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computers / comp.ai.philosophy / Re: Tarski Undefinability Theorem is refuted

SubjectAuthor
* Tarski Undefinability Theorem is refutedolcott
+* Re: Tarski Undefinability Theorem is refutedRichard Damon
|`* Re: Tarski Undefinability Theorem is refutedolcott
| `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|  `* Re: Tarski Undefinability Theorem is refutedolcott
|   `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|    `* Re: Tarski Undefinability Theorem is refutedolcott
|     `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|      `* Re: Tarski Undefinability Theorem is refutedolcott
|       `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|        `* Re: Tarski Undefinability Theorem is refutedolcott
|         `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|          `* Re: Tarski Undefinability Theorem is refutedolcott
|           `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|            `* Re: Tarski Undefinability Theorem is refutedolcott
|             `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|              `* Re: Tarski Undefinability Theorem is refutedolcott
|               `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|                `* Re: Tarski Undefinability Theorem is refutedolcott
|                 `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|                  `* Re: Tarski Undefinability Theorem is refutedolcott
|                   `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|                    `* Re: Tarski Undefinability Theorem is refutedolcott
|                     `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|                      +* Re: Tarski Undefinability Theorem is refutedolcott
|                      |`* Re: Tarski Undefinability Theorem is refutedRichard Damon
|                      | `* Re: Tarski Undefinability Theorem is refutedolcott
|                      |  `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|                      |   `* Re: Tarski Undefinability Theorem is refutedolcott
|                      |    `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|                      |     `* Re: Tarski Undefinability Theorem is refutedolcott
|                      |      `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|                      |       `* Re: Tarski Undefinability Theorem is refutedolcott
|                      |        `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|                      |         `* Re: Tarski Undefinability Theorem is refutedolcott
|                      |          +* Re: Tarski Undefinability Theorem is refutedDon Stockbauer
|                      |          |`- Re: Tarski Undefinability Theorem is refutedolcott
|                      |          `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|                      |           `* Re: Tarski Undefinability Theorem is refutedolcott
|                      |            `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|                      |             `* Re: Tarski Undefinability Theorem is refuted [also Golcott
|                      |              `* Re: Tarski Undefinability Theorem is refuted [also GRichard Damon
|                      |               +* Re: Tarski Undefinability Theorem is refuted [also Golcott
|                      |               |`* Re: Tarski Undefinability Theorem is refuted [also GRichard Damon
|                      |               | `* Re: Tarski Undefinability Theorem is refuted [also Golcott
|                      |               |  `* Re: Tarski Undefinability Theorem is refuted [also GRichard Damon
|                      |               |   +* Re: Tarski Undefinability Theorem is refuted [also Golcott
|                      |               |   |`* Re: Tarski Undefinability Theorem is refuted [also GRichard Damon
|                      |               |   | +* Re: Tarski Undefinability Theorem is refuted [also Golcott
|                      |               |   | |`* Re: Tarski Undefinability Theorem is refuted [also GRichard Damon
|                      |               |   | | `* Re: Tarski Undefinability Theorem is refuted [also Golcott
|                      |               |   | |  `* Re: Tarski Undefinability Theorem is refuted [also GRichard Damon
|                      |               |   | |   `* Re: Tarski Undefinability Theorem is refuted [also Golcott
|                      |               |   | |    `* Re: Tarski Undefinability Theorem is refuted [also GRichard Damon
|                      |               |   | |     `* Re: Tarski Undefinability Theorem is refuted [also Golcott
|                      |               |   | |      `* Re: Tarski Undefinability Theorem is refuted [also GRichard Damon
|                      |               |   | |       `* Re: Tarski Undefinability Theorem is refuted [also Golcott
|                      |               |   | |        `* Re: Tarski Undefinability Theorem is refuted [also GRichard Damon
|                      |               |   | |         +* Re: Tarski Undefinability Theorem is refuted [also Golcott
|                      |               |   | |         |`* Re: Tarski Undefinability Theorem is refuted [also GRichard Damon
|                      |               |   | |         | +* Re: Tarski Undefinability Theorem is refuted [also Golcott
|                      |               |   | |         | |`* Re: Tarski Undefinability Theorem is refuted [also GRichard Damon
|                      |               |   | |         | | `* Re: Tarski Undefinability Theorem is refuted [also Golcott
|                      |               |   | |         | |  `- Re: Tarski Undefinability Theorem is refuted [also GRichard Damon
|                      |               |   | |         | `* Re: Tarski Undefinability Theorem is refuted [also Golcott
|                      |               |   | |         |  `- Re: Tarski Undefinability Theorem is refuted [also GRichard Damon
|                      |               |   | |         `* Re: Tarski Undefinability Theorem is refuted [also Golcott
|                      |               |   | |          `* Re: Tarski Undefinability Theorem is refuted [also GRichard Damon
|                      |               |   | |           `* Re: Tarski Undefinability Theorem is refuted [also Golcott
|                      |               |   | |            `- Re: Tarski Undefinability Theorem is refuted [also GRichard Damon
|                      |               |   | `- Re: Tarski Undefinability Theorem is refuted [also GDon Stockbauer
|                      |               |   `* Re: Tarski Undefinability Theorem is refuted [also Golcott
|                      |               |    `- Re: Tarski Undefinability Theorem is refuted [also GRichard Damon
|                      |               `* Re: Tarski Undefinability Theorem is refuted [also Golcott
|                      |                `- Re: Tarski Undefinability Theorem is refuted [also GRichard Damon
|                      +* Re: Tarski Undefinability Theorem is refutedolcott
|                      |`* Re: Tarski Undefinability Theorem is refutedRichard Damon
|                      | `* Re: Tarski Undefinability Theorem is refutedolcott
|                      |  `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|                      |   +* Re: Tarski Undefinability Theorem is refutedolcott
|                      |   |`* Re: Tarski Undefinability Theorem is refutedRichard Damon
|                      |   | `* Re: Tarski Undefinability Theorem is refutedolcott
|                      |   |  `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|                      |   |   `- Re: Tarski Undefinability Theorem is refutedolcott
|                      |   +* Re: Tarski Undefinability Theorem is refutedolcott
|                      |   |`* Re: Tarski Undefinability Theorem is refutedRichard Damon
|                      |   | `* Re: Tarski Undefinability Theorem is refutedolcott
|                      |   |  `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|                      |   |   `* Re: Tarski Undefinability Theorem is refutedolcott
|                      |   |    `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|                      |   |     `- Re: Tarski Undefinability Theorem is refutedolcott
|                      |   `* Re: Tarski Undefinability Theorem is refutedolcott
|                      |    `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|                      |     `* Re: Tarski Undefinability Theorem is refutedolcott
|                      |      `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|                      |       `* Re: Tarski Undefinability Theorem is refutedolcott
|                      |        `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|                      |         `* Re: Tarski Undefinability Theorem is refutedolcott
|                      |          `* Re: Tarski Undefinability Theorem is refutedRichard Damon
|                      |           `* Re: Tarski Undefinability Theorem is refuted [also Golcott
|                      |            +* Re: Tarski Undefinability Theorem is refuted [also GRichard Damon
|                      |            `- Re: Tarski Undefinability Theorem is refuted [also GDon Stockbauer
|                      `* Re: Tarski Undefinability Theorem is refutedolcott
+- Re: Tarski Undefinability Theorem is refutedolcott
`* Re: Tarski Undefinability Theorem is refutedolcott

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Re: Tarski Undefinability Theorem is refuted

<totm1i$1lrpp$3@dont-email.me>

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https://www.novabbs.com/computers/article-flat.php?id=10141&group=comp.ai.philosophy#10141

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From: polco...@gmail.com (olcott)
Newsgroups: comp.theory,comp.ai.philosophy,sci.logic
Subject: Re: Tarski Undefinability Theorem is refuted
Date: Sun, 1 Jan 2023 22:20:01 -0600
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 by: olcott - Mon, 2 Jan 2023 04:20 UTC

On 1/1/2023 9:14 PM, Richard Damon wrote:
> On 1/1/23 9:47 PM, olcott wrote:
>
>> I don't believe that you have an IQ anywhere near the top 1% much less
>> than the 185 IQ of top 2 in a billion. I could easily believe the top
>> 5%, most everyone here is in the top 5%.
>>
>
> Doesn't matter what you believe, as you have demonstrated that you don't
> understand what is actually Truth.
>
>
>

You have not demonstrated any very significant understanding of these
things. It does seem that you have demonstrated key misunderstandings of
Tarski. I guy with a 2 in one billion IQ would not make these mistakes.
A guy with a top 1% IQ might make these mistakes if they barely skimmed
the material.

You can see that the proof is only two pages long, not too much to
carefully study.

http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf

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

Re: Tarski Undefinability Theorem is refuted

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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Mon, 2 Jan 2023 04:25 UTC

On 1/1/23 10:59 PM, olcott wrote:
> On 1/1/2023 8:32 PM, Richard Damon wrote:
>> On 1/1/23 8:04 PM, olcott wrote:
>>> All expressions of language that are analytically true require a
>>> semantic connection to their truth maker.
>>>
>>> Try and show how an expression of language can be true in a formal
>>> system when that formal system cannot express any connection to the
>>> required truth maker of this expression.
>>>
>>
>> So you still don't understand the difference between having a semantic
>> connenction (which might be infinite) to being proven (which must be
>> finite in the system in question).
>>
>
> Tarski and Gödel were not referring to infinite proofs, thus infinite
> proofs are irrelevant to Tarski and Gödel.

Right

>
> When we exclude things that are irrelevant to Tarski and Gödel then
> True(x) means that there is a semantic connection to a truth maker thus
> providing the path for a formal proof.
>

So they are talking about things that are Analytic Truths because they
are connected to a known Truth Maker by an infinite series of
connections, but are not Provable, because that connection is Infinite
(and thus not a proof).

For instance, Godel sentence G is True, because there does not exist any
number that matches the criteria (as G claims), demonstratable by noting
that every number (all infinte number of them) when tested by the criteria.

The statement is not provable, because, as shown in the Meta Theory,
there is no finite proof of G in existance, since if there WAS one, then
from that proof we could compute a number g that would satisfy the
criteria, which we just established there was none.

You keep on trying to say that G is not a Analytic Truth, when it is,
because it IS connected to known Truth Bearers via a set of Semantic
Connections, even though infinite.

The problem is you just don't understand the statements, so you can't
see the connections.

Re: Tarski Undefinability Theorem is refuted

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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Mon, 2 Jan 2023 04:36 UTC

On 1/1/23 11:13 PM, olcott wrote:
> On 1/1/2023 8:39 PM, Richard Damon wrote:
>> On 1/1/23 8:29 PM, olcott wrote:
>>> On 1/1/2023 3:37 PM, Richard Damon wrote:
>>>> On 1/1/23 2:51 PM, olcott wrote:
>>
>>>>> Hardly anyone seems to understand that the Liar Paradox is simply
>>>>> not a
>>>>> truth bearer otherwise tertiary logic would have never been created.
>>>>
>>>> No Nearly EVERYONE understands that in Binary Logic, the Liar
>>>> Paracos is simply not a Truth Bearer.
>>>
>>> I don't think that all the people writing papers about how to resolve
>>> the Liar Paradox fail to understand binary logic.
>>>
>>
>> Most INTELEGENT people trying to resolve the Liar's Paradox understand
>> Binary Logic, and are looking for logic beyond Binary Logic to see if
>> other Logical Paradigms might be able to handle that sort of thing
>> (and actually are probably looking at things more complicated then the
>> simple Liar's Paradox).
>>
>
> Anyone that is trying to resolve an expression of language that is not a
> truth bearer to a truth value is on a fools errand.
>
>>
>> I will admit, that are probably a lot of DUMB people, who don't
>> understand logic, and are doing all sorts of dumb things, and if those
>> are hiting your radar, you need a better selection filter.
>>
>
> Saul Kripke was by no means any sort of dumb
> https://www.impan.pl/~kz/truthseminar/Kripke_Outline.pdf

And he isn't trying to say the Liar's Paradox is a Truth Beared.

At a quick glance he seems to be working on logic that handles
ill-defined statments with partial knowledge

>
>> Of course, those are probably the works that you can sort of
>> understand, since they are at your level.
>>
>> And actually, MOST people just understand that non-truth of the Liar's
>> Paradox and they leave it at that.
>>
>
> Tarski "proved" that truth cannot be specified and used the Liar Paradox
> as the foundation of this proof.

Not quite.

He Showed that if you presume a complete specification for truth could
exist in a system, that it is neccessarily possible to prove that the
Liar's Paradox is True.

Since we know that is a false statement, the Premise assumed must be False.

>
> That is like proving the angel food cakes cannot be baked because the
> cannot be made from house bricks.
>

Just shows you don't understand the technique of Proof By Contradiction.
Perhaps because your logic system can't handle it.

> His entire proof is on pages 275-276:
> http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf
>
> I was able to get Adobe Acrobat to OCR that text, it worked quite well.
> This allows keyword searches.
>
>

So, since you don't seem to understand what you read, OCR'ing to search
won't help you.

You don't need to search for sinppets, your need to read it fully to
understand it (but firt make sure you understand the logical
prerequisites for the material.

Your technique seems similar to the Error of Prooftexting. (Taking
statements in the material out of their context to try to show the point
you have pre-decided to be the point of the text)

Re: Tarski Undefinability Theorem is refuted

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From: polco...@gmail.com (olcott)
Newsgroups: comp.theory,comp.ai.philosophy,sci.logic
Subject: Re: Tarski Undefinability Theorem is refuted
Date: Sun, 1 Jan 2023 22:39:48 -0600
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 by: olcott - Mon, 2 Jan 2023 04:39 UTC

On 1/1/2023 10:25 PM, Richard Damon wrote:
> On 1/1/23 10:59 PM, olcott wrote:
>> On 1/1/2023 8:32 PM, Richard Damon wrote:
>>> On 1/1/23 8:04 PM, olcott wrote:
>>>> All expressions of language that are analytically true require a
>>>> semantic connection to their truth maker.
>>>>
>>>> Try and show how an expression of language can be true in a formal
>>>> system when that formal system cannot express any connection to the
>>>> required truth maker of this expression.
>>>>
>>>
>>> So you still don't understand the difference between having a
>>> semantic connenction (which might be infinite) to being proven (which
>>> must be finite in the system in question).
>>>
>>
>> Tarski and Gödel were not referring to infinite proofs, thus infinite
>> proofs are irrelevant to Tarski and Gödel.
>
> Right
>
>>
>> When we exclude things that are irrelevant to Tarski and Gödel then
>> True(x) means that there is a semantic connection to a truth maker
>> thus providing the path for a formal proof.
>>
>
> So they are talking about things that are Analytic Truths because they
> are connected to a known Truth Maker by an infinite series of
> connections, but are not Provable, because that connection is Infinite
> (and thus not a proof).
>

Not in the ballpark of anywhere nearly correct. They both anchor their
work in epistemological antinomies that are necessarily not truth
bearers. No infinite proof is required, simply reject the
epistemological antinomy as not any member of any formal system.

