't prove the liar's paradox, his proof must be wrong, i.e
there is no definition of Truth.


I say that his proof shows that if a Definition of Truth (meaning a
determinate procedure to determine if any statement is true or false)
existed, then it would be possible to prove that the liar's paradox
is a true statement,

Where did you get that nutty idea?

FROM HIS PROOF!

He first does a lot of work to establish a number of properties.

In other words you agree that Tarski did "prove" that the notion of
Truth cannot be fully formalized on a fundamental basis directly related
to the Liar Paradox?

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

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XPost: comp.theory, sci.logic

On 5/11/23 10:34 PM, olcott wrote:

FROM HIS PROOF!

He first does a lot of work to establish a number of properties.

In other words you agree that Tarski did "prove" that the notion of
Truth cannot be fully formalized on a fundamental basis directly related
to the Liar Paradox?

Only in the sense that since we KNOW the Liar's paradox can't be true,
and a "Definition of Truth" (not a "notion of Truth) would lead to being
able to prove that the Liar's paradox is true,

This isn't what most people would consider proving using as a basis, as
that normally means proving something because the basis is true.

Also, your use of the word "Notion" seems to indicate that you really
don't understand what Tarski was even talking about. It isn't that we
don't know the nature of Truth, and he goes into a lot of explanation of
a lot of the nature of Truth, but we can't come up with a formulaic "Definition" that we can use to "test" an arbitrary statement to
determine if it is True or not.

This just goes back to your utter lack of understanding of anything that
these people are talking about.

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XPost: comp.theory, sci.logic

On 5/11/2023 9:54 PM, Richard Damon wrote:

On 5/11/23 10:34 PM, olcott wrote:

FROM HIS PROOF!

He first does a lot of work to establish a number of properties.

In other words you agree that Tarski did "prove" that the notion of
Truth cannot be fully formalized on a fundamental basis directly related
to the Liar Paradox?

Only in the sense that since we KNOW the Liar's paradox can't be true,
and a "Definition of Truth" (not a "notion of Truth) would lead to being
able to prove that the Liar's paradox is true,

That is ridiculous.


--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

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XPost: comp.theory, sci.logic

On 5/11/23 11:30 PM, olcott wrote:

On 5/11/2023 9:54 PM, Richard Damon wrote:

On 5/11/23 10:34 PM, olcott wrote:

FROM HIS PROOF!

He first does a lot of work to establish a number of properties.

In other words you agree that Tarski did "prove" that the notion of
Truth cannot be fully formalized on a fundamental basis directly related >>> to the Liar Paradox?

Only in the sense that since we KNOW the Liar's paradox can't be true,
and a "Definition of Truth" (not a "notion of Truth) would lead to
being able to prove that the Liar's paradox is true,

That is ridiculous.

Why? Do you think the Liar's Paradox should be provable to be True?

You seem to want to put him down for "basing" his proof on a
contradiction, but he isn't basing it in the way you want to do so.

You are just stuck trying to push a LIE, but can't quite figure out how
to do it.

Sorry, you are just too stupid to handle logic.

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XPost: comp.theory, sci.logic

On 5/11/2023 10:45 PM, Richard Damon wrote:

On 5/11/23 11:30 PM, olcott wrote:

On 5/11/2023 9:54 PM, Richard Damon wrote:

On 5/11/23 10:34 PM, olcott wrote:

FROM HIS PROOF!

He first does a lot of work to establish a number of properties.

In other words you agree that Tarski did "prove" that the notion of
Truth cannot be fully formalized on a fundamental basis directly
related
to the Liar Paradox?

Only in the sense that since we KNOW the Liar's paradox can't be
true, and a "Definition of Truth" (not a "notion of Truth) would lead
to being able to prove that the Liar's paradox is true,

That is ridiculous.

Why? Do you think the Liar's Paradox should be provable to be True?

The Liar Paradox is not a truth bearer, END-OF-STORY !!!

You seem to want to put him down for "basing" his proof on a
contradiction, but he isn't basing it in the way you want to do so.

You are just stuck trying to push a LIE, but can't quite figure out how
to do it.

Sorry, you are just too stupid to handle logic.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

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XPost: comp.theory, sci.logic

On 5/12/23 12:51 AM, olcott wrote:

On 5/11/2023 10:45 PM, Richard Damon wrote:

On 5/11/23 11:30 PM, olcott wrote:

On 5/11/2023 9:54 PM, Richard Damon wrote:

On 5/11/23 10:34 PM, olcott wrote:

FROM HIS PROOF!

He first does a lot of work to establish a number of properties.

In other words you agree that Tarski did "prove" that the notion of
Truth cannot be fully formalized on a fundamental basis directly
related
to the Liar Paradox?

Only in the sense that since we KNOW the Liar's paradox can't be
true, and a "Definition of Truth" (not a "notion of Truth) would
lead to being able to prove that the Liar's paradox is true,

That is ridiculous.

Why? Do you think the Liar's Paradox should be provable to be True?

The Liar Paradox is not a truth bearer, END-OF-STORY !!!

Right, so why do you fault Tarski for saying that?

His proof shows that if a "Definition of Truth" existed, it provides a
way to prove the Liar's Paradox is True.

Therefore, there can be no "Definition of Truth".

I've explained that to you many times, but you say that is invalid logic.

The only way it is invalid is if you think it is possible to actually
prove the Liar's paradox.

You are just showing your stupidity.

You seem to want to put him down for "basing" his proof on a
contradiction, but he isn't basing it in the way you want to do so.

You are just stuck trying to push a LIE, but can't quite figure out
how to do it.

Sorry, you are just too stupid to handle logic.

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XPost: comp.theory, sci.logic

On 5/12/2023 9:06 AM, Richard Damon wrote:

On 5/12/23 12:51 AM, olcott wrote:

On 5/11/2023 10:45 PM, Richard Damon wrote:

On 5/11/23 11:30 PM, olcott wrote:

On 5/11/2023 9:54 PM, Richard Damon wrote:

On 5/11/23 10:34 PM, olcott wrote:

FROM HIS PROOF!

He first does a lot of work to establish a number of properties.

In other words you agree that Tarski did "prove" that the notion of >>>>>> Truth cannot be fully formalized on a fundamental basis directly
related
to the Liar Paradox?

Only in the sense that since we KNOW the Liar's paradox can't be
true, and a "Definition of Truth" (not a "notion of Truth) would
lead to being able to prove that the Liar's paradox is true,

That is ridiculous.

Why? Do you think the Liar's Paradox should be provable to be True?

The Liar Paradox is not a truth bearer, END-OF-STORY !!!

Right, so why do you fault Tarski for saying that?

His proof shows that if a "Definition of Truth" existed, it provides a
way to prove the Liar's Paradox is True.

That is a nutty idea.
Any system that proves that a self-contradictory expression is true is a
broken system.

Analytic truth is derived from applying truth preserving operations to expressions of language that have been stipulated to be true.
This cannot possibly derive non-truth bearers as true.

Prolog uses the exact same system that I just specified expressions that
are stipulated to be true are Prolog facts with Prolog rules as a set of
truth preserving operations.

Prolog is smart enough to reject the Liar Paradox.

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

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

The above test shows that LP is infinitely recursive never resolving to
a truth value.


--
Copyright 2023 Olcott

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

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XPost: comp.theory, sci.logic

On 5/12/23 11:04 AM, olcott wrote:

On 5/12/2023 9:06 AM, Richard Damon wrote:

On 5/12/23 12:51 AM, olcott wrote:

On 5/11/2023 10:45 PM, Richard Damon wrote:

On 5/11/23 11:30 PM, olcott wrote:

On 5/11/2023 9:54 PM, Richard Damon wrote:

On 5/11/23 10:34 PM, olcott wrote:

FROM HIS PROOF!

He first does a lot of work to establish a number of properties. >>>>>>> In other words you agree that Tarski did "prove" that the notion of >>>>>>> Truth cannot be fully formalized on a fundamental basis directly >>>>>>> related

to the Liar Paradox?

Only in the sense that since we KNOW the Liar's paradox can't be
true, and a "Definition of Truth" (not a "notion of Truth) would
lead to being able to prove that the Liar's paradox is true,

That is ridiculous.

Why? Do you think the Liar's Paradox should be provable to be True?

The Liar Paradox is not a truth bearer, END-OF-STORY !!!

Right, so why do you fault Tarski for saying that?

His proof shows that if a "Definition of Truth" existed, it provides a
way to prove the Liar's Paradox is True.

That is a nutty idea.
Any system that proves that a self-contradictory expression is true is a broken system.

Right, and the proof shows that would be any system with a "definition
of Truth", so you AGREE with Tarski.

Analytic truth is derived from applying truth preserving operations to expressions of language that have been stipulated to be true.
This cannot possibly derive non-truth bearers as true.

Right, so you agre with Tarksi that there can not be a "Definition of
Truth".

Prolog uses the exact same system that I just specified expressions that
are stipulated to be true are Prolog facts with Prolog rules as a set of truth preserving operations.

Prolog is limited in the logic it can do,

But, so it seems are you.

Prolog is smart enough to reject the Liar Paradox.

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

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

The above test shows that LP is infinitely recursive never resolving to
a truth value.

So?

--- SoupGate-Win32 v1.05
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XPost: comp.theory, sci.logic

On 5/12/2023 1:42 PM, Richard Damon wrote:

On 5/12/23 11:04 AM, olcott wrote:

On 5/12/2023 9:06 AM, Richard Damon wrote:

On 5/12/23 12:51 AM, olcott wrote:

On 5/11/2023 10:45 PM, Richard Damon wrote:

On 5/11/23 11:30 PM, olcott wrote:

On 5/11/2023 9:54 PM, Richard Damon wrote:

On 5/11/23 10:34 PM, olcott wrote:

FROM HIS PROOF!

He first does a lot of work to establish a number of properties. >>>>>>>> In other words you agree that Tarski did "prove" that the notion of >>>>>>>> Truth cannot be fully formalized on a fundamental basis directly >>>>>>>> related

to the Liar Paradox?