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

Re: Tarski Undefinability Theorem is refuted

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Subject: Re: Tarski Undefinability Theorem is refuted
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 by: olcott - Mon, 2 Jan 2023 04:49 UTC

On 1/1/2023 10:36 PM, Richard Damon wrote:
> On 1/1/23 11:13 PM, olcott wrote:
>> On 1/1/2023 8:39 PM, Richard Damon wrote:
>>> On 1/1/23 8:29 PM, olcott wrote:
>>>> On 1/1/2023 3:37 PM, Richard Damon wrote:
>>>>> On 1/1/23 2:51 PM, olcott wrote:
>>>
>>>>>> Hardly anyone seems to understand that the Liar Paradox is simply
>>>>>> not a
>>>>>> truth bearer otherwise tertiary logic would have never been created.
>>>>>
>>>>> No Nearly EVERYONE understands that in Binary Logic, the Liar
>>>>> Paracos is simply not a Truth Bearer.
>>>>
>>>> I don't think that all the people writing papers about how to
>>>> resolve the Liar Paradox fail to understand binary logic.
>>>>
>>>
>>> Most INTELEGENT people trying to resolve the Liar's Paradox
>>> understand Binary Logic, and are looking for logic beyond Binary
>>> Logic to see if other Logical Paradigms might be able to handle that
>>> sort of thing (and actually are probably looking at things more
>>> complicated then the simple Liar's Paradox).
>>>
>>
>> Anyone that is trying to resolve an expression of language that is not a
>> truth bearer to a truth value is on a fools errand.
>>
>>>
>>> I will admit, that are probably a lot of DUMB people, who don't
>>> understand logic, and are doing all sorts of dumb things, and if
>>> those are hiting your radar, you need a better selection filter.
>>>
>>
>> Saul Kripke was by no means any sort of dumb
>> https://www.impan.pl/~kz/truthseminar/Kripke_Outline.pdf
>
> And he isn't trying to say the Liar's Paradox is a Truth Beared.
>
> At a quick glance he seems to be working on logic that handles
> ill-defined statments with partial knowledge
>
>>
>>> Of course, those are probably the works that you can sort of
>>> understand, since they are at your level.
>>>
>>> And actually, MOST people just understand that non-truth of the
>>> Liar's Paradox and they leave it at that.
>>>
>>
>> Tarski "proved" that truth cannot be specified and used the Liar
>> Paradox as the foundation of this proof.
>
> Not quite.
>
> He Showed that if you presume a complete specification for truth could
> exist in a system, that it is neccessarily possible to prove that the
> Liar's Paradox is True.
>

Maybe Tarski made that same mistake you are are making.
If Tarski believed that he proved this sentence is true in his
meta-theory: "This sentence is not true" then Tarski made a terrible
mistake.

{This sentence is not true: "This sentence is not true"} would be true.
"This sentence is not true" is never true.

My key skill from software engineering is to boil complex things down to
their barest possible essence. Tarski already mostly did that for Gödel.

Did you verify that his proof is only two pages yet?

http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf

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

Re: Tarski Undefinability Theorem is refuted

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 by: Richard Damon - Mon, 2 Jan 2023 05:07 UTC

On 1/1/23 11:20 PM, olcott wrote:
> On 1/1/2023 9:14 PM, Richard Damon wrote:
>> On 1/1/23 9:47 PM, olcott wrote:
>>
>>> I don't believe that you have an IQ anywhere near the top 1% much less
>>> than the 185 IQ of top 2 in a billion. I could easily believe the top
>>> 5%, most everyone here is in the top 5%.
>>>
>>
>> Doesn't matter what you believe, as you have demonstrated that you
>> don't understand what is actually Truth.
>>
>>
>>
>
> You have not demonstrated any very significant understanding of these
> things. It does seem that you have demonstrated key misunderstandings of
> Tarski. I guy with a 2 in one billion IQ would not make these mistakes.
> A guy with a top 1% IQ might make these mistakes if they barely skimmed
> the material.
>
> You can see that the proof is only two pages long, not too much to
> carefully study.
>
> http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf
>

First, you confuse Intelgence with Knowledge.

As I have mentioned before, this is an area that I admit I haven't
studied in great detail (but it seems I still understand some of the
point better than you, which shows your lack of intelegence).

You claim Tarski bases his proof on the Liar needing a Truth Value.

In fact, a simple reading of the text shows that he is using the
standard Proof by Contradiction to show that IF the "Thesis A" which
resumes a definition of Truth was actually True, then we can prove that
the Liar's Paradox is True.

Since we know the Liar's Paradox is not a Truth Bearer, and thus not
True, the Thesis can not be true.

IF I find the time, I might put the effort to read the papers you have
linked to and see if I can make some more detailed comments on them.

My first guess is a few days effort would probably be sufficent, which
compared to your decades, seems a reasonable ratio considering our
comparative intelegence.

Re: Tarski Undefinability Theorem is refuted

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 by: Richard Damon - Mon, 2 Jan 2023 05:13 UTC

On 1/1/23 11:39 PM, olcott wrote:
> On 1/1/2023 10:25 PM, Richard Damon wrote:
>> On 1/1/23 10:59 PM, olcott wrote:
>>> On 1/1/2023 8:32 PM, Richard Damon wrote:
>>>> On 1/1/23 8:04 PM, olcott wrote:
>>>>> All expressions of language that are analytically true require a
>>>>> semantic connection to their truth maker.
>>>>>
>>>>> Try and show how an expression of language can be true in a formal
>>>>> system when that formal system cannot express any connection to the
>>>>> required truth maker of this expression.
>>>>>
>>>>
>>>> So you still don't understand the difference between having a
>>>> semantic connenction (which might be infinite) to being proven
>>>> (which must be finite in the system in question).
>>>>
>>>
>>> Tarski and Gödel were not referring to infinite proofs, thus infinite
>>> proofs are irrelevant to Tarski and Gödel.
>>
>> Right
>>
>>>
>>> When we exclude things that are irrelevant to Tarski and Gödel then
>>> True(x) means that there is a semantic connection to a truth maker
>>> thus providing the path for a formal proof.
>>>
>>
>> So they are talking about things that are Analytic Truths because they
>> are connected to a known Truth Maker by an infinite series of
>> connections, but are not Provable, because that connection is Infinite
>> (and thus not a proof).
>>
>
> Not in the ballpark of anywhere nearly correct. They both anchor their
> work in epistemological antinomies that are necessarily not truth
> bearers. No infinite proof is required, simply reject the
> epistemological antinomy as not any member of any formal system.
>

Nope, you just show you don't know what you are taking about.

What in the question of if a number existes with a property defined by
an always halting program is a epistemological antinomy?

Since that IS what Godel statement G is.

The epistemolgical antinomey is used help derive the nature of that
always halting program, as it is transformed from a statement about the
truth of a statement into about the proof of a statement (which is
always a Truth Beared)

Your repeating this error just shows that you haven't actually read any
good description of what Godel did.

You are just showing your total ignorance of the material you have been
"studing" for decades.

Re: Tarski Undefinability Theorem is refuted

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 by: olcott - Mon, 2 Jan 2023 05:47 UTC

On 1/1/2023 11:13 PM, Richard Damon wrote:
> On 1/1/23 11:39 PM, olcott wrote:
>> On 1/1/2023 10:25 PM, Richard Damon wrote:
>>> On 1/1/23 10:59 PM, olcott wrote:
>>>> On 1/1/2023 8:32 PM, Richard Damon wrote:
>>>>> On 1/1/23 8:04 PM, olcott wrote:
>>>>>> All expressions of language that are analytically true require a
>>>>>> semantic connection to their truth maker.
>>>>>>
>>>>>> Try and show how an expression of language can be true in a formal
>>>>>> system when that formal system cannot express any connection to the
>>>>>> required truth maker of this expression.
>>>>>>
>>>>>
>>>>> So you still don't understand the difference between having a
>>>>> semantic connenction (which might be infinite) to being proven
>>>>> (which must be finite in the system in question).
>>>>>
>>>>
>>>> Tarski and Gödel were not referring to infinite proofs, thus
>>>> infinite proofs are irrelevant to Tarski and Gödel.
>>>
>>> Right
>>>
>>>>
>>>> When we exclude things that are irrelevant to Tarski and Gödel then
>>>> True(x) means that there is a semantic connection to a truth maker
>>>> thus providing the path for a formal proof.
>>>>
>>>
>>> So they are talking about things that are Analytic Truths because
>>> they are connected to a known Truth Maker by an infinite series of
>>> connections, but are not Provable, because that connection is
>>> Infinite (and thus not a proof).
>>>
>>
>> Not in the ballpark of anywhere nearly correct. They both anchor their
>> work in epistemological antinomies that are necessarily not truth
>> bearers. No infinite proof is required, simply reject the
>> epistemological antinomy as not any member of any formal system.
>>
>
> Nope, you just show you don't know what you are taking about.
>
> What in the question of if a number existes with a property defined by
> an always halting program is a epistemological antinomy?
>
> Since that IS what Godel statement G is.
>
> The epistemolgical antinomey is used help derive the nature of that
> always halting program, as it is transformed from a statement about the
> truth of a statement into about the proof of a statement (which is
> always a Truth Beared)
>
> Your repeating this error just shows that you haven't actually read any
> good description of what Godel did.
>
> You are just showing your total ignorance of the material you have been
> "studing" for decades.

Tarski essentially greatly simplified the same proof that Gödel did.
That he anchored this proof in an epistemological antinomy was his big
mistake. You cannot correctly use an untrue expression as a basis for
analyzing the notion of truth, untrue expressions are simply excluded.

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

Re: Tarski Undefinability Theorem is refuted

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From: polco...@gmail.com (olcott)
Newsgroups: comp.theory,comp.ai.philosophy,sci.logic
Subject: Re: Tarski Undefinability Theorem is refuted
Date: Sun, 1 Jan 2023 23:51:27 -0600
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 by: olcott - Mon, 2 Jan 2023 05:51 UTC

On 1/1/2023 11:07 PM, Richard Damon wrote:
> On 1/1/23 11:20 PM, olcott wrote:
>> On 1/1/2023 9:14 PM, Richard Damon wrote:
>>> On 1/1/23 9:47 PM, olcott wrote:
>>>
>>>> I don't believe that you have an IQ anywhere near the top 1% much less
>>>> than the 185 IQ of top 2 in a billion. I could easily believe the top
>>>> 5%, most everyone here is in the top 5%.
>>>>
>>>
>>> Doesn't matter what you believe, as you have demonstrated that you
>>> don't understand what is actually Truth.
>>>
>>>
>>>
>>
>> You have not demonstrated any very significant understanding of these
>> things. It does seem that you have demonstrated key misunderstandings of
>> Tarski. I guy with a 2 in one billion IQ would not make these mistakes.
>> A guy with a top 1% IQ might make these mistakes if they barely skimmed
>> the material.
>>
>> You can see that the proof is only two pages long, not too much to
>> carefully study.
>>
>> http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf
>>
>
> First, you confuse Intelgence with Knowledge.
>
> As I have mentioned before, this is an area that I admit I haven't
> studied in great detail (but it seems I still understand some of the
> point better than you, which shows your lack of intelegence).
>
> You claim Tarski bases his proof on the Liar needing a Truth Value.
>
> In fact, a simple reading of the text shows that he is using the
> standard Proof by Contradiction to show that IF the "Thesis A" which
> resumes a definition of Truth was actually True, then we can prove that
> the Liar's Paradox is True.
>
> Since we know the Liar's Paradox is not a Truth Bearer, and thus not
> True, the Thesis can not be true.
>
> IF I find the time, I might put the effort to read the papers you have
> linked to and see if I can make some more detailed comments on them.
>
> My first guess is a few days effort would probably be sufficent, which
> compared to your decades, seems a reasonable ratio considering our
> comparative intelegence.

Finite Truth is all about showing that a truth maker semantic connection
exists. If exists then true else untrue.

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

Re: Tarski Undefinability Theorem is refuted

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 by: Richard Damon - Mon, 2 Jan 2023 06:01 UTC

On 1/1/23 11:49 PM, olcott wrote:
> On 1/1/2023 10:36 PM, Richard Damon wrote:
>> On 1/1/23 11:13 PM, olcott wrote:
>>> On 1/1/2023 8:39 PM, Richard Damon wrote:
>>>> On 1/1/23 8:29 PM, olcott wrote:
>>>>> On 1/1/2023 3:37 PM, Richard Damon wrote:
>>>>>> On 1/1/23 2:51 PM, olcott wrote:
>>>>
>>>>>>> Hardly anyone seems to understand that the Liar Paradox is simply
>>>>>>> not a
>>>>>>> truth bearer otherwise tertiary logic would have never been created.
>>>>>>
>>>>>> No Nearly EVERYONE understands that in Binary Logic, the Liar
>>>>>> Paracos is simply not a Truth Bearer.
>>>>>
>>>>> I don't think that all the people writing papers about how to
>>>>> resolve the Liar Paradox fail to understand binary logic.
>>>>>
>>>>
>>>> Most INTELEGENT people trying to resolve the Liar's Paradox
>>>> understand Binary Logic, and are looking for logic beyond Binary
>>>> Logic to see if other Logical Paradigms might be able to handle that
>>>> sort of thing (and actually are probably looking at things more
>>>> complicated then the simple Liar's Paradox).
>>>>
>>>
>>> Anyone that is trying to resolve an expression of language that is not a
>>> truth bearer to a truth value is on a fools errand.
>>>
>>>>
>>>> I will admit, that are probably a lot of DUMB people, who don't
>>>> understand logic, and are doing all sorts of dumb things, and if
>>>> those are hiting your radar, you need a better selection filter.
>>>>
>>>
>>> Saul Kripke was by no means any sort of dumb
>>> https://www.impan.pl/~kz/truthseminar/Kripke_Outline.pdf
>>
>> And he isn't trying to say the Liar's Paradox is a Truth Beared.
>>
>> At a quick glance he seems to be working on logic that handles
>> ill-defined statments with partial knowledge
>>
>>>
>>>> Of course, those are probably the works that you can sort of
>>>> understand, since they are at your level.
>>>>
>>>> And actually, MOST people just understand that non-truth of the
>>>> Liar's Paradox and they leave it at that.
>>>>
>>>
>>> Tarski "proved" that truth cannot be specified and used the Liar
>>> Paradox as the foundation of this proof.
>>
>> Not quite.
>>
>> He Showed that if you presume a complete specification for truth could
>> exist in a system, that it is neccessarily possible to prove that the
>> Liar's Paradox is True.
>>
>
> Maybe Tarski made that same mistake you are are making.
> If Tarski believed that he proved this sentence is true in his
> meta-theory: "This sentence is not true" then Tarski made a terrible
> mistake.
>
> {This sentence is not true: "This sentence is not true"} would be true.
> "This sentence is not true" is never true.
>
> My key skill from software engineering is to boil complex things down to
> their barest possible essence. Tarski already mostly did that for Gödel.
>
> Did you verify that his proof is only two pages yet?
>
> http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf
>

Where in those pages do you see your summary expressed?

Note, the construction of the Meta Theory is such that any statement in
the Theory means exactly the same thing in the Meta Theory, so it isn't
the meta theory having a statement referencing the statement in the
theory, but is a proof of the actual original statement.

The proof you reference on pages 275-276 is just a simple proof that it
is possible to construct in the Theory a statement that says, in effect,
that statement x is not provable in the Theory if and only if p is True.
With p being a reference to the whole sentence (Which is sort of Godels
statement in the Meta-theory),

This is NOT the "Liars Paradox", as the liar's paradox is about a
statement being TRUE, not about it being PROVABLE. (and in fact, it
looks like the top of page 275 is him showing why this statement IS a
Truth Bearer, using his words that "We can construct a sentence x of the
science in question". I beleive you will find this is his terminology to
describe sentneces which are what you call Truth Bearers.

Since the premise x is provable, or it is not true that x is provable
are BY DEFINITION truth bears.

Also, x being an element of the True Statements is ALSO a truth bearer,
as if x was a non-truth bearer, that statement would be false (as
non-truth beares are not true).

He then manipulates these terms and shows that neither x or not x are in
the set of provable statements, but x is in the set of True Statements
(since if x was not true, it would be provable, but provabe statements
are always true).

If you want to point out exactly which step in this proof you think he
makes an error.

I think you intend to make it about the statement x not being a truth
bearer, but he shows from the material at the begining of page 275 that
it IS, but mostly by refering to other parts of his work which he is
assuming you understand at this point.

If you want to disagree with the statement being a Truth Bearer, or as
he calls it "A Sentence of the Science", you need to show where the
things he references are wrong.

Again, it seems to be another of your errors by reading just the cliff
notes and not actually understanding what he is saying.

In partictular, I think you need to find the error in the previous proof
for the sentence:

In accordance with the first part of Th. I we can obtain the negation of
one of the sentences in condition (a) of convention T of §3 as a
consequence of the definition of the symbol 'Pr' (provided we replace
'Tr' in this convention by 'Pr').

Re: Tarski Undefinability Theorem is refuted

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 by: Richard Damon - Mon, 2 Jan 2023 06:07 UTC

On 1/2/23 12:51 AM, olcott wrote:
> On 1/1/2023 11:07 PM, Richard Damon wrote:
>> On 1/1/23 11:20 PM, olcott wrote:
>>> On 1/1/2023 9:14 PM, Richard Damon wrote:
>>>> On 1/1/23 9:47 PM, olcott wrote:
>>>>
>>>>> I don't believe that you have an IQ anywhere near the top 1% much less
>>>>> than the 185 IQ of top 2 in a billion. I could easily believe the top
>>>>> 5%, most everyone here is in the top 5%.
>>>>>
>>>>
>>>> Doesn't matter what you believe, as you have demonstrated that you
>>>> don't understand what is actually Truth.
>>>>
>>>>
>>>>
>>>
>>> You have not demonstrated any very significant understanding of these
>>> things. It does seem that you have demonstrated key misunderstandings of
>>> Tarski. I guy with a 2 in one billion IQ would not make these mistakes.
>>> A guy with a top 1% IQ might make these mistakes if they barely skimmed
>>> the material.
>>>
>>> You can see that the proof is only two pages long, not too much to
>>> carefully study.
>>>
>>> http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf
>>>
>>
>> First, you confuse Intelgence with Knowledge.
>>
>> As I have mentioned before, this is an area that I admit I haven't
>> studied in great detail (but it seems I still understand some of the
>> point better than you, which shows your lack of intelegence).
>>
>> You claim Tarski bases his proof on the Liar needing a Truth Value.
>>
>> In fact, a simple reading of the text shows that he is using the
>> standard Proof by Contradiction to show that IF the "Thesis A" which
>> resumes a definition of Truth was actually True, then we can prove
>> that the Liar's Paradox is True.
>>
>> Since we know the Liar's Paradox is not a Truth Bearer, and thus not
>> True, the Thesis can not be true.
>>
>> IF I find the time, I might put the effort to read the papers you have
>> linked to and see if I can make some more detailed comments on them.
>>
>> My first guess is a few days effort would probably be sufficent, which
>> compared to your decades, seems a reasonable ratio considering our
>> comparative intelegence.
>
> Finite Truth is all about showing that a truth maker semantic connection
> exists. If exists then true else untrue.
>

Where are you getting the term "Finite Truth".

Truth is allowed to be base on a infinite set of connections.

It is True if ANY (including infinte) set of connections exist.

It is only provable if a FINITE set of connections exist.

You keep on confusing these two terms, because in your mind you have
crossed their connections and mix up Truth with Knowledge, perhaps
because you studied some theries of Knowledge, and are confusing what is
known to be True with what is actually True.

You keep on makeing that sort of mistake in your words, by talking of
what we can KNOW to be true, and applying that to what is actually True.

Re: Tarski Undefinability Theorem is refuted

<toupqb$1q3c5$1@dont-email.me>

  copy mid

https://www.novabbs.com/computers/article-flat.php?id=10152&group=comp.ai.philosophy#10152

  copy link   Newsgroups: comp.theory comp.ai.philosophy sci.logic
Path: i2pn2.org!i2pn.org!eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail
From: polco...@gmail.com (olcott)
Newsgroups: comp.theory,comp.ai.philosophy,sci.logic
Subject: Re: Tarski Undefinability Theorem is refuted
Date: Mon, 2 Jan 2023 08:30:34 -0600
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 by: olcott - Mon, 2 Jan 2023 14:30 UTC

On 1/2/2023 12:07 AM, Richard Damon wrote:
> On 1/2/23 12:51 AM, olcott wrote:
>> On 1/1/2023 11:07 PM, Richard Damon wrote:
>>> On 1/1/23 11:20 PM, olcott wrote:
>>>> On 1/1/2023 9:14 PM, Richard Damon wrote:
>>>>> On 1/1/23 9:47 PM, olcott wrote:
>>>>>
>>>>>> I don't believe that you have an IQ anywhere near the top 1% much
>>>>>> less
>>>>>> than the 185 IQ of top 2 in a billion. I could easily believe the top
>>>>>> 5%, most everyone here is in the top 5%.
>>>>>>
>>>>>
>>>>> Doesn't matter what you believe, as you have demonstrated that you
>>>>> don't understand what is actually Truth.
>>>>>
>>>>>
>>>>>
>>>>
>>>> You have not demonstrated any very significant understanding of these
>>>> things. It does seem that you have demonstrated key
>>>> misunderstandings of
>>>> Tarski. I guy with a 2 in one billion IQ would not make these mistakes.
>>>> A guy with a top 1% IQ might make these mistakes if they barely skimmed
>>>> the material.
>>>>
>>>> You can see that the proof is only two pages long, not too much to
>>>> carefully study.
>>>>
>>>> http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf
>>>>
>>>
>>> First, you confuse Intelgence with Knowledge.
>>>
>>> As I have mentioned before, this is an area that I admit I haven't
>>> studied in great detail (but it seems I still understand some of the
>>> point better than you, which shows your lack of intelegence).
>>>
>>> You claim Tarski bases his proof on the Liar needing a Truth Value.
>>>
>>> In fact, a simple reading of the text shows that he is using the
>>> standard Proof by Contradiction to show that IF the "Thesis A" which
>>> resumes a definition of Truth was actually True, then we can prove
>>> that the Liar's Paradox is True.
>>>
>>> Since we know the Liar's Paradox is not a Truth Bearer, and thus not
>>> True, the Thesis can not be true.
>>>
>>> IF I find the time, I might put the effort to read the papers you
>>> have linked to and see if I can make some more detailed comments on
>>> them.
>>>
>>> My first guess is a few days effort would probably be sufficent,
>>> which compared to your decades, seems a reasonable ratio considering
>>> our comparative intelegence.
>>
>> Finite Truth is all about showing that a truth maker semantic
>> connection exists. If exists then true else untrue.
>>
>
> Where are you getting the term "Finite Truth".
>

Even a guy with a top 1% IQ would be able to figure out from our prior
context that I must mean expressions of language that have finite
semantic connections to their truth maker.

> Truth is allowed to be base on a infinite set of connections.
>

Off topic because we are only talking about Tarski's simplification of
Gödel. The liar paradox has zero semantic connections to a truth maker,
thus lacks infinite connections to a truth maker.

As I have already pointed out Prolog detects and rejects both the liar
paradox and the simplified Gödel sentence on the basis that they lack
connections to their truth maker.

?- 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.

This is not saying that the LP has an infinite proof it is saying that
the LP never reaches a truth maker.

"This sentence is not true"
It is not true about what?
It is not true about being not true.
It is not true about being not true about what?
It is not true about being not true about being not true...

> It is True if ANY (including infinte) set of connections exist.
>
> It is only provable if a FINITE set of connections exist.
>
> You keep on confusing these two terms, because in your mind you have
> crossed their connections and mix up Truth with Knowledge, perhaps
> because you studied some theries of Knowledge, and are confusing what is
> known to be True with what is actually True.
>
> You keep on makeing that sort of mistake in your words, by talking of
> what we can KNOW to be true, and applying that to what is actually True.

It is not that I keep confusing these terms it is that you continue to
fail to understand that it can be proven in a finite number of steps
that the LP has no semantic connection to any truth maker.

Here is an example of formalizing the Liar Paradox in C++

void main()
{ bool LP = (LP != true);
}

Even the “C++” compiler recognizes the value is tested before it has
been initialized.
liarparadox.cpp(3) : warning C4700: uninitialized local variable 'LP' used
Microsoft (R) Incremental Linker Version 9.00.30729.01
Copyright (C) Microsoft Corporation. All rights reserved.

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

Re: Tarski Undefinability Theorem is refuted

<51c95b22-ec23-4a95-8409-a34d31e8fc03n@googlegroups.com>

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Subject: Re: Tarski Undefinability Theorem is refuted
From: donstock...@hotmail.com (Don Stockbauer)
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 by: Don Stockbauer - Mon, 2 Jan 2023 14:51 UTC

pop On Monday, January 2, 2023 at 8:30:38 AM UTC-6, olcott wrote:
> On 1/2/2023 12:07 AM, Richard Damon wrote:
> > On 1/2/23 12:51 AM, olcott wrote:
> >> On 1/1/2023 11:07 PM, Richard Damon wrote:
> >>> On 1/1/23 11:20 PM, olcott wrote:
> >>>> On 1/1/2023 9:14 PM, Richard Damon wrote:
> >>>>> On 1/1/23 9:47 PM, olcott wrote:
> >>>>>
> >>>>>> I don't believe that you have an IQ anywhere near the top 1% much
> >>>>>> less
> >>>>>> than the 185 IQ of top 2 in a billion. I could easily believe the top
> >>>>>> 5%, most everyone here is in the top 5%.
> >>>>>>
> >>>>>
> >>>>> Doesn't matter what you believe, as you have demonstrated that you
> >>>>> don't understand what is actually Truth.
> >>>>>
> >>>>>
> >>>>>
> >>>>
> >>>> You have not demonstrated any very significant understanding of these
> >>>> things. It does seem that you have demonstrated key
> >>>> misunderstandings of
> >>>> Tarski. I guy with a 2 in one billion IQ would not make these mistakes.
> >>>> A guy with a top 1% IQ might make these mistakes if they barely skimmed
> >>>> the material.
> >>>>
> >>>> You can see that the proof is only two pages long, not too much to
> >>>> carefully study.
> >>>>
> >>>> http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf
> >>>>
> >>>
> >>> First, you confuse Intelgence with Knowledge.
> >>>
> >>> As I have mentioned before, this is an area that I admit I haven't
> >>> studied in great detail (but it seems I still understand some of the
> >>> point better than you, which shows your lack of intelegence).
> >>>
> >>> You claim Tarski bases his proof on the Liar needing a Truth Value.
> >>>
> >>> In fact, a simple reading of the text shows that he is using the
> >>> standard Proof by Contradiction to show that IF the "Thesis A" which
> >>> resumes a definition of Truth was actually True, then we can prove
> >>> that the Liar's Paradox is True.
> >>>
> >>> Since we know the Liar's Paradox is not a Truth Bearer, and thus not
> >>> True, the Thesis can not be true.
> >>>
> >>> IF I find the time, I might put the effort to read the papers you
> >>> have linked to and see if I can make some more detailed comments on
> >>> them.
> >>>
> >>> My first guess is a few days effort would probably be sufficent,
> >>> which compared to your decades, seems a reasonable ratio considering
> >>> our comparative intelegence.
> >>
> >> Finite Truth is all about showing that a truth maker semantic
> >> connection exists. If exists then true else untrue.
> >>
> >
> > Where are you getting the term "Finite Truth".
> >
> Even a guy with a top 1% IQ would be able to figure out from our prior
> context that I must mean expressions of language that have finite
> semantic connections to their truth maker.
> > Truth is allowed to be base on a infinite set of connections.
> >
> Off topic because we are only talking about Tarski's simplification of
> Gödel. The liar paradox has zero semantic connections to a truth maker,
> thus lacks infinite connections to a truth maker.
>
> As I have already pointed out Prolog detects and rejects both the liar
> paradox and the simplified Gödel sentence on the basis that they lack
> connections to their truth maker.
>
> ?- 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.
>
> This is not saying that the LP has an infinite proof it is saying that
> the LP never reaches a truth maker.
> "This sentence is not true"
> It is not true about what?
> It is not true about being not true.
> It is not true about being not true about what?
> It is not true about being not true about being not true...
> > It is True if ANY (including infinte) set of connections exist.
> >
> > It is only provable if a FINITE set of connections exist.
> >
> > You keep on confusing these two terms, because in your mind you have
> > crossed their connections and mix up Truth with Knowledge, perhaps
> > because you studied some theries of Knowledge, and are confusing what is
> > known to be True with what is actually True.
> >
> > You keep on makeing that sort of mistake in your words, by talking of
> > what we can KNOW to be true, and applying that to what is actually True..
> It is not that I keep confusing these terms it is that you continue to
> fail to understand that it can be proven in a finite number of steps
> that the LP has no semantic connection to any truth maker.
>
> Here is an example of formalizing the Liar Paradox in C++
>
> void main()
> {
> bool LP = (LP != true);
> }
>
> Even the “C++” compiler recognizes the value is tested before it has
> been initialized.
> liarparadox.cpp(3) : warning C4700: uninitialized local variable 'LP' used
> Microsoft (R) Incremental Linker Version 9.00.30729.01
> Copyright (C) Microsoft Corporation. All rights reserved.
> --
> Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
> hits a target no one else can see." Arthur Schopenhauer

Are you related to William Tyler Olcott, the famous astronomer?