Only in the sense that since we KNOW the Liar's paradox can't be >>>>>>> true, and a "Definition of Truth" (not a "notion of Truth) would >>>>>>> lead to being able to prove that the Liar's paradox is true,

That is ridiculous.

Why? Do you think the Liar's Paradox should be provable to be True?

The Liar Paradox is not a truth bearer, END-OF-STORY !!!

Right, so why do you fault Tarski for saying that?

His proof shows that if a "Definition of Truth" existed, it provides
a way to prove the Liar's Paradox is True.

That is a nutty idea.
Any system that proves that a self-contradictory expression is true is
a broken system.

Right, and the proof shows that would be any system with a "definition
of Truth", so you AGREE with Tarski.

Not at all, Tarski's system is incorrect. All of analytical truth1 is a
body of semantic tautologies that excludes the liar paradox.

1 It is commonly known that analytical truth includes all of math and
all of logic. My new idea is that it also includes the model of the
world.

Analytic truth is derived from applying truth preserving operations to
expressions of language that have been stipulated to be true.
This cannot possibly derive non-truth bearers as true.

Right, so you agre with Tarksi that there can not be a "Definition of
Truth".

Not at all.

Prolog uses the exact same system that I just specified expressions that
are stipulated to be true are Prolog facts with Prolog rules as a set of
truth preserving operations.

Prolog is limited in the logic it can do,

But, so it seems are you.

Prolog is smart enough to reject the Liar Paradox.

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

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

The above test shows that LP is infinitely recursive never resolving
to a truth value.

So?

Tarski was too stupid (on this one issue) to understand that the Liar
Paradox is excluded from the body of truth.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XPost: comp.theory, sci.logic

On 5/12/2023 1:42 PM, Richard Damon wrote:

On 5/12/23 11:04 AM, olcott wrote:

On 5/12/2023 9:06 AM, Richard Damon wrote:

On 5/12/23 12:51 AM, olcott wrote:

On 5/11/2023 10:45 PM, Richard Damon wrote:

On 5/11/23 11:30 PM, olcott wrote:

On 5/11/2023 9:54 PM, Richard Damon wrote:

On 5/11/23 10:34 PM, olcott wrote:

FROM HIS PROOF!

He first does a lot of work to establish a number of properties. >>>>>>>> In other words you agree that Tarski did "prove" that the notion of >>>>>>>> Truth cannot be fully formalized on a fundamental basis directly >>>>>>>> related

to the Liar Paradox?

Only in the sense that since we KNOW the Liar's paradox can't be >>>>>>> true, and a "Definition of Truth" (not a "notion of Truth) would >>>>>>> lead to being able to prove that the Liar's paradox is true,

That is ridiculous.

Why? Do you think the Liar's Paradox should be provable to be True?

The Liar Paradox is not a truth bearer, END-OF-STORY !!!

Right, so why do you fault Tarski for saying that?

His proof shows that if a "Definition of Truth" existed, it provides
a way to prove the Liar's Paradox is True.

That is a nutty idea.
Any system that proves that a self-contradictory expression is true is
a broken system.

Right, and the proof shows that would be any system with a "definition
of Truth", so you AGREE with Tarski.

Not at all, Tarski's system is incorrect. All of analytical truth1 is a
body of semantic tautologies that excludes the liar paradox.

1 It is commonly known that analytical truth includes all of math and
all of logic. My new idea is that it also includes the model of the
world.

Prolog is smart enough to reject the Liar Paradox because it uses the
same system that I use, only expressions of language that have been
derived by applying truth preserving operations [Prolog rules] to
expressions of language that have been stipulated to be true [Prolog
facts] are true. Everything else [Prolog's negation as failure] counts
as untrue.

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

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

The above test shows that LP is infinitely recursive never resolving to
a truth value.


--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XPost: comp.theory, sci.logic

On 5/12/23 5:57 PM, olcott wrote:

On 5/12/2023 1:42 PM, Richard Damon wrote:

On 5/12/23 11:04 AM, olcott wrote:

On 5/12/2023 9:06 AM, Richard Damon wrote:

On 5/12/23 12:51 AM, olcott wrote:

On 5/11/2023 10:45 PM, Richard Damon wrote:

On 5/11/23 11:30 PM, olcott wrote:

On 5/11/2023 9:54 PM, Richard Damon wrote:

On 5/11/23 10:34 PM, olcott wrote:

FROM HIS PROOF!

He first does a lot of work to establish a number of properties. >>>>>>>>> In other words you agree that Tarski did "prove" that the

notion of
Truth cannot be fully formalized on a fundamental basis
directly related
to the Liar Paradox?

Only in the sense that since we KNOW the Liar's paradox can't be >>>>>>>> true, and a "Definition of Truth" (not a "notion of Truth) would >>>>>>>> lead to being able to prove that the Liar's paradox is true,

That is ridiculous.

Why? Do you think the Liar's Paradox should be provable to be True? >>>>>>

The Liar Paradox is not a truth bearer, END-OF-STORY !!!