Re: Tarski Undefinability Theorem is refuted

<tour22$1qami$1@dont-email.me>

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https://www.novabbs.com/computers/article-flat.php?id=10154&group=comp.ai.philosophy#10154

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Path: i2pn2.org!i2pn.org!eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail
From: polco...@gmail.com (olcott)
Newsgroups: comp.theory,comp.ai.philosophy,sci.logic
Subject: Re: Tarski Undefinability Theorem is refuted
Date: Mon, 2 Jan 2023 08:51:45 -0600
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 by: olcott - Mon, 2 Jan 2023 14:51 UTC

On 1/2/2023 12:01 AM, Richard Damon wrote:
> On 1/1/23 11:49 PM, olcott wrote:
>> On 1/1/2023 10:36 PM, Richard Damon wrote:
>>> On 1/1/23 11:13 PM, olcott wrote:
>>>> On 1/1/2023 8:39 PM, Richard Damon wrote:
>>>>> On 1/1/23 8:29 PM, olcott wrote:
>>>>>> On 1/1/2023 3:37 PM, Richard Damon wrote:
>>>>>>> On 1/1/23 2:51 PM, olcott wrote:
>>>>>
>>>>>>>> Hardly anyone seems to understand that the Liar Paradox is
>>>>>>>> simply not a
>>>>>>>> truth bearer otherwise tertiary logic would have never been
>>>>>>>> created.
>>>>>>>
>>>>>>> No Nearly EVERYONE understands that in Binary Logic, the Liar
>>>>>>> Paracos is simply not a Truth Bearer.
>>>>>>
>>>>>> I don't think that all the people writing papers about how to
>>>>>> resolve the Liar Paradox fail to understand binary logic.
>>>>>>
>>>>>
>>>>> Most INTELEGENT people trying to resolve the Liar's Paradox
>>>>> understand Binary Logic, and are looking for logic beyond Binary
>>>>> Logic to see if other Logical Paradigms might be able to handle
>>>>> that sort of thing (and actually are probably looking at things
>>>>> more complicated then the simple Liar's Paradox).
>>>>>
>>>>
>>>> Anyone that is trying to resolve an expression of language that is
>>>> not a
>>>> truth bearer to a truth value is on a fools errand.
>>>>
>>>>>
>>>>> I will admit, that are probably a lot of DUMB people, who don't
>>>>> understand logic, and are doing all sorts of dumb things, and if
>>>>> those are hiting your radar, you need a better selection filter.
>>>>>
>>>>
>>>> Saul Kripke was by no means any sort of dumb
>>>> https://www.impan.pl/~kz/truthseminar/Kripke_Outline.pdf
>>>
>>> And he isn't trying to say the Liar's Paradox is a Truth Beared.
>>>
>>> At a quick glance he seems to be working on logic that handles
>>> ill-defined statments with partial knowledge
>>>
>>>>
>>>>> Of course, those are probably the works that you can sort of
>>>>> understand, since they are at your level.
>>>>>
>>>>> And actually, MOST people just understand that non-truth of the
>>>>> Liar's Paradox and they leave it at that.
>>>>>
>>>>
>>>> Tarski "proved" that truth cannot be specified and used the Liar
>>>> Paradox as the foundation of this proof.
>>>
>>> Not quite.
>>>
>>> He Showed that if you presume a complete specification for truth
>>> could exist in a system, that it is neccessarily possible to prove
>>> that the Liar's Paradox is True.
>>>
>>
>> Maybe Tarski made that same mistake you are are making.
>> If Tarski believed that he proved this sentence is true in his
>> meta-theory: "This sentence is not true" then Tarski made a terrible
>> mistake.
>>
>> {This sentence is not true: "This sentence is not true"} would be true.
>> "This sentence is not true" is never true.
>>
>> My key skill from software engineering is to boil complex things down
>> to their barest possible essence. Tarski already mostly did that for
>> Gödel.
>>
>> Did you verify that his proof is only two pages yet?
>>
>> http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf
>>
>
> Where in those pages do you see your summary expressed?
>
> Note, the construction of the Meta Theory is such that any statement in
> the Theory means exactly the same thing in the Meta Theory, so it isn't
> the meta theory having a statement referencing the statement in the
> theory, but is a proof of the actual original statement.
>

This sentence is not true: "This sentence is not true"
The outer-sentence has the same words as the inner sentence yet has a
different semantic meaning because the inner sentence is self-
referential and the outer sentence is not self-referential.

> The proof you reference on pages 275-276 is just a simple proof that it
> is possible to construct in the Theory a statement that says, in effect,
> that statement x is not provable in the Theory if and only if p is True.
> With p being a reference to the whole sentence (Which is sort of Godels
> statement in the Meta-theory),
>

LP := "this sentence is not true" // theory
~True(LP) // meta-theory

> This is NOT the "Liars Paradox", as the liar's paradox is about a
> statement being TRUE, not about it being PROVABLE. (and in fact, it

Everywhere, both in the formulation of the
theorem and in its proof, we replace the symbol 'Tr' by the
symbol 'Pr' which denotes the class of all provable sentences
of the theory under consideration

*Tarski used Pr as a proxy for Tr*

(3) x ∉ Pr if and only if x ∈ Tr.

x ∉ Provable if and only if x ∈ True.
~Provable(x) ↔ True(x).
x is true if and only if x is unprovable

x is true if and only if x lacks the required semantic connection to a
truth maker is false.

It is the same sort of thing as saying that one can only bake an angel
food cake when one lacks the ingredients for an angel food cake.

> looks like the top of page 275 is him showing why this statement IS a
> Truth Bearer, using his words that "We can construct a sentence x of the
> science in question". I beleive you will find this is his terminology to
> describe sentneces which are what you call Truth Bearers.
>
> Since the premise x is provable, or it is not true that x is provable
> are BY DEFINITION truth bears.
>

It is not a little bear that always tells the truth, it is that the
expression of language has a Boolean semantic value of true or false.

> Also, x being an element of the True Statements is ALSO a truth bearer,
> as if x was a non-truth bearer, that statement would be false (as
> non-truth beares are not true).
>
> He then manipulates these terms and shows that neither x or not x are in
> the set of provable statements, but x is in the set of True Statements
> (since if x was not true, it would be provable, but provabe statements
> are always true).
>
> If you want to point out exactly which step in this proof you think he
> makes an error.
>
> I think you intend to make it about the statement x not being a truth
> bearer, but he shows from the material at the begining of page 275 that
> it IS, but mostly by refering to other parts of his work which he is
> assuming you understand at this point.
>
> If you want to disagree with the statement being a Truth Bearer, or as
> he calls it "A Sentence of the Science", you need to show where the
> things he references are wrong.
>
> Again, it seems to be another of your errors by reading just the cliff
> notes and not actually understanding what he is saying.
>
> In partictular, I think you need to find the error in the previous proof
> for the sentence:
>
> In accordance with the first part of Th. I we can obtain the negation of
> one of the sentences in condition (a) of convention T of §3 as a
> consequence of the definition of the symbol 'Pr' (provided we replace
> 'Tr' in this convention by 'Pr').

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

Re: Tarski Undefinability Theorem is refuted

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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Mon, 2 Jan 2023 14:52 UTC

On 1/2/23 9:30 AM, olcott wrote:
> On 1/2/2023 12:07 AM, Richard Damon wrote:
>> On 1/2/23 12:51 AM, olcott wrote:
>>> On 1/1/2023 11:07 PM, Richard Damon wrote:
>>>> On 1/1/23 11:20 PM, olcott wrote:
>>>>> On 1/1/2023 9:14 PM, Richard Damon wrote:
>>>>>> On 1/1/23 9:47 PM, olcott wrote:
>>>>>>
>>>>>>> I don't believe that you have an IQ anywhere near the top 1% much
>>>>>>> less
>>>>>>> than the 185 IQ of top 2 in a billion. I could easily believe the
>>>>>>> top
>>>>>>> 5%, most everyone here is in the top 5%.
>>>>>>>
>>>>>>
>>>>>> Doesn't matter what you believe, as you have demonstrated that you
>>>>>> don't understand what is actually Truth.
>>>>>>
>>>>>>
>>>>>>
>>>>>
>>>>> You have not demonstrated any very significant understanding of these
>>>>> things. It does seem that you have demonstrated key
>>>>> misunderstandings of
>>>>> Tarski. I guy with a 2 in one billion IQ would not make these
>>>>> mistakes.
>>>>> A guy with a top 1% IQ might make these mistakes if they barely
>>>>> skimmed
>>>>> the material.
>>>>>
>>>>> You can see that the proof is only two pages long, not too much to
>>>>> carefully study.
>>>>>
>>>>> http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf
>>>>>
>>>>
>>>> First, you confuse Intelgence with Knowledge.
>>>>
>>>> As I have mentioned before, this is an area that I admit I haven't
>>>> studied in great detail (but it seems I still understand some of the
>>>> point better than you, which shows your lack of intelegence).
>>>>
>>>> You claim Tarski bases his proof on the Liar needing a Truth Value.
>>>>
>>>> In fact, a simple reading of the text shows that he is using the
>>>> standard Proof by Contradiction to show that IF the "Thesis A" which
>>>> resumes a definition of Truth was actually True, then we can prove
>>>> that the Liar's Paradox is True.
>>>>
>>>> Since we know the Liar's Paradox is not a Truth Bearer, and thus not
>>>> True, the Thesis can not be true.
>>>>
>>>> IF I find the time, I might put the effort to read the papers you
>>>> have linked to and see if I can make some more detailed comments on
>>>> them.
>>>>
>>>> My first guess is a few days effort would probably be sufficent,
>>>> which compared to your decades, seems a reasonable ratio considering
>>>> our comparative intelegence.
>>>
>>> Finite Truth is all about showing that a truth maker semantic
>>> connection exists. If exists then true else untrue.
>>>
>>
>> Where are you getting the term "Finite Truth".
>>
>
> Even a guy with a top 1% IQ would be able to figure out from our prior
> context that I must mean expressions of language that have finite
> semantic connections to their truth maker.

Which means you aren't talking about ANYTHING that anyone else we have
been talking about would call "True", and thus meaningless for this
conversation.

Limiting your definition of "True" to finite connections is the
equivalent of limiting it to Provable, which has been shown (though you
don't understand it) to leads either logic system that are constrained
in what they can handle, or they become inconsistent.

If that is the sort of logic system you want to talk about, ok, but make
it clear, and admit you aren't talking about fields like the properties
of the Natural Numbers.

>
>> Truth is allowed to be base on a infinite set of connections.
>>
>
> Off topic because we are only talking about Tarski's simplification of
> Gödel. The liar paradox has zero semantic connections to a truth maker,
> thus lacks infinite connections to a truth maker.

No, OM TOPIC because that is the definition of Truth used by everyone
you are talking about.

Maybe the point is that everything YOU are talking about has been OFF
TOPIC because you aren't talking about the logic systems you claim to.

>
> As I have already pointed out Prolog detects and rejects both the liar
> paradox and the simplified Gödel sentence on the basis that they lack
> connections to their truth maker.

So, your "Simplified Godel Sentence" isn't actually the Godel Sentence,
and the fact you think they are equivalent shows your ignorance.

>
> ?- 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.

Note, Prolog, as I understand it, would be incapable of handling Godel
Sentence as Prolog doesn't implement a high enough level of logic.

>
> This is not saying that the LP has an infinite proof it is saying that
> the LP never reaches a truth maker.

Who ever said the Liar Paradox has an infinite proof.

The fact you are making that claim just shows you don't understand the
problems you are talking about.

Note, when Tarski "Proves" the statement that is like the Liar's
Paradox, he does so with a finite proof, but he does it by assuming a
Hypothosis which shows that that Hypothosis can't be true, thus proving
it false.

That is a standard Proof by Contradiction.

>
> "This sentence is not true"
> It is not true about what?
> It is not true about being not true.
> It is not true about being not true about what?
> It is not true about being not true about being not true...

Which isn't done in the proofs.

The fact you think it is shows you don't understand them.

>
>> It is True if ANY (including infinte) set of connections exist.
>>
>> It is only provable if a FINITE set of connections exist.
>>
>> You keep on confusing these two terms, because in your mind you have
>> crossed their connections and mix up Truth with Knowledge, perhaps
>> because you studied some theries of Knowledge, and are confusing what
>> is known to be True with what is actually True.
>>
>> You keep on makeing that sort of mistake in your words, by talking of
>> what we can KNOW to be true, and applying that to what is actually True.
>
> It is not that I keep confusing these terms it is that you continue to
> fail to understand that it can be proven in a finite number of steps
> that the LP has no semantic connection to any truth maker.

So?

No one is arguing that fact.

You do like to serve your Herring with Red Sauce.

>
> Here is an example of formalizing the Liar Paradox in C++
>
> void main()
> {
>   bool LP = (LP != true);
> }

Which isn't actually the Liar's Paradox, because the computation model
of C++ doesn't provide for a way to express it.
>
> Even the “C++” compiler recognizes the value is tested before it has
> been initialized.
> liarparadox.cpp(3) : warning C4700: uninitialized local variable 'LP' used
> Microsoft (R) Incremental Linker Version 9.00.30729.01
> Copyright (C) Microsoft Corporation. All rights reserved.
>

Right, so the compiler recognises that you did it wrong.

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

Re: Tarski Undefinability Theorem is refuted

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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Mon, 2 Jan 2023 15:09 UTC

On 1/2/23 9:51 AM, olcott wrote:
> On 1/2/2023 12:01 AM, Richard Damon wrote:
>> On 1/1/23 11:49 PM, olcott wrote:
>>> On 1/1/2023 10:36 PM, Richard Damon wrote:
>>>> On 1/1/23 11:13 PM, olcott wrote:
>>>>> On 1/1/2023 8:39 PM, Richard Damon wrote:
>>>>>> On 1/1/23 8:29 PM, olcott wrote:
>>>>>>> On 1/1/2023 3:37 PM, Richard Damon wrote:
>>>>>>>> On 1/1/23 2:51 PM, olcott wrote:
>>>>>>
>>>>>>>>> Hardly anyone seems to understand that the Liar Paradox is
>>>>>>>>> simply not a
>>>>>>>>> truth bearer otherwise tertiary logic would have never been
>>>>>>>>> created.
>>>>>>>>
>>>>>>>> No Nearly EVERYONE understands that in Binary Logic, the Liar
>>>>>>>> Paracos is simply not a Truth Bearer.
>>>>>>>
>>>>>>> I don't think that all the people writing papers about how to
>>>>>>> resolve the Liar Paradox fail to understand binary logic.
>>>>>>>
>>>>>>
>>>>>> Most INTELEGENT people trying to resolve the Liar's Paradox
>>>>>> understand Binary Logic, and are looking for logic beyond Binary
>>>>>> Logic to see if other Logical Paradigms might be able to handle
>>>>>> that sort of thing (and actually are probably looking at things
>>>>>> more complicated then the simple Liar's Paradox).
>>>>>>
>>>>>
>>>>> Anyone that is trying to resolve an expression of language that is
>>>>> not a
>>>>> truth bearer to a truth value is on a fools errand.
>>>>>
>>>>>>
>>>>>> I will admit, that are probably a lot of DUMB people, who don't
>>>>>> understand logic, and are doing all sorts of dumb things, and if
>>>>>> those are hiting your radar, you need a better selection filter.
>>>>>>
>>>>>
>>>>> Saul Kripke was by no means any sort of dumb
>>>>> https://www.impan.pl/~kz/truthseminar/Kripke_Outline.pdf
>>>>
>>>> And he isn't trying to say the Liar's Paradox is a Truth Beared.
>>>>
>>>> At a quick glance he seems to be working on logic that handles
>>>> ill-defined statments with partial knowledge
>>>>
>>>>>
>>>>>> Of course, those are probably the works that you can sort of
>>>>>> understand, since they are at your level.
>>>>>>
>>>>>> And actually, MOST people just understand that non-truth of the
>>>>>> Liar's Paradox and they leave it at that.
>>>>>>
>>>>>
>>>>> Tarski "proved" that truth cannot be specified and used the Liar
>>>>> Paradox as the foundation of this proof.
>>>>
>>>> Not quite.
>>>>
>>>> He Showed that if you presume a complete specification for truth
>>>> could exist in a system, that it is neccessarily possible to prove
>>>> that the Liar's Paradox is True.
>>>>
>>>
>>> Maybe Tarski made that same mistake you are are making.
>>> If Tarski believed that he proved this sentence is true in his
>>> meta-theory: "This sentence is not true" then Tarski made a terrible
>>> mistake.
>>>
>>> {This sentence is not true: "This sentence is not true"} would be true.
>>> "This sentence is not true" is never true.
>>>
>>> My key skill from software engineering is to boil complex things down
>>> to their barest possible essence. Tarski already mostly did that for
>>> Gödel.
>>>
>>> Did you verify that his proof is only two pages yet?
>>>
>>> http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf
>>>
>>
>> Where in those pages do you see your summary expressed?
>>
>> Note, the construction of the Meta Theory is such that any statement
>> in the Theory means exactly the same thing in the Meta Theory, so it
>> isn't the meta theory having a statement referencing the statement in
>> the theory, but is a proof of the actual original statement.
>>
>
> This sentence is not true: "This sentence is not true"
> The outer-sentence has the same words as the inner sentence yet has a
> different semantic meaning because the inner sentence is self-
> referential and the outer sentence is not self-referential.

And where are you getting these two sentences from?

>
>> The proof you reference on pages 275-276 is just a simple proof that
>> it is possible to construct in the Theory a statement that says, in
>> effect, that statement x is not provable in the Theory if and only if
>> p is True. With p being a reference to the whole sentence (Which is
>> sort of Godels statement in the Meta-theory),
>>
>
> LP := "this sentence is not true" // theory
> ~True(LP) // meta-theory

Nope, you apperently don't understand the concept of a Meta Theory.

Sentence x exists in the domain of the Theory.

That exact same Sentence exist in the Meta-Theory, not a sentence
REFERING to the sentence in the Theory. It means the same thing, but
with a wider context by the definition of the Meta Theory.

>
>> This is NOT the "Liars Paradox", as the liar's paradox is about a
>> statement being TRUE, not about it being PROVABLE. (and in fact, it
>
>   Everywhere, both in the formulation of the
>   theorem and in its proof, we replace the symbol 'Tr' by the
>   symbol 'Pr' which denotes the class of all provable sentences
>   of the theory under consideration
>
> *Tarski used Pr as a proxy for Tr*

You understand that is a direct result of the Theory he referenced?

This is no "Proxy".

Maybe you need to study THAT Theory to understand it.

>
> (3) x ∉ Pr if and only if x ∈ Tr.
>
> x ∉ Provable if and only if x ∈ True.
> ~Provable(x) ↔ True(x).
> x is true if and only if x is unprovable
>
> x is true if and only if x lacks the required semantic connection to a
> truth maker is false.
>
> It is the same sort of thing as saying that one can only bake an angel
> food cake when one lacks the ingredients for an angel food cake.

Nope, You are arguing with the result of the mentioned Theory.

Try to find the flaw in its proof.

It is a necessary consequence of the requirements of the system that
such a statement is allowed to be created.

Your failure to understand it shows how LOW your IQ is.

>
>> looks like the top of page 275 is him showing why this statement IS a
>> Truth Bearer, using his words that "We can construct a sentence x of
>> the science in question". I beleive you will find this is his
>> terminology to describe sentneces which are what you call Truth Bearers.
>>
>> Since the premise x is provable, or it is not true that x is provable
>> are BY DEFINITION truth bears.
>>
>
> It is not a little bear that always tells the truth, it is that the
> expression of language has a Boolean semantic value of true or false.

Right. The statements x is Provable, x is not Provable, and x is True
are all statements which are Truth Bearers.

From the previously mentiond Theory, the whole statement is a Truth
Bearer, and that Requires that the only possible case is that x is True
and x is not Provable.

You can't just take a proven statement and say it can't be true because
you don't like it or it breaks something you would like to be a rule.

If you think Tarski is incorrect in making that statement, you have to
find the error in him making it, and since it is based directly on a
Theorem that he proved, you need to find the error in that proof, which
it seems you haven't even read.

Re: Tarski Undefinability Theorem is refuted

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Subject: Re: Tarski Undefinability Theorem is refuted
Date: Mon, 2 Jan 2023 09:46:18 -0600
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 by: olcott - Mon, 2 Jan 2023 15:46 UTC

On 1/2/2023 8:52 AM, Richard Damon wrote:
> On 1/2/23 9:30 AM, olcott wrote:
>> On 1/2/2023 12:07 AM, Richard Damon wrote:
>>> On 1/2/23 12:51 AM, olcott wrote:
>>>> On 1/1/2023 11:07 PM, Richard Damon wrote:
>>>>> On 1/1/23 11:20 PM, olcott wrote:
>>>>>> On 1/1/2023 9:14 PM, Richard Damon wrote:
>>>>>>> On 1/1/23 9:47 PM, olcott wrote:
>>>>>>>
>>>>>>>> I don't believe that you have an IQ anywhere near the top 1%
>>>>>>>> much less
>>>>>>>> than the 185 IQ of top 2 in a billion. I could easily believe
>>>>>>>> the top
>>>>>>>> 5%, most everyone here is in the top 5%.
>>>>>>>>
>>>>>>>
>>>>>>> Doesn't matter what you believe, as you have demonstrated that
>>>>>>> you don't understand what is actually Truth.
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> You have not demonstrated any very significant understanding of these
>>>>>> things. It does seem that you have demonstrated key
>>>>>> misunderstandings of
>>>>>> Tarski. I guy with a 2 in one billion IQ would not make these
>>>>>> mistakes.
>>>>>> A guy with a top 1% IQ might make these mistakes if they barely
>>>>>> skimmed
>>>>>> the material.
>>>>>>
>>>>>> You can see that the proof is only two pages long, not too much to
>>>>>> carefully study.
>>>>>>
>>>>>> http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf
>>>>>>
>>>>>
>>>>> First, you confuse Intelgence with Knowledge.
>>>>>
>>>>> As I have mentioned before, this is an area that I admit I haven't
>>>>> studied in great detail (but it seems I still understand some of
>>>>> the point better than you, which shows your lack of intelegence).
>>>>>
>>>>> You claim Tarski bases his proof on the Liar needing a Truth Value.
>>>>>
>>>>> In fact, a simple reading of the text shows that he is using the
>>>>> standard Proof by Contradiction to show that IF the "Thesis A"
>>>>> which resumes a definition of Truth was actually True, then we can
>>>>> prove that the Liar's Paradox is True.
>>>>>
>>>>> Since we know the Liar's Paradox is not a Truth Bearer, and thus
>>>>> not True, the Thesis can not be true.
>>>>>
>>>>> IF I find the time, I might put the effort to read the papers you
>>>>> have linked to and see if I can make some more detailed comments on
>>>>> them.
>>>>>
>>>>> My first guess is a few days effort would probably be sufficent,
>>>>> which compared to your decades, seems a reasonable ratio
>>>>> considering our comparative intelegence.
>>>>
>>>> Finite Truth is all about showing that a truth maker semantic
>>>> connection exists. If exists then true else untrue.
>>>>
>>>
>>> Where are you getting the term "Finite Truth".
>>>
>>
>> Even a guy with a top 1% IQ would be able to figure out from our prior
>> context that I must mean expressions of language that have finite
>> semantic connections to their truth maker.
>
> Which means you aren't talking about ANYTHING that anyone else we have
> been talking about would call "True", and thus meaningless for this
> conversation.
>

The subset of expressions of language that have finite semantic
connections to their truth maker is not an entirely different subject
than the set of expressions of language having semantic connections
to their truth maker.

> Limiting your definition of "True" to finite connections is the
> equivalent of limiting it to Provable, which has been shown (though you
> don't understand it) to leads either logic system that are constrained
> in what they can handle, or they become inconsistent.
>

Not at all. It leads to rejecting expressions of language that have no
possible connection to any truth maker. Prolog can already do this.

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

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

> If that is the sort of logic system you want to talk about, ok, but make
> it clear, and admit you aren't talking about fields like the properties
> of the Natural Numbers.
>

Any expression of formal or natural language that cannot possibly have
any connection to a truth maker is not true. Epistemological antinomies
cannot possibly have a semantic connection to any truth maker, thus are
always untrue.

>>
>>> Truth is allowed to be base on a infinite set of connections.
>>>
>>
>> Off topic because we are only talking about Tarski's simplification of
>> Gödel. The liar paradox has zero semantic connections to a truth maker,
>> thus lacks infinite connections to a truth maker.
>
> No, OM TOPIC because that is the definition of Truth used by everyone
> you are talking about.
>

Epistemological antinomies are proven to lack a semantic connection to
any truth maker.

> Maybe the point is that everything YOU are talking about has been OFF
> TOPIC because you aren't talking about the logic systems you claim to.
>

Everyone that I have been talking to believes that sentences can be true
and lack any semantic connection to a truth maker because formal logic
makes sure to ignore semantics as off-topic.

>>
>> As I have already pointed out Prolog detects and rejects both the liar
>> paradox and the simplified Gödel sentence on the basis that they lack
>> connections to their truth maker.
>
> So, your "Simplified Godel Sentence" isn't actually the Godel Sentence,
> and the fact you think they are equivalent shows your ignorance.
>

14 Every epistemological antinomy can likewise be used for a similar
undecidability proof.

thus the Liar Paradox can be used as a proxy for the Gödel sentence.

>>
>> ?- 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.
>
> Note, Prolog, as I understand it, would be incapable of handling Godel
> Sentence as Prolog doesn't implement a high enough level of logic.
>

Then you understand it incorrectly.

>>
>> This is not saying that the LP has an infinite proof it is saying that
>> the LP never reaches a truth maker.
>
> Who ever said the Liar Paradox has an infinite proof.
>

Ah so now you see that you have been off-topic with your reference to
infinite connections to semantic truth makers.

> The fact you are making that claim just shows you don't understand the
> problems you are talking about.
>
> Note, when Tarski "Proves" the statement that is like the Liar's
> Paradox, he does so with a finite proof, but he does it by assuming a
> Hypothosis which shows that that Hypothosis can't be true, thus proving
> it false.
>

If Tarski in any way proved that the Liar Paradox is true then Tarski
necessarily made a mistake because the Liar Paradox has zero finite or
infinite connections to any truth maker.

This sentence is not true: "This sentence is not true"
is true.

> That is a standard Proof by Contradiction.
>
>>
>> "This sentence is not true"
>> It is not true about what?
>> It is not true about being not true.
>> It is not true about being not true about what?
>> It is not true about being not true about being not true...
>
> Which isn't done in the proofs.
>

That is their mistake. The LP is recognized and rejected by Prolog.

> The fact you think it is shows you don't understand them.
>

That brand new knowledge does not conform to preexisting misconceptions
is the way that brand new knowledge is supposed to work.


Click here to read the complete article
Re: Tarski Undefinability Theorem is refuted [also Gödel]

<tov02j$1r0rp$1@dont-email.me>

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https://www.novabbs.com/computers/article-flat.php?id=10158&group=comp.ai.philosophy#10158

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From: polco...@gmail.com (olcott)
Newsgroups: comp.theory,comp.ai.philosophy,sci.logic
Subject: Re:_Tarski_Undefinability_Theorem_is_refuted_[also_G
ödel]
Date: Mon, 2 Jan 2023 10:17:22 -0600
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 by: olcott - Mon, 2 Jan 2023 16:17 UTC

On 1/2/2023 9:09 AM, Richard Damon wrote:
> On 1/2/23 9:51 AM, olcott wrote:
>> On 1/2/2023 12:01 AM, Richard Damon wrote:
>>> On 1/1/23 11:49 PM, olcott wrote:
>>>> On 1/1/2023 10:36 PM, Richard Damon wrote:
>>>>> On 1/1/23 11:13 PM, olcott wrote:
>>>>>> On 1/1/2023 8:39 PM, Richard Damon wrote:
>>>>>>> On 1/1/23 8:29 PM, olcott wrote:
>>>>>>>> On 1/1/2023 3:37 PM, Richard Damon wrote:
>>>>>>>>> On 1/1/23 2:51 PM, olcott wrote:
>>>>>>>
>>>>>>>>>> Hardly anyone seems to understand that the Liar Paradox is
>>>>>>>>>> simply not a
>>>>>>>>>> truth bearer otherwise tertiary logic would have never been
>>>>>>>>>> created.
>>>>>>>>>
>>>>>>>>> No Nearly EVERYONE understands that in Binary Logic, the Liar
>>>>>>>>> Paracos is simply not a Truth Bearer.
>>>>>>>>
>>>>>>>> I don't think that all the people writing papers about how to
>>>>>>>> resolve the Liar Paradox fail to understand binary logic.
>>>>>>>>
>>>>>>>
>>>>>>> Most INTELEGENT people trying to resolve the Liar's Paradox
>>>>>>> understand Binary Logic, and are looking for logic beyond Binary
>>>>>>> Logic to see if other Logical Paradigms might be able to handle
>>>>>>> that sort of thing (and actually are probably looking at things
>>>>>>> more complicated then the simple Liar's Paradox).
>>>>>>>
>>>>>>
>>>>>> Anyone that is trying to resolve an expression of language that is
>>>>>> not a
>>>>>> truth bearer to a truth value is on a fools errand.
>>>>>>
>>>>>>>
>>>>>>> I will admit, that are probably a lot of DUMB people, who don't
>>>>>>> understand logic, and are doing all sorts of dumb things, and if
>>>>>>> those are hiting your radar, you need a better selection filter.
>>>>>>>
>>>>>>
>>>>>> Saul Kripke was by no means any sort of dumb
>>>>>> https://www.impan.pl/~kz/truthseminar/Kripke_Outline.pdf
>>>>>
>>>>> And he isn't trying to say the Liar's Paradox is a Truth Beared.
>>>>>
>>>>> At a quick glance he seems to be working on logic that handles
>>>>> ill-defined statments with partial knowledge
>>>>>
>>>>>>
>>>>>>> Of course, those are probably the works that you can sort of
>>>>>>> understand, since they are at your level.
>>>>>>>
>>>>>>> And actually, MOST people just understand that non-truth of the
>>>>>>> Liar's Paradox and they leave it at that.
>>>>>>>
>>>>>>
>>>>>> Tarski "proved" that truth cannot be specified and used the Liar
>>>>>> Paradox as the foundation of this proof.
>>>>>
>>>>> Not quite.
>>>>>
>>>>> He Showed that if you presume a complete specification for truth
>>>>> could exist in a system, that it is neccessarily possible to prove
>>>>> that the Liar's Paradox is True.
>>>>>
>>>>
>>>> Maybe Tarski made that same mistake you are are making.
>>>> If Tarski believed that he proved this sentence is true in his
>>>> meta-theory: "This sentence is not true" then Tarski made a terrible
>>>> mistake.
>>>>
>>>> {This sentence is not true: "This sentence is not true"} would be true.
>>>> "This sentence is not true" is never true.
>>>>
>>>> My key skill from software engineering is to boil complex things
>>>> down to their barest possible essence. Tarski already mostly did
>>>> that for Gödel.
>>>>
>>>> Did you verify that his proof is only two pages yet?
>>>>
>>>> http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf
>>>>
>>>
>>> Where in those pages do you see your summary expressed?
>>>
>>> Note, the construction of the Meta Theory is such that any statement
>>> in the Theory means exactly the same thing in the Meta Theory, so it
>>> isn't the meta theory having a statement referencing the statement in
>>> the theory, but is a proof of the actual original statement.
>>>
>>
>> This sentence is not true: "This sentence is not true"
>> The outer-sentence has the same words as the inner sentence yet has a
>> different semantic meaning because the inner sentence is self-
>> referential and the outer sentence is not self-referential.
>
> And where are you getting these two sentences from?
>

It is common knowledge that this is a version of the Liar Paradox:
"This sentence is not true".