Right, so why do you fault Tarski for saying that?

His proof shows that if a "Definition of Truth" existed, it provides
a way to prove the Liar's Paradox is True.

That is a nutty idea.
Any system that proves that a self-contradictory expression is true
is a broken system.

Right, and the proof shows that would be any system with a "definition
of Truth", so you AGREE with Tarski.

Not at all, Tarski's system is incorrect. All of analytical truth1 is a
body of semantic tautologies that excludes the liar paradox.

1 It is commonly known that analytical truth includes all of math and
all of logic. My new idea is that it also includes the model of the
world.

Analytic truth is derived from applying truth preserving operations to
expressions of language that have been stipulated to be true.
This cannot possibly derive non-truth bearers as true.

Right, so you agre with Tarksi that there can not be a "Definition of
Truth".

Not at all.

Prolog uses the exact same system that I just specified expressions that >>> are stipulated to be true are Prolog facts with Prolog rules as a set of >>> truth preserving operations.

Prolog is limited in the logic it can do,

But, so it seems are you.

Prolog is smart enough to reject the Liar Paradox.

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

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

The above test shows that LP is infinitely recursive never resolving
to a truth value.

So?

Tarski was too stupid (on this one issue) to understand that the Liar
Paradox is excluded from the body of truth.

Why do you say that? WHere does he say what you say he is saying?

Please point out the pont where he is ACCEPTING the Liar's paradox.

The point where the Liar coms up, he uses that fact to point out that
the intial assumption MUST be incorrect, as it lead to proving a
non-true statement.

I think your problem is that you just don't understand the proof you are reading and reading into it the errors that you yourself make.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XPost: comp.theory, sci.logic

On 5/12/2023 9:18 PM, Richard Damon wrote:

On 5/12/23 8:13 PM, olcott wrote:

On 5/12/2023 1:42 PM, Richard Damon wrote:

On 5/12/23 11:04 AM, olcott wrote:

On 5/12/2023 9:06 AM, Richard Damon wrote:

On 5/12/23 12:51 AM, olcott wrote:

On 5/11/2023 10:45 PM, Richard Damon wrote:

On 5/11/23 11:30 PM, olcott wrote:

On 5/11/2023 9:54 PM, Richard Damon wrote:

On 5/11/23 10:34 PM, olcott wrote:

FROM HIS PROOF!

He first does a lot of work to establish a number of properties. >>>>>>>>>> In other words you agree that Tarski did "prove" that the

notion of
Truth cannot be fully formalized on a fundamental basis
directly related
to the Liar Paradox?

Only in the sense that since we KNOW the Liar's paradox can't >>>>>>>>> be true, and a "Definition of Truth" (not a "notion of Truth) >>>>>>>>> would lead to being able to prove that the Liar's paradox is true, >>>>>>>>>

That is ridiculous.

Why? Do you think the Liar's Paradox should be provable to be True? >>>>>>>

The Liar Paradox is not a truth bearer, END-OF-STORY !!!

Right, so why do you fault Tarski for saying that?

His proof shows that if a "Definition of Truth" existed, it
provides a way to prove the Liar's Paradox is True.

That is a nutty idea.
Any system that proves that a self-contradictory expression is true
is a broken system.

Right, and the proof shows that would be any system with a
"definition of Truth", so you AGREE with Tarski.

Not at all, Tarski's system is incorrect. All of analytical truth1 is a
body of semantic tautologies that excludes the liar paradox.

Then why does that "Definition of Truth" PROVE the Liar's Paradox?

If his system is "incorrect" what SPECIFIC step did he do that was
improper? (not conclusion, what STEP).

The step where he used the Liar Paradox as the basis of his proof.

Your problem is you don't actually understand how logic works.

My problem is that others do not understand the philosophical
foundations of logic as deeply as I do, they merely follow what they
read in a textbook as if it was the infallible word of God.

1 It is commonly known that analytical truth includes all of math and
all of logic. My new idea is that it also includes the model of the
world.

Except since your model doesn't work at all, you have a problem.

When-so-ever an expression of language is derived by applying only truth preserving operations to expressions of language that have been
stipulated to be true we are guaranteed that this expression is true.

Prolog is smart enough to reject the Liar Paradox because it uses the
same system that I use, only expressions of language that have been
derived by applying truth preserving operations [Prolog rules] to
expressions of language that have been stipulated to be true [Prolog
facts] are true. Everything else [Prolog's negation as failure] counts
as untrue.

And Prolog is too limited to handle the logic of these proofs.

It is not in fact too limited to handle these proofs as I have
concretely proved. I invented Minimal Type Theory that translates logic expressions into directed graphs and a cycle in the graph indicates the expression never resolves to a truth value.

Prolog simply does this same thing.

The fact that you can't understand that just shows how stupid you are.