I discovered that when the pathological self-reference(Olcott 2004) has
been removed by applying the sentence to another instance of itself,
then this new sentence is true.

>>
>>> The proof you reference on pages 275-276 is just a simple proof that
>>> it is possible to construct in the Theory a statement that says, in
>>> effect, that statement x is not provable in the Theory if and only if
>>> p is True. With p being a reference to the whole sentence (Which is
>>> sort of Godels statement in the Meta-theory),
>>>
>>
>> LP := "this sentence is not true" // theory
>> ~True(LP) // meta-theory
>
> Nope, you apperently don't understand the concept of a Meta Theory.
>

A meta-theory merely has an additional level of indirection when
referring to expression in the theory.

LP := "This sentence is not true" // LP in the theory
~True(LP) // LP in the meta-theory

> Sentence x exists in the domain of the Theory.
>
> That exact same Sentence exist in the Meta-Theory, not a sentence

Not, not at all, this is incorrect. The sentence in the meta-theory has
exactly one level of indirect reference to the sentence in the theory.

> REFERING to the sentence in the Theory. It means the same thing, but
> with a wider context by the definition of the Meta Theory.
>
>>
>>> This is NOT the "Liars Paradox", as the liar's paradox is about a
>>> statement being TRUE, not about it being PROVABLE. (and in fact, it
>>
>>    Everywhere, both in the formulation of the
>>    theorem and in its proof, we replace the symbol 'Tr' by the
>>    symbol 'Pr' which denotes the class of all provable sentences
>>    of the theory under consideration
>>
>> *Tarski used Pr as a proxy for Tr*
>
> You understand that is a direct result of the Theory he referenced?
>
> This is no "Proxy".
>
> Maybe you need to study THAT Theory to understand it.

When Tarski substitutes the symbol Tr with the symbol Pr he is saying
that he is construing True to mean Provable.

>>
>> (3) x ∉ Pr if and only if x ∈ Tr.
>>
>> x ∉ Provable if and only if x ∈ True.
>> ~Provable(x) ↔ True(x).
>> x is true if and only if x is unprovable
>>
>> x is true if and only if x lacks the required semantic connection to a
>> truth maker is false.
>>
>> It is the same sort of thing as saying that one can only bake an angel
>> food cake when one lacks the ingredients for an angel food cake.
>
> Nope, You are arguing with the result of the mentioned Theory.
>
> Try to find the flaw in its proof.
>
> It is a necessary consequence of the requirements of the system that
> such a statement is allowed to be created.
>
> Your failure to understand it shows how LOW your IQ is.
>
>
>>
>>> looks like the top of page 275 is him showing why this statement IS a
>>> Truth Bearer, using his words that "We can construct a sentence x of
>>> the science in question". I beleive you will find this is his
>>> terminology to describe sentneces which are what you call Truth Bearers.
>>>
>>> Since the premise x is provable, or it is not true that x is provable
>>> are BY DEFINITION truth bears.
>>>
>>
>> It is not a little bear that always tells the truth, it is that the
>> expression of language has a Boolean semantic value of true or false.
>
> Right. The statements x is Provable, x is not Provable, and x is True
> are all statements which are Truth Bearers.
>


Click here to read the complete article
Re: Tarski Undefinability Theorem is refuted

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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Mon, 2 Jan 2023 16:25 UTC

On 1/2/23 10:46 AM, olcott wrote:
> On 1/2/2023 8:52 AM, Richard Damon wrote:
>> On 1/2/23 9:30 AM, olcott wrote:
>>> On 1/2/2023 12:07 AM, Richard Damon wrote:
>>>> On 1/2/23 12:51 AM, olcott wrote:
>>>>> On 1/1/2023 11:07 PM, Richard Damon wrote:
>>>>>> On 1/1/23 11:20 PM, olcott wrote:
>>>>>>> On 1/1/2023 9:14 PM, Richard Damon wrote:
>>>>>>>> On 1/1/23 9:47 PM, olcott wrote:
>>>>>>>>
>>>>>>>>> I don't believe that you have an IQ anywhere near the top 1%
>>>>>>>>> much less
>>>>>>>>> than the 185 IQ of top 2 in a billion. I could easily believe
>>>>>>>>> the top
>>>>>>>>> 5%, most everyone here is in the top 5%.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Doesn't matter what you believe, as you have demonstrated that
>>>>>>>> you don't understand what is actually Truth.
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> You have not demonstrated any very significant understanding of
>>>>>>> these
>>>>>>> things. It does seem that you have demonstrated key
>>>>>>> misunderstandings of
>>>>>>> Tarski. I guy with a 2 in one billion IQ would not make these
>>>>>>> mistakes.
>>>>>>> A guy with a top 1% IQ might make these mistakes if they barely
>>>>>>> skimmed
>>>>>>> the material.
>>>>>>>
>>>>>>> You can see that the proof is only two pages long, not too much
>>>>>>> to carefully study.
>>>>>>>
>>>>>>> http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf
>>>>>>>
>>>>>>
>>>>>> First, you confuse Intelgence with Knowledge.
>>>>>>
>>>>>> As I have mentioned before, this is an area that I admit I haven't
>>>>>> studied in great detail (but it seems I still understand some of
>>>>>> the point better than you, which shows your lack of intelegence).
>>>>>>
>>>>>> You claim Tarski bases his proof on the Liar needing a Truth Value.
>>>>>>
>>>>>> In fact, a simple reading of the text shows that he is using the
>>>>>> standard Proof by Contradiction to show that IF the "Thesis A"
>>>>>> which resumes a definition of Truth was actually True, then we can
>>>>>> prove that the Liar's Paradox is True.
>>>>>>
>>>>>> Since we know the Liar's Paradox is not a Truth Bearer, and thus
>>>>>> not True, the Thesis can not be true.
>>>>>>
>>>>>> IF I find the time, I might put the effort to read the papers you
>>>>>> have linked to and see if I can make some more detailed comments
>>>>>> on them.
>>>>>>
>>>>>> My first guess is a few days effort would probably be sufficent,
>>>>>> which compared to your decades, seems a reasonable ratio
>>>>>> considering our comparative intelegence.
>>>>>
>>>>> Finite Truth is all about showing that a truth maker semantic
>>>>> connection exists. If exists then true else untrue.
>>>>>
>>>>
>>>> Where are you getting the term "Finite Truth".
>>>>
>>>
>>> Even a guy with a top 1% IQ would be able to figure out from our prior
>>> context that I must mean expressions of language that have finite
>>> semantic connections to their truth maker.
>>
>> Which means you aren't talking about ANYTHING that anyone else we have
>> been talking about would call "True", and thus meaningless for this
>> conversation.
>>
>
> The subset of expressions of language that have finite semantic
> connections to their truth maker is not an entirely different subject
> than the set of expressions of language having semantic connections
> to their truth maker.
>
>> Limiting your definition of "True" to finite connections is the
>> equivalent of limiting it to Provable, which has been shown (though
>> you don't understand it) to leads either logic system that are
>> constrained in what they can handle, or they become inconsistent.
>>
>
> Not at all. It leads to rejecting expressions of language that have no
> possible connection to any truth maker. Prolog can already do this.

Bo, it leads to rejecting expression of language that DO have a
connection to a truth maker, because such a connect is infinite.

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

Fallacy of Proof by Example.

Proving your Stupidity.

>
>> If that is the sort of logic system you want to talk about, ok, but
>> make it clear, and admit you aren't talking about fields like the
>> properties of the Natural Numbers.
>>
>
> Any expression of formal or natural language that cannot possibly have
> any connection to a truth maker is not true. Epistemological antinomies
> cannot possibly have a semantic connection to any truth maker, thus are
> always untrue.

So? I haven't been talking about Epistemological antinomies having a
semantic connection to a truth maker, but that some actually TRUE
statement, having an infinite set of connections to a Truth Maker,
actually ARE TRUE by definition, but are also not provable, since a
proof needs a FINITE connect.

The fact you keep going to the antinomies shows you don't understand
this basic concept, because you are just too stupid,

It seems your mind is just too small to understand the concept of an
infinite set.

>
>>>
>>>> Truth is allowed to be base on a infinite set of connections.
>>>>
>>>
>>> Off topic because we are only talking about Tarski's simplification of
>>> Gödel. The liar paradox has zero semantic connections to a truth maker,
>>> thus lacks infinite connections to a truth maker.
>>
>> No, OM TOPIC because that is the definition of Truth used by everyone
>> you are talking about.
>>
>
> Epistemological antinomies are proven to lack a semantic connection to
> any truth maker.

So?

It seems you don't understand the topic you are talking about, which
seems to be about TRUTH.

>
>> Maybe the point is that everything YOU are talking about has been OFF
>> TOPIC because you aren't talking about the logic systems you claim to.
>>
>
> Everyone that I have been talking to believes that sentences can be true
> and lack any semantic connection to a truth maker because formal logic
> makes sure to ignore semantics as off-topic.

Then you are talking to a lot of people just as dumb as you.

Note, most logic system actually use semantics to establish the
fundamental properties, and then use semantic preserving syntatic
transformations to do the logic.

Trying to do abstract logic with JUST semantic operations is extreamely
difficult, if not impossible.

>
>>>
>>> As I have already pointed out Prolog detects and rejects both the liar
>>> paradox and the simplified Gödel sentence on the basis that they lack
>>> connections to their truth maker.
>>
>> So, your "Simplified Godel Sentence" isn't actually the Godel
>> Sentence, and the fact you think they are equivalent shows your
>> ignorance.
>>
>
>    14 Every epistemological antinomy can likewise be used for a similar
>       undecidability proof.
>
> thus the Liar Paradox can be used as a proxy for the Gödel sentence.

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

Since you don't understand how the proof works, you don't understand
what that statement says.

>
>>>
>>> ?- 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.
>>
>> Note, Prolog, as I understand it, would be incapable of handling Godel
>> Sentence as Prolog doesn't implement a high enough level of logic.
>>
>
> Then you understand it incorrectly.


Click here to read the complete article
Re: Tarski Undefinability Theorem is refuted [also Gödel]

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Subject: Re:_Tarski_Undefinability_Theorem_is_refuted_[also_G
ödel]
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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Mon, 2 Jan 2023 16:40 UTC

On 1/2/23 11:17 AM, olcott wrote:
> On 1/2/2023 9:09 AM, Richard Damon wrote:
>> On 1/2/23 9:51 AM, olcott wrote:
>>> On 1/2/2023 12:01 AM, Richard Damon wrote:
>>>> On 1/1/23 11:49 PM, olcott wrote:
>>>>> On 1/1/2023 10:36 PM, Richard Damon wrote:
>>>>>> On 1/1/23 11:13 PM, olcott wrote:
>>>>>>> On 1/1/2023 8:39 PM, Richard Damon wrote:
>>>>>>>> On 1/1/23 8:29 PM, olcott wrote:
>>>>>>>>> On 1/1/2023 3:37 PM, Richard Damon wrote:
>>>>>>>>>> On 1/1/23 2:51 PM, olcott wrote:
>>>>>>>>
>>>>>>>>>>> Hardly anyone seems to understand that the Liar Paradox is
>>>>>>>>>>> simply not a
>>>>>>>>>>> truth bearer otherwise tertiary logic would have never been
>>>>>>>>>>> created.
>>>>>>>>>>
>>>>>>>>>> No Nearly EVERYONE understands that in Binary Logic, the Liar
>>>>>>>>>> Paracos is simply not a Truth Bearer.
>>>>>>>>>
>>>>>>>>> I don't think that all the people writing papers about how to
>>>>>>>>> resolve the Liar Paradox fail to understand binary logic.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Most INTELEGENT people trying to resolve the Liar's Paradox
>>>>>>>> understand Binary Logic, and are looking for logic beyond Binary
>>>>>>>> Logic to see if other Logical Paradigms might be able to handle
>>>>>>>> that sort of thing (and actually are probably looking at things
>>>>>>>> more complicated then the simple Liar's Paradox).
>>>>>>>>
>>>>>>>
>>>>>>> Anyone that is trying to resolve an expression of language that
>>>>>>> is not a
>>>>>>> truth bearer to a truth value is on a fools errand.
>>>>>>>
>>>>>>>>
>>>>>>>> I will admit, that are probably a lot of DUMB people, who don't
>>>>>>>> understand logic, and are doing all sorts of dumb things, and if
>>>>>>>> those are hiting your radar, you need a better selection filter.
>>>>>>>>
>>>>>>>
>>>>>>> Saul Kripke was by no means any sort of dumb
>>>>>>> https://www.impan.pl/~kz/truthseminar/Kripke_Outline.pdf
>>>>>>
>>>>>> And he isn't trying to say the Liar's Paradox is a Truth Beared.
>>>>>>
>>>>>> At a quick glance he seems to be working on logic that handles
>>>>>> ill-defined statments with partial knowledge
>>>>>>
>>>>>>>
>>>>>>>> Of course, those are probably the works that you can sort of
>>>>>>>> understand, since they are at your level.
>>>>>>>>
>>>>>>>> And actually, MOST people just understand that non-truth of the
>>>>>>>> Liar's Paradox and they leave it at that.
>>>>>>>>
>>>>>>>
>>>>>>> Tarski "proved" that truth cannot be specified and used the Liar
>>>>>>> Paradox as the foundation of this proof.
>>>>>>
>>>>>> Not quite.
>>>>>>
>>>>>> He Showed that if you presume a complete specification for truth
>>>>>> could exist in a system, that it is neccessarily possible to prove
>>>>>> that the Liar's Paradox is True.
>>>>>>
>>>>>
>>>>> Maybe Tarski made that same mistake you are are making.
>>>>> If Tarski believed that he proved this sentence is true in his
>>>>> meta-theory: "This sentence is not true" then Tarski made a
>>>>> terrible mistake.
>>>>>
>>>>> {This sentence is not true: "This sentence is not true"} would be
>>>>> true.
>>>>> "This sentence is not true" is never true.
>>>>>
>>>>> My key skill from software engineering is to boil complex things
>>>>> down to their barest possible essence. Tarski already mostly did
>>>>> that for Gödel.
>>>>>
>>>>> Did you verify that his proof is only two pages yet?
>>>>>
>>>>> http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf
>>>>>
>>>>
>>>> Where in those pages do you see your summary expressed?
>>>>
>>>> Note, the construction of the Meta Theory is such that any statement
>>>> in the Theory means exactly the same thing in the Meta Theory, so it
>>>> isn't the meta theory having a statement referencing the statement
>>>> in the theory, but is a proof of the actual original statement.
>>>>
>>>
>>> This sentence is not true: "This sentence is not true"
>>> The outer-sentence has the same words as the inner sentence yet has a
>>> different semantic meaning because the inner sentence is self-
>>> referential and the outer sentence is not self-referential.
>>
>> And where are you getting these two sentences from?
>>
>
> It is common knowledge that this is a version of the Liar Paradox:
> "This sentence is not true".
>

so, what happened to the sentences:

> This sentence is not true: "This sentence is not true"
> The outer-sentence has the same words as the inner sentence yet has a
> different semantic meaning because the inner sentence is self-
> referential and the outer sentence is not self-referential.

You seem to like editing out the parts being refered to.

Just shows how little you understand about what is True.

> I discovered that when the pathological self-reference(Olcott 2004) has
> been removed by applying the sentence to another instance of itself,
> then this new sentence is true.
>

So? Since this isn't what the Theories are doing, it doesn't matter.

>>>
>>>> The proof you reference on pages 275-276 is just a simple proof that
>>>> it is possible to construct in the Theory a statement that says, in
>>>> effect, that statement x is not provable in the Theory if and only
>>>> if p is True. With p being a reference to the whole sentence (Which
>>>> is sort of Godels statement in the Meta-theory),
>>>>
>>>
>>> LP := "this sentence is not true" // theory
>>> ~True(LP) // meta-theory
>>
>> Nope, you apperently don't understand the concept of a Meta Theory.
>>
>
> A meta-theory merely has an additional level of indirection when
> referring to expression in the theory.

Nope, says you don't understand the concept of the Meta-Theory,

>
> LP := "This sentence is not true" // LP in the theory
> ~True(LP) // LP in the meta-theory

Nope. You aren't understanding the Meta Theory. I guess you mind is just
too week.

>
>> Sentence x exists in the domain of the Theory.
>>
>> That exact same Sentence exist in the Meta-Theory, not a sentence
>
> Not, not at all, this is incorrect. The sentence in the meta-theory has
> exactly one level of indirect reference to the sentence in the theory.

Nope, because the statement in the Theory is ALSO a statement in the
Meta-Theory, because of the rules used to create the Meta-Theory.

>
>> REFERING to the sentence in the Theory. It means the same thing, but
>> with a wider context by the definition of the Meta Theory.
>>
>>>
>>>> This is NOT the "Liars Paradox", as the liar's paradox is about a
>>>> statement being TRUE, not about it being PROVABLE. (and in fact, it
>>>
>>>    Everywhere, both in the formulation of the
>>>    theorem and in its proof, we replace the symbol 'Tr' by the
>>>    symbol 'Pr' which denotes the class of all provable sentences
>>>    of the theory under consideration
>>>
>>> *Tarski used Pr as a proxy for Tr*
>>
>> You understand that is a direct result of the Theory he referenced?
>>
>> This is no "Proxy".
>>
>> Maybe you need to study THAT Theory to understand it.
>
> When Tarski substitutes the symbol Tr with the symbol Pr he is saying
> that he is construing True to mean Provable.


Click here to read the complete article
Re: Tarski Undefinability Theorem is refuted [also Gödel]

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Subject: Re:_Tarski_Undefinability_Theorem_is_refuted_[also_G
ödel]
From: donstock...@hotmail.com (Don Stockbauer)
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 by: Don Stockbauer - Mon, 2 Jan 2023 19:20 UTC

On Monday, January 2, 2023 at 10:40:11 AM UTC-6, Richard Damon wrote:
> On 1/2/23 11:17 AM, olcott wrote:
> > On 1/2/2023 9:09 AM, Richard Damon wrote:
> >> On 1/2/23 9:51 AM, olcott wrote:
> >>> On 1/2/2023 12:01 AM, Richard Damon wrote:
> >>>> On 1/1/23 11:49 PM, olcott wrote:
> >>>>> On 1/1/2023 10:36 PM, Richard Damon wrote:
> >>>>>> On 1/1/23 11:13 PM, olcott wrote:
> >>>>>>> On 1/1/2023 8:39 PM, Richard Damon wrote:
> >>>>>>>> On 1/1/23 8:29 PM, olcott wrote:
> >>>>>>>>> On 1/1/2023 3:37 PM, Richard Damon wrote:
> >>>>>>>>>> On 1/1/23 2:51 PM, olcott wrote:
> >>>>>>>>
> >>>>>>>>>>> Hardly anyone seems to understand that the Liar Paradox is
> >>>>>>>>>>> simply not a
> >>>>>>>>>>> truth bearer otherwise tertiary logic would have never been
> >>>>>>>>>>> created.
> >>>>>>>>>>
> >>>>>>>>>> No Nearly EVERYONE understands that in Binary Logic, the Liar
> >>>>>>>>>> Paracos is simply not a Truth Bearer.
> >>>>>>>>>
> >>>>>>>>> I don't think that all the people writing papers about how to
> >>>>>>>>> resolve the Liar Paradox fail to understand binary logic.
> >>>>>>>>>
> >>>>>>>>
> >>>>>>>> Most INTELEGENT people trying to resolve the Liar's Paradox
> >>>>>>>> understand Binary Logic, and are looking for logic beyond Binary
> >>>>>>>> Logic to see if other Logical Paradigms might be able to handle
> >>>>>>>> that sort of thing (and actually are probably looking at things
> >>>>>>>> more complicated then the simple Liar's Paradox).
> >>>>>>>>
> >>>>>>>
> >>>>>>> Anyone that is trying to resolve an expression of language that
> >>>>>>> is not a
> >>>>>>> truth bearer to a truth value is on a fools errand.
> >>>>>>>
> >>>>>>>>
> >>>>>>>> I will admit, that are probably a lot of DUMB people, who don't
> >>>>>>>> understand logic, and are doing all sorts of dumb things, and if
> >>>>>>>> those are hiting your radar, you need a better selection filter.
> >>>>>>>>
> >>>>>>>
> >>>>>>> Saul Kripke was by no means any sort of dumb
> >>>>>>> https://www.impan.pl/~kz/truthseminar/Kripke_Outline.pdf
> >>>>>>
> >>>>>> And he isn't trying to say the Liar's Paradox is a Truth Beared.
> >>>>>>
> >>>>>> At a quick glance he seems to be working on logic that handles
> >>>>>> ill-defined statments with partial knowledge
> >>>>>>
> >>>>>>>
> >>>>>>>> Of course, those are probably the works that you can sort of
> >>>>>>>> understand, since they are at your level.
> >>>>>>>>
> >>>>>>>> And actually, MOST people just understand that non-truth of the
> >>>>>>>> Liar's Paradox and they leave it at that.
> >>>>>>>>
> >>>>>>>
> >>>>>>> Tarski "proved" that truth cannot be specified and used the Liar
> >>>>>>> Paradox as the foundation of this proof.
> >>>>>>
> >>>>>> Not quite.
> >>>>>>
> >>>>>> He Showed that if you presume a complete specification for truth
> >>>>>> could exist in a system, that it is neccessarily possible to prove
> >>>>>> that the Liar's Paradox is True.
> >>>>>>
> >>>>>
> >>>>> Maybe Tarski made that same mistake you are are making.
> >>>>> If Tarski believed that he proved this sentence is true in his
> >>>>> meta-theory: "This sentence is not true" then Tarski made a
> >>>>> terrible mistake.
> >>>>>
> >>>>> {This sentence is not true: "This sentence is not true"} would be
> >>>>> true.
> >>>>> "This sentence is not true" is never true.
> >>>>>
> >>>>> My key skill from software engineering is to boil complex things
> >>>>> down to their barest possible essence. Tarski already mostly did
> >>>>> that for Gödel.
> >>>>>
> >>>>> Did you verify that his proof is only two pages yet?
> >>>>>
> >>>>> http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf
> >>>>>
> >>>>
> >>>> Where in those pages do you see your summary expressed?
> >>>>
> >>>> Note, the construction of the Meta Theory is such that any statement
> >>>> in the Theory means exactly the same thing in the Meta Theory, so it
> >>>> isn't the meta theory having a statement referencing the statement
> >>>> in the theory, but is a proof of the actual original statement.
> >>>>
> >>>
> >>> This sentence is not true: "This sentence is not true"
> >>> The outer-sentence has the same words as the inner sentence yet has a
> >>> different semantic meaning because the inner sentence is self-
> >>> referential and the outer sentence is not self-referential.
> >>
> >> And where are you getting these two sentences from?
> >>
> >
> > It is common knowledge that this is a version of the Liar Paradox:
> > "This sentence is not true".
> >
> so, what happened to the sentences:
> > This sentence is not true: "This sentence is not true"
> > The outer-sentence has the same words as the inner sentence yet has a
> > different semantic meaning because the inner sentence is self-
> > referential and the outer sentence is not self-referential.
> You seem to like editing out the parts being refered to.
>
> Just shows how little you understand about what is True.
> > I discovered that when the pathological self-reference(Olcott 2004) has
> > been removed by applying the sentence to another instance of itself,
> > then this new sentence is true.
> >
> So? Since this isn't what the Theories are doing, it doesn't matter.
> >>>
> >>>> The proof you reference on pages 275-276 is just a simple proof that
> >>>> it is possible to construct in the Theory a statement that says, in
> >>>> effect, that statement x is not provable in the Theory if and only
> >>>> if p is True. With p being a reference to the whole sentence (Which
> >>>> is sort of Godels statement in the Meta-theory),
> >>>>
> >>>
> >>> LP := "this sentence is not true" // theory
> >>> ~True(LP) // meta-theory
> >>
> >> Nope, you apperently don't understand the concept of a Meta Theory.
> >>
> >
> > A meta-theory merely has an additional level of indirection when
> > referring to expression in the theory.
> Nope, says you don't understand the concept of the Meta-Theory,
> >
> > LP := "This sentence is not true" // LP in the theory
> > ~True(LP) // LP in the meta-theory
> Nope. You aren't understanding the Meta Theory. I guess you mind is just
> too week.
> >
> >> Sentence x exists in the domain of the Theory.
> >>
> >> That exact same Sentence exist in the Meta-Theory, not a sentence
> >
> > Not, not at all, this is incorrect. The sentence in the meta-theory has
> > exactly one level of indirect reference to the sentence in the theory.
> Nope, because the statement in the Theory is ALSO a statement in the
> Meta-Theory, because of the rules used to create the Meta-Theory.
> >
> >> REFERING to the sentence in the Theory. It means the same thing, but
> >> with a wider context by the definition of the Meta Theory.
> >>
> >>>
> >>>> This is NOT the "Liars Paradox", as the liar's paradox is about a
> >>>> statement being TRUE, not about it being PROVABLE. (and in fact, it
> >>>
> >>> Everywhere, both in the formulation of the
> >>> theorem and in its proof, we replace the symbol 'Tr' by the
> >>> symbol 'Pr' which denotes the class of all provable sentences
> >>> of the theory under consideration
> >>>
> >>> *Tarski used Pr as a proxy for Tr*
> >>
> >> You understand that is a direct result of the Theory he referenced?
> >>
> >> This is no "Proxy".
> >>
> >> Maybe you need to study THAT Theory to understand it.
> >
> > When Tarski substitutes the symbol Tr with the symbol Pr he is saying
> > that he is construing True to mean Provable.
> Nope. You don't understand what he is doing.
>
> You seem to be missing that he is using the NEGATION of the first
> sentence built according to the Theory he is referencing.
> >
> >>>
> >>> (3) x ∉ Pr if and only if x ∈ Tr.
> >>>
> >>> x ∉ Provable if and only if x ∈ True.
> >>> ~Provable(x) ↔ True(x).
> >>> x is true if and only if x is unprovable
> >>>
> >>> x is true if and only if x lacks the required semantic connection to a
> >>> truth maker is false.
> >>>
> >>> It is the same sort of thing as saying that one can only bake an angel
> >>> food cake when one lacks the ingredients for an angel food cake.
> >>
> >> Nope, You are arguing with the result of the mentioned Theory.
> >>
> >> Try to find the flaw in its proof.
> >>
> >> It is a necessary consequence of the requirements of the system that
> >> such a statement is allowed to be created.
> >>
> >> Your failure to understand it shows how LOW your IQ is.
> >>
> >>
> >>>
> >>>> looks like the top of page 275 is him showing why this statement IS
> >>>> a Truth Bearer, using his words that "We can construct a sentence x
> >>>> of the science in question". I beleive you will find this is his
> >>>> terminology to describe sentneces which are what you call Truth
> >>>> Bearers.
> >>>>
> >>>> Since the premise x is provable, or it is not true that x is
> >>>> provable are BY DEFINITION truth bears.
> >>>>
> >>>
> >>> It is not a little bear that always tells the truth, it is that the
> >>> expression of language has a Boolean semantic value of true or false.
> >>
> >> Right. The statements x is Provable, x is not Provable, and x is True
> >> are all statements which are Truth Bearers.
> >>
> >
> > Every sentence that claims that it has zero semantic connections to a
> > truth maker either has a semantic connection to a truth maker making
> > it false or has no semantic connection to a truth maker making it
> > untrue.
> >
> But becaue of the Theorem, the statement IS a truth Bearer, so untrue is
> false.
>
> You are ignoring the Theorem he is referencing, probably because you
> don't understand it.
> >> From the previously mentiond Theory, the whole statement is a Truth
> >> Bearer, and that Requires that the only possible case is that x is
> >> True and x is not Provable.
> >>
> >
> > Already addressed above. Provable means having a finite semantic
> > connection to a truth maker, thus every sentence that has zero semantic
> > connections to a truth maker has zero finite connections to a truth
> > maker. Epistemological antinomies have zero connections to any truth
> > maker, thus are both untrue and unprovable.
> >
> But the statement isn't an Epistemolgogical antinomy, because it was
> proven to be a Truth Bearer by the Theorem.
>
> You just THINK is is an Epistemological antinomy because you confuse
> Provable with Truth,
> >> You can't just take a proven statement and say it can't be true
> >> because you don't like it or it breaks something you would like to be
> >> a rule.
> >>
> >
> > You already agreed that every expression of language that has zero
> > finite or infinite connections to a truth maker is untrue.
> No, I never agreed that an infinite set of connections makes a statment
> untrue, it make it TRUE.
>
> It makes it UNPROVABLE, and thus UNKNOWABLE, not UNTRUE.
>
> You are just showing yourself to be a LIAR or and IDIOT.
> >
> >> If you think Tarski is incorrect in making that statement, you have to
> >> find the error in him making it, and since it is based directly on a
> >> Theorem that he proved, you need to find the error in that proof,
> >> which it seems you haven't even read.
> >
> > Epistemological antinomies have zero connections to any truth
> > maker, thus are both untrue and unprovable.
> Right, but the sentence in question isn't an Epistemolgical antinomy, as
> it has been proven to be a Truth Bearer, and thus can't be such a thing.
> >
> > The Tarski proof made the mistake of failing to reject an
> > Epistemological antinomy as not a member of any formal system.
> No, you make the mistake of not understanding what he is saying.
> >
> > When we eliminate the use of Epistemological antinomies from the Tarski
> > and Gödel proofs these proofs lose their entire basis.
> >
> Nope.
>
> You are just proving you don't understand what they are actually saying
> because you over simplify their words to mean something they don't
> actually mean.
>
> Probably because you mind can't actually handle the actual meaning of
> the statements because your mind is so weak.