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

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

The above test shows that LP is infinitely recursive never resolving
to a truth value.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XPost: comp.theory, sci.logic

On 5/12/23 11:49 PM, olcott wrote:

On 5/12/2023 9:18 PM, Richard Damon wrote:

On 5/12/23 8:13 PM, olcott wrote:

On 5/12/2023 1:42 PM, Richard Damon wrote:

On 5/12/23 11:04 AM, olcott wrote:

On 5/12/2023 9:06 AM, Richard Damon wrote:

On 5/12/23 12:51 AM, olcott wrote:

On 5/11/2023 10:45 PM, Richard Damon wrote:

On 5/11/23 11:30 PM, olcott wrote:

On 5/11/2023 9:54 PM, Richard Damon wrote:

On 5/11/23 10:34 PM, olcott wrote:

FROM HIS PROOF!

He first does a lot of work to establish a number of
properties.

In other words you agree that Tarski did "prove" that the >>>>>>>>>>> notion of
Truth cannot be fully formalized on a fundamental basis
directly related
to the Liar Paradox?

Only in the sense that since we KNOW the Liar's paradox can't >>>>>>>>>> be true, and a "Definition of Truth" (not a "notion of Truth) >>>>>>>>>> would lead to being able to prove that the Liar's paradox is >>>>>>>>>> true,

That is ridiculous.

Why? Do you think the Liar's Paradox should be provable to be True? >>>>>>>>

The Liar Paradox is not a truth bearer, END-OF-STORY !!!

Right, so why do you fault Tarski for saying that?

His proof shows that if a "Definition of Truth" existed, it
provides a way to prove the Liar's Paradox is True.

That is a nutty idea.
Any system that proves that a self-contradictory expression is true
is a broken system.

Right, and the proof shows that would be any system with a
"definition of Truth", so you AGREE with Tarski.

Not at all, Tarski's system is incorrect. All of analytical truth1 is a
body of semantic tautologies that excludes the liar paradox.

Then why does that "Definition of Truth" PROVE the Liar's Paradox?

If his system is "incorrect" what SPECIFIC step did he do that was
improper? (not conclusion, what STEP).

The step where he used the Liar Paradox as the basis of his proof.

Your problem is you don't actually understand how logic works.

My problem is that others do not understand the philosophical
foundations of logic as deeply as I do, they merely follow what they
read in a textbook as if it was the infallible word of God.

1 It is commonly known that analytical truth includes all of math and
all of logic. My new idea is that it also includes the model of the
world.

Except since your model doesn't work at all, you have a problem.

When-so-ever an expression of language is derived by applying only truth preserving operations to expressions of language that have been
stipulated to be true we are guaranteed that this expression is true.

Prolog is smart enough to reject the Liar Paradox because it uses the
same system that I use, only expressions of language that have been
derived by applying truth preserving operations [Prolog rules] to
expressions of language that have been stipulated to be true [Prolog
facts] are true. Everything else [Prolog's negation as failure] counts
as untrue.

And Prolog is too limited to handle the logic of these proofs.

It is not in fact too limited to handle these proofs as I have
concretely proved. I invented Minimal Type Theory that translates logic expressions into directed graphs and a cycle in the graph indicates the expression never resolves to a truth value.

Then your logic is too simple to handle the needed logic.

Prolog only does FIRST order logic, and not all of it.

The logic used here is at least Second order, so out of the reach of Prolog.

If you want to claim differently, show how Prolog verifies a proof of
the Pythagorean Theorem.

In fact, almost all of the examples you actaully try to run with are
down at the simple level of Categorical logic which only handles things
of one super-class divided into sub-classes. That logic is way to simple
to handle the things the theorems have been talking about. My guess is
that is as complicated of logic that you can understand, so you try to
force everything into it, and FAIL.

Prolog simply does this same thing.

The fact that you can't understand that just shows how stupid you are.

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

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

The above test shows that LP is infinitely recursive never resolving
to a truth value.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XPost: comp.theory, sci.logic

On 5/13/2023 8:17 AM, Richard Damon wrote:

On 5/12/23 11:49 PM, olcott wrote:

On 5/12/2023 9:18 PM, Richard Damon wrote:

On 5/12/23 8:13 PM, olcott wrote:

On 5/12/2023 1:42 PM, Richard Damon wrote:

On 5/12/23 11:04 AM, olcott wrote:

On 5/12/2023 9:06 AM, Richard Damon wrote:

On 5/12/23 12:51 AM, olcott wrote:

On 5/11/2023 10:45 PM, Richard Damon wrote:

On 5/11/23 11:30 PM, olcott wrote:

On 5/11/2023 9:54 PM, Richard Damon wrote:

On 5/11/23 10:34 PM, olcott wrote:

FROM HIS PROOF!

He first does a lot of work to establish a number of >>>>>>>>>>>>> properties.

In other words you agree that Tarski did "prove" that the >>>>>>>>>>>> notion of
Truth cannot be fully formalized on a fundamental basis >>>>>>>>>>>> directly related
to the Liar Paradox?

Only in the sense that since we KNOW the Liar's paradox can't >>>>>>>>>>> be true, and a "Definition of Truth" (not a "notion of Truth) >>>>>>>>>>> would lead to being able to prove that the Liar's paradox is >>>>>>>>>>> true,

That is ridiculous.

Why? Do you think the Liar's Paradox should be provable to be >>>>>>>>> True?

The Liar Paradox is not a truth bearer, END-OF-STORY !!!

Right, so why do you fault Tarski for saying that?

His proof shows that if a "Definition of Truth" existed, it
provides a way to prove the Liar's Paradox is True.

That is a nutty idea.
Any system that proves that a self-contradictory expression is
true is a broken system.

Right, and the proof shows that would be any system with a
"definition of Truth", so you AGREE with Tarski.

Not at all, Tarski's system is incorrect. All of analytical truth1 is a >>>> body of semantic tautologies that excludes the liar paradox.

Then why does that "Definition of Truth" PROVE the Liar's Paradox?

If his system is "incorrect" what SPECIFIC step did he do that was
improper? (not conclusion, what STEP).

The step where he used the Liar Paradox as the basis of his proof.

Your problem is you don't actually understand how logic works.

My problem is that others do not understand the philosophical
foundations of logic as deeply as I do, they merely follow what they
read in a textbook as if it was the infallible word of God.

1 It is commonly known that analytical truth includes all of math and
all of logic. My new idea is that it also includes the model of the
world.

Except since your model doesn't work at all, you have a problem.

When-so-ever an expression of language is derived by applying only truth
preserving operations to expressions of language that have been
stipulated to be true we are guaranteed that this expression is true.

Prolog is smart enough to reject the Liar Paradox because it uses the
same system that I use, only expressions of language that have been
derived by applying truth preserving operations [Prolog rules] to
expressions of language that have been stipulated to be true [Prolog
facts] are true. Everything else [Prolog's negation as failure] counts >>>> as untrue.

And Prolog is too limited to handle the logic of these proofs.

It is not in fact too limited to handle these proofs as I have
concretely proved. I invented Minimal Type Theory that translates logic
expressions into directed graphs and a cycle in the graph indicates the
expression never resolves to a truth value.

Then your logic is too simple to handle the needed logic.

Prolog only does FIRST order logic, and not all of it.

The logic used here is at least Second order, so out of the reach of
Prolog.

If you want to claim differently, show how Prolog verifies a proof of
the Pythagorean Theorem.

In fact, almost all of the examples you actaully try to run with are
down at the simple level of Categorical logic which only handles things
of one super-class divided into sub-classes. That logic is way to simple
to handle the things the theorems have been talking about. My guess is
that is as complicated of logic that you can understand, so you try to
force everything into it, and FAIL.

Please explain this in English:

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

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

ChatGPT
The first statement in Prolog is an assignment where LP is defined as
the negation of the truth value of LP itself. This means that LP is the
logical negation of LP, indicating that LP is false if it is true, and
true if it is false.

The second statement is a query that checks if there exists a
unification between LP and not(true(LP)). It attempts to find a
consistent value for LP that satisfies the equation.

In this case, the result of the query is false, indicating that there is
no valid unification between LP and not(true(LP)). In other words, there
is no consistent value that can simultaneously satisfy the equation LP = not(true(LP)). This suggests that there is a contradiction in the logic,
as the equation cannot hold true for any value of LP.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XPost: comp.theory, sci.logic

On 5/12/2023 9:18 PM, Richard Damon wrote:

On 5/12/23 5:57 PM, olcott wrote:

On 5/12/2023 1:42 PM, Richard Damon wrote:

On 5/12/23 11:04 AM, olcott wrote:

On 5/12/2023 9:06 AM, Richard Damon wrote:

On 5/12/23 12:51 AM, olcott wrote:

On 5/11/2023 10:45 PM, Richard Damon wrote:

On 5/11/23 11:30 PM, olcott wrote:

On 5/11/2023 9:54 PM, Richard Damon wrote:

On 5/11/23 10:34 PM, olcott wrote:

FROM HIS PROOF!

He first does a lot of work to establish a number of properties. >>>>>>>>>> In other words you agree that Tarski did "prove" that the

notion of
Truth cannot be fully formalized on a fundamental basis
directly related
to the Liar Paradox?

Only in the sense that since we KNOW the Liar's paradox can't >>>>>>>>> be true, and a "Definition of Truth" (not a "notion of Truth) >>>>>>>>> would lead to being able to prove that the Liar's paradox is true, >>>>>>>>>

That is ridiculous.

Why? Do you think the Liar's Paradox should be provable to be True? >>>>>>>

The Liar Paradox is not a truth bearer, END-OF-STORY !!!

Right, so why do you fault Tarski for saying that?

His proof shows that if a "Definition of Truth" existed, it
provides a way to prove the Liar's Paradox is True.

That is a nutty idea.
Any system that proves that a self-contradictory expression is true
is a broken system.

Right, and the proof shows that would be any system with a
"definition of Truth", so you AGREE with Tarski.

Not at all, Tarski's system is incorrect. All of analytical truth1 is a
body of semantic tautologies that excludes the liar paradox.

1 It is commonly known that analytical truth includes all of math and
all of logic. My new idea is that it also includes the model of the
world.

Analytic truth is derived from applying truth preserving operations to >>>> expressions of language that have been stipulated to be true.
This cannot possibly derive non-truth bearers as true.