Click here to read the complete article
Re: Tarski Undefinability Theorem is refuted

<tovdji$1samp$1@dont-email.me>

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From: polco...@gmail.com (olcott)
Newsgroups: comp.ai.philosophy
Subject: Re: Tarski Undefinability Theorem is refuted
Date: Mon, 2 Jan 2023 14:08:18 -0600
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 by: olcott - Mon, 2 Jan 2023 20:08 UTC

On 1/2/2023 8:51 AM, Don Stockbauer wrote:
> pop On Monday, January 2, 2023 at 8:30:38 AM UTC-6, olcott wrote:
>> On 1/2/2023 12:07 AM, Richard Damon wrote:
>>> On 1/2/23 12:51 AM, olcott wrote:
>>>> On 1/1/2023 11:07 PM, Richard Damon wrote:
>>>>> On 1/1/23 11:20 PM, olcott wrote:
>>>>>> On 1/1/2023 9:14 PM, Richard Damon wrote:
>>>>>>> On 1/1/23 9:47 PM, olcott wrote:
>>>>>>>
>>>>>>>> I don't believe that you have an IQ anywhere near the top 1% much
>>>>>>>> less
>>>>>>>> than the 185 IQ of top 2 in a billion. I could easily believe the top
>>>>>>>> 5%, most everyone here is in the top 5%.
>>>>>>>>
>>>>>>>
>>>>>>> Doesn't matter what you believe, as you have demonstrated that you
>>>>>>> don't understand what is actually Truth.
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> You have not demonstrated any very significant understanding of these
>>>>>> things. It does seem that you have demonstrated key
>>>>>> misunderstandings of
>>>>>> Tarski. I guy with a 2 in one billion IQ would not make these mistakes.
>>>>>> A guy with a top 1% IQ might make these mistakes if they barely skimmed
>>>>>> the material.
>>>>>>
>>>>>> You can see that the proof is only two pages long, not too much to
>>>>>> carefully study.
>>>>>>
>>>>>> http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf
>>>>>>
>>>>>
>>>>> First, you confuse Intelgence with Knowledge.
>>>>>
>>>>> As I have mentioned before, this is an area that I admit I haven't
>>>>> studied in great detail (but it seems I still understand some of the
>>>>> point better than you, which shows your lack of intelegence).
>>>>>
>>>>> You claim Tarski bases his proof on the Liar needing a Truth Value.
>>>>>
>>>>> In fact, a simple reading of the text shows that he is using the
>>>>> standard Proof by Contradiction to show that IF the "Thesis A" which
>>>>> resumes a definition of Truth was actually True, then we can prove
>>>>> that the Liar's Paradox is True.
>>>>>
>>>>> Since we know the Liar's Paradox is not a Truth Bearer, and thus not
>>>>> True, the Thesis can not be true.
>>>>>
>>>>> IF I find the time, I might put the effort to read the papers you
>>>>> have linked to and see if I can make some more detailed comments on
>>>>> them.
>>>>>
>>>>> My first guess is a few days effort would probably be sufficent,
>>>>> which compared to your decades, seems a reasonable ratio considering
>>>>> our comparative intelegence.
>>>>
>>>> Finite Truth is all about showing that a truth maker semantic
>>>> connection exists. If exists then true else untrue.
>>>>
>>>
>>> Where are you getting the term "Finite Truth".
>>>
>> Even a guy with a top 1% IQ would be able to figure out from our prior
>> context that I must mean expressions of language that have finite
>> semantic connections to their truth maker.
>>> Truth is allowed to be base on a infinite set of connections.
>>>
>> Off topic because we are only talking about Tarski's simplification of
>> Gödel. The liar paradox has zero semantic connections to a truth maker,
>> thus lacks infinite connections to a truth maker.
>>
>> As I have already pointed out Prolog detects and rejects both the liar
>> paradox and the simplified Gödel sentence on the basis that they lack
>> connections to their truth maker.
>>
>> ?- 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.
>>
>> This is not saying that the LP has an infinite proof it is saying that
>> the LP never reaches a truth maker.
>> "This sentence is not true"
>> It is not true about what?
>> It is not true about being not true.
>> It is not true about being not true about what?
>> It is not true about being not true about being not true...
>>> It is True if ANY (including infinte) set of connections exist.
>>>
>>> It is only provable if a FINITE set of connections exist.
>>>
>>> You keep on confusing these two terms, because in your mind you have
>>> crossed their connections and mix up Truth with Knowledge, perhaps
>>> because you studied some theries of Knowledge, and are confusing what is
>>> known to be True with what is actually True.
>>>
>>> You keep on makeing that sort of mistake in your words, by talking of
>>> what we can KNOW to be true, and applying that to what is actually True.
>> It is not that I keep confusing these terms it is that you continue to
>> fail to understand that it can be proven in a finite number of steps
>> that the LP has no semantic connection to any truth maker.
>>
>> Here is an example of formalizing the Liar Paradox in C++
>>
>> void main()
>> {
>> bool LP = (LP != true);
>> }
>>
>> Even the “C++” compiler recognizes the value is tested before it has
>> been initialized.
>> liarparadox.cpp(3) : warning C4700: uninitialized local variable 'LP' used
>> Microsoft (R) Incremental Linker Version 9.00.30729.01
>> Copyright (C) Microsoft Corporation. All rights reserved.
>> --
>> Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
>> hits a target no one else can see." Arthur Schopenhauer
>
> Are you related to William Tyler Olcott, the famous astronomer?

IDK, I am related to Henry Steele Olcott the most famous American
Buddhist that is celebrated every year in Sri Lanka.

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

Re: Tarski Undefinability Theorem is refuted [also Gödel]

<tovecj$1samp$2@dont-email.me>

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Newsgroups: comp.theory,comp.ai.philosophy,sci.logic
Subject: Re:_Tarski_Undefinability_Theorem_is_refuted_[also_G
ödel]
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 by: olcott - Mon, 2 Jan 2023 20:21 UTC

On 1/2/2023 10:25 AM, Richard Damon wrote:
> On 1/2/23 10:46 AM, olcott wrote:
>> On 1/2/2023 8:52 AM, Richard Damon wrote:
>>> On 1/2/23 9:30 AM, olcott wrote:
>>>> On 1/2/2023 12:07 AM, Richard Damon wrote:
>>>>> On 1/2/23 12:51 AM, olcott wrote:
>>>>>> On 1/1/2023 11:07 PM, Richard Damon wrote:
>>>>>>> On 1/1/23 11:20 PM, olcott wrote:
>>>>>>>> On 1/1/2023 9:14 PM, Richard Damon wrote:
>>>>>>>>> On 1/1/23 9:47 PM, olcott wrote:
>>>>>>>>>
>>>>>>>>>> I don't believe that you have an IQ anywhere near the top 1%
>>>>>>>>>> much less
>>>>>>>>>> than the 185 IQ of top 2 in a billion. I could easily believe
>>>>>>>>>> the top
>>>>>>>>>> 5%, most everyone here is in the top 5%.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Doesn't matter what you believe, as you have demonstrated that
>>>>>>>>> you don't understand what is actually Truth.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> You have not demonstrated any very significant understanding of
>>>>>>>> these
>>>>>>>> things. It does seem that you have demonstrated key
>>>>>>>> misunderstandings of
>>>>>>>> Tarski. I guy with a 2 in one billion IQ would not make these
>>>>>>>> mistakes.
>>>>>>>> A guy with a top 1% IQ might make these mistakes if they barely
>>>>>>>> skimmed
>>>>>>>> the material.
>>>>>>>>
>>>>>>>> You can see that the proof is only two pages long, not too much
>>>>>>>> to carefully study.
>>>>>>>>
>>>>>>>> http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf
>>>>>>>>
>>>>>>>
>>>>>>> First, you confuse Intelgence with Knowledge.
>>>>>>>
>>>>>>> As I have mentioned before, this is an area that I admit I
>>>>>>> haven't studied in great detail (but it seems I still understand
>>>>>>> some of the point better than you, which shows your lack of
>>>>>>> intelegence).
>>>>>>>
>>>>>>> You claim Tarski bases his proof on the Liar needing a Truth Value.
>>>>>>>
>>>>>>> In fact, a simple reading of the text shows that he is using the
>>>>>>> standard Proof by Contradiction to show that IF the "Thesis A"
>>>>>>> which resumes a definition of Truth was actually True, then we
>>>>>>> can prove that the Liar's Paradox is True.
>>>>>>>
>>>>>>> Since we know the Liar's Paradox is not a Truth Bearer, and thus
>>>>>>> not True, the Thesis can not be true.
>>>>>>>
>>>>>>> IF I find the time, I might put the effort to read the papers you
>>>>>>> have linked to and see if I can make some more detailed comments
>>>>>>> on them.
>>>>>>>
>>>>>>> My first guess is a few days effort would probably be sufficent,
>>>>>>> which compared to your decades, seems a reasonable ratio
>>>>>>> considering our comparative intelegence.
>>>>>>
>>>>>> Finite Truth is all about showing that a truth maker semantic
>>>>>> connection exists. If exists then true else untrue.
>>>>>>
>>>>>
>>>>> Where are you getting the term "Finite Truth".
>>>>>
>>>>
>>>> Even a guy with a top 1% IQ would be able to figure out from our prior
>>>> context that I must mean expressions of language that have finite
>>>> semantic connections to their truth maker.
>>>
>>> Which means you aren't talking about ANYTHING that anyone else we
>>> have been talking about would call "True", and thus meaningless for
>>> this conversation.
>>>
>>
>> The subset of expressions of language that have finite semantic
>> connections to their truth maker is not an entirely different subject
>> than the set of expressions of language having semantic connections
>> to their truth maker.
>>
>>> Limiting your definition of "True" to finite connections is the
>>> equivalent of limiting it to Provable, which has been shown (though
>>> you don't understand it) to leads either logic system that are
>>> constrained in what they can handle, or they become inconsistent.
>>>
>>
>> Not at all. It leads to rejecting expressions of language that have no
>> possible connection to any truth maker. Prolog can already do this.
>
> Bo, it leads to rejecting expression of language that DO have a
> connection to a truth maker, because such a connect is infinite.
>

You and I and the set of human knowledge can all see that
epistemological antinomies have no finite or infinite semantic
connection to any truth maker, thus are not truth bearers.

That Gödel and Tarski included expressions of language that cannot
possibly have a correct Boolean value in their respective formal systems
was their key mistake invalidating both of their proofs.

>>
>> ?- LP = not(true(LP)).
>> LP = not(true(LP)).
>>
>> ?- unify_with_occurs_check(LP, not(true(LP))).
>> false.
>
> Fallacy of Proof by Example.
>
> Proving your Stupidity.

Prolog correctly determines that LP is not a truth bearer because it
correctly determines that is has no semantic connection to any truth
maker.

>>
>>> If that is the sort of logic system you want to talk about, ok, but
>>> make it clear, and admit you aren't talking about fields like the
>>> properties of the Natural Numbers.
>>>
>>
>> Any expression of formal or natural language that cannot possibly have
>> any connection to a truth maker is not true. Epistemological antinomies
>> cannot possibly have a semantic connection to any truth maker, thus are
>> always untrue.
>
> So? I haven't been talking about Epistemological antinomies having a
> semantic connection to a truth maker,

Then you have been dodging the key point because the Gödel and Tarski
proofs require an epistemological antinomy or they fail.

> but that some actually TRUE
> statement, having an infinite set of connections to a Truth Maker,
> actually ARE TRUE by definition, but are also not provable, since a
> proof needs a FINITE connect.
>
> The fact you keep going to the antinomies shows you don't understand
> this basic concept, because you are just too stupid,
>

Verbatim quote of Gödel anchoring his key mistake:
14 Every epistemological antinomy can likewise be used for a similar
undecidability proof.

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

Re: Tarski Undefinability Theorem is refuted [also Gödel]

<tovfp7$1sht2$1@dont-email.me>

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ödel]
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 by: olcott - Mon, 2 Jan 2023 20:45 UTC

On 1/2/2023 10:40 AM, Richard Damon wrote:
> On 1/2/23 11:17 AM, olcott wrote:
>> On 1/2/2023 9:09 AM, Richard Damon wrote:
>>> On 1/2/23 9:51 AM, olcott wrote:
>>>> On 1/2/2023 12:01 AM, Richard Damon wrote:
>>>>> On 1/1/23 11:49 PM, olcott wrote:
>>>>>> On 1/1/2023 10:36 PM, Richard Damon wrote:
>>>>>>> On 1/1/23 11:13 PM, olcott wrote:
>>>>>>>> On 1/1/2023 8:39 PM, Richard Damon wrote:
>>>>>>>>> On 1/1/23 8:29 PM, olcott wrote:
>>>>>>>>>> On 1/1/2023 3:37 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/1/23 2:51 PM, olcott wrote:
>>>>>>>>>
>>>>>>>>>>>> Hardly anyone seems to understand that the Liar Paradox is
>>>>>>>>>>>> simply not a
>>>>>>>>>>>> truth bearer otherwise tertiary logic would have never been
>>>>>>>>>>>> created.
>>>>>>>>>>>
>>>>>>>>>>> No Nearly EVERYONE understands that in Binary Logic, the Liar
>>>>>>>>>>> Paracos is simply not a Truth Bearer.
>>>>>>>>>>
>>>>>>>>>> I don't think that all the people writing papers about how to
>>>>>>>>>> resolve the Liar Paradox fail to understand binary logic.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Most INTELEGENT people trying to resolve the Liar's Paradox
>>>>>>>>> understand Binary Logic, and are looking for logic beyond
>>>>>>>>> Binary Logic to see if other Logical Paradigms might be able to
>>>>>>>>> handle that sort of thing (and actually are probably looking at
>>>>>>>>> things more complicated then the simple Liar's Paradox).
>>>>>>>>>
>>>>>>>>
>>>>>>>> Anyone that is trying to resolve an expression of language that
>>>>>>>> is not a
>>>>>>>> truth bearer to a truth value is on a fools errand.
>>>>>>>>
>>>>>>>>>
>>>>>>>>> I will admit, that are probably a lot of DUMB people, who don't
>>>>>>>>> understand logic, and are doing all sorts of dumb things, and
>>>>>>>>> if those are hiting your radar, you need a better selection
>>>>>>>>> filter.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Saul Kripke was by no means any sort of dumb
>>>>>>>> https://www.impan.pl/~kz/truthseminar/Kripke_Outline.pdf
>>>>>>>
>>>>>>> And he isn't trying to say the Liar's Paradox