Right, so you agre with Tarksi that there can not be a "Definition of
Truth".

Not at all.

Prolog uses the exact same system that I just specified expressions
that
are stipulated to be true are Prolog facts with Prolog rules as a
set of
truth preserving operations.

Prolog is limited in the logic it can do,

But, so it seems are you.

Prolog is smart enough to reject the Liar Paradox.

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

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

The above test shows that LP is infinitely recursive never resolving
to a truth value.

So?

Tarski was too stupid (on this one issue) to understand that the Liar
Paradox is excluded from the body of truth.

Why do you say that? WHere does he say what you say he is saying?

Please point out the pont where he is ACCEPTING the Liar's paradox.

The point where the Liar coms up, he uses that fact to point out that
the intial assumption MUST be incorrect, as it lead to proving a
non-true statement.

I think your problem is that you just don't understand the proof you are reading and reading into it the errors that you yourself make.

Anyone that uses the Liar Paradox as any basis for showing the
properties of truth has committed a category error1, the Liar Paradox is excluded from the category of truth.

1 Flibble's key insight


--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

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XPost: comp.theory, sci.logic

On 5/13/23 4:28 PM, olcott wrote:

On 5/12/2023 9:18 PM, Richard Damon wrote:

On 5/12/23 5:57 PM, olcott wrote:

On 5/12/2023 1:42 PM, Richard Damon wrote:

On 5/12/23 11:04 AM, olcott wrote:

On 5/12/2023 9:06 AM, Richard Damon wrote:

On 5/12/23 12:51 AM, olcott wrote:

On 5/11/2023 10:45 PM, Richard Damon wrote:

On 5/11/23 11:30 PM, olcott wrote:

On 5/11/2023 9:54 PM, Richard Damon wrote:

On 5/11/23 10:34 PM, olcott wrote:

FROM HIS PROOF!

He first does a lot of work to establish a number of
properties.

In other words you agree that Tarski did "prove" that the >>>>>>>>>>> notion of
Truth cannot be fully formalized on a fundamental basis
directly related
to the Liar Paradox?

Only in the sense that since we KNOW the Liar's paradox can't >>>>>>>>>> be true, and a "Definition of Truth" (not a "notion of Truth) >>>>>>>>>> would lead to being able to prove that the Liar's paradox is >>>>>>>>>> true,

That is ridiculous.

Why? Do you think the Liar's Paradox should be provable to be True? >>>>>>>>

The Liar Paradox is not a truth bearer, END-OF-STORY !!!

Right, so why do you fault Tarski for saying that?

His proof shows that if a "Definition of Truth" existed, it
provides a way to prove the Liar's Paradox is True.

That is a nutty idea.
Any system that proves that a self-contradictory expression is true
is a broken system.

Right, and the proof shows that would be any system with a
"definition of Truth", so you AGREE with Tarski.

Not at all, Tarski's system is incorrect. All of analytical truth1 is a
body of semantic tautologies that excludes the liar paradox.

1 It is commonly known that analytical truth includes all of math and
all of logic. My new idea is that it also includes the model of the
world.

Analytic truth is derived from applying truth preserving operations to >>>>> expressions of language that have been stipulated to be true.
This cannot possibly derive non-truth bearers as true.

Right, so you agre with Tarksi that there can not be a "Definition
of Truth".

Not at all.

Prolog uses the exact same system that I just specified expressions
that
are stipulated to be true are Prolog facts with Prolog rules as a
set of
truth preserving operations.

Prolog is limited in the logic it can do,

But, so it seems are you.

Prolog is smart enough to reject the Liar Paradox.

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

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

The above test shows that LP is infinitely recursive never
resolving to a truth value.

So?

Tarski was too stupid (on this one issue) to understand that the Liar
Paradox is excluded from the body of truth.

Why do you say that? WHere does he say what you say he is saying?

Please point out the pont where he is ACCEPTING the Liar's paradox.

The point where the Liar coms up, he uses that fact to point out that
the intial assumption MUST be incorrect, as it lead to proving a
non-true statement.

I think your problem is that you just don't understand the proof you
are reading and reading into it the errors that you yourself make.

Anyone that uses the Liar Paradox as any basis for showing the
properties of truth has committed a category error1, the Liar Paradox is excluded from the category of truth.

1 Flibble's key insight

So, you jut don't understand the concept of a proof by contradiction?

I guess your understanding of logic is too primative.

You yourself said that any system that accepts the Liar's Paradox as a
truth bearer must be broken.

Since what Tarski shows is that any system with a "Definition of Truth"
will accept the Liar's Paradox as a True Statement, you must agree that
he is correct.

That, or you are admitting that you speak with forked tounge and nothin
gyou say actually makes sense.

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XPost: comp.theory, sci.logic

On 5/13/23 11:01 AM, olcott wrote:

On 5/13/2023 8:17 AM, Richard Damon wrote:

On 5/12/23 11:49 PM, olcott wrote:

On 5/12/2023 9:18 PM, Richard Damon wrote:

On 5/12/23 8:13 PM, olcott wrote:

On 5/12/2023 1:42 PM, Richard Damon wrote:

On 5/12/23 11:04 AM, olcott wrote:

On 5/12/2023 9:06 AM, Richard Damon wrote:

On 5/12/23 12:51 AM, olcott wrote:

On 5/11/2023 10:45 PM, Richard Damon wrote:

On 5/11/23 11:30 PM, olcott wrote:

On 5/11/2023 9:54 PM, Richard Damon wrote:

On 5/11/23 10:34 PM, olcott wrote:

FROM HIS PROOF!

He first does a lot of work to establish a number of >>>>>>>>>>>>>> properties.

In other words you agree that Tarski did "prove" that the >>>>>>>>>>>>> notion of
Truth cannot be fully formalized on a fundamental basis >>>>>>>>>>>>> directly related
to the Liar Paradox?

Only in the sense that since we KNOW the Liar's paradox >>>>>>>>>>>> can't be true, and a "Definition of Truth" (not a "notion of >>>>>>>>>>>> Truth) would lead to being able to prove that the Liar's >>>>>>>>>>>> paradox is true,

That is ridiculous.

Why? Do you think the Liar's Paradox should be provable to be >>>>>>>>>> True?

The Liar Paradox is not a truth bearer, END-OF-STORY !!!

Right, so why do you fault Tarski for saying that?

His proof shows that if a "Definition of Truth" existed, it
provides a way to prove the Liar's Paradox is True.

That is a nutty idea.
Any system that proves that a self-contradictory expression is
true is a broken system.

Right, and the proof shows that would be any system with a
"definition of Truth", so you AGREE with Tarski.

Not at all, Tarski's system is incorrect. All of analytical truth1
is a
body of semantic tautologies that excludes the liar paradox.

Then why does that "Definition of Truth" PROVE the Liar's Paradox?

If his system is "incorrect" what SPECIFIC step did he do that was
improper? (not conclusion, what STEP).

The step where he used the Liar Paradox as the basis of his proof.

Your problem is you don't actually understand how logic works.

My problem is that others do not understand the philosophical
foundations of logic as deeply as I do, they merely follow what they
read in a textbook as if it was the infallible word of God.

1 It is commonly known that analytical truth includes all of math and >>>>> all of logic. My new idea is that it also includes the model of the
world.

Except since your model doesn't work at all, you have a problem.

When-so-ever an expression of language is derived by applying only truth >>> preserving operations to expressions of language that have been
stipulated to be true we are guaranteed that this expression is true.

Prolog is smart enough to reject the Liar Paradox because it uses the >>>>> same system that I use, only expressions of language that have been
derived by applying truth preserving operations [Prolog rules] to
expressions of language that have been stipulated to be true [Prolog >>>>> facts] are true. Everything else [Prolog's negation as failure] counts >>>>> as untrue.

And Prolog is too limited to handle the logic of these proofs.

It is not in fact too limited to handle these proofs as I have
concretely proved. I invented Minimal Type Theory that translates logic
expressions into directed graphs and a cycle in the graph indicates the
expression never resolves to a truth value.

Then your logic is too simple to handle the needed logic.

Prolog only does FIRST order logic, and not all of it.

The logic used here is at least Second order, so out of the reach of
Prolog.

If you want to claim differently, show how Prolog verifies a proof of
the Pythagorean Theorem.

In fact, almost all of the examples you actaully try to run with are
down at the simple level of Categorical logic which only handles
things of one super-class divided into sub-classes. That logic is way
to simple to handle the things the theorems have been talking about.
My guess is that is as complicated of logic that you can understand,
so you try to force everything into it, and FAIL.

Please explain this in English:

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

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

ChatGPT
The first statement in Prolog is an assignment where LP is defined as
the negation of the truth value of LP itself. This means that LP is the logical negation of LP, indicating that LP is false if it is true, and
true if it is false.

The second statement is a query that checks if there exists a
unification between LP and not(true(LP)). It attempts to find a
consistent value for LP that satisfies the equation.

In this case, the result of the query is false, indicating that there is
no valid unification between LP and not(true(LP)). In other words, there
is no consistent value that can simultaneously satisfy the equation LP = not(true(LP)). This suggests that there is a contradiction in the logic,
as the equation cannot hold true for any value of LP.

So?

the Liar's paradox is built on very simple logic.

I don't diagree that the Liar's Paradox is a non-truth-bearer, and the
fact that you keep arguing about it just shows how little you understand
about the conversation you are having.

Prolog is incapable of handling the level of logic needed to handle
Tarski or Godel, and since your understanding of Logic seems to be no
better than Prolog, you can't handle them either.

You are just confirming your utter stupidity and ignorance about all of
this.

What did any of what ChatGPT say that negates my comments.

You are just proving your stupidity.

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On 5/13/23 4:28 PM, olcott wrote:

Anyone that uses the Liar Paradox as any basis for showing the
properties of truth has committed a category error1, the Liar Paradox is excluded from the category of truth.

So, since YOUR arguement uses the Liar's Paradox as a basis of
determining true, YOU have committed a category error?

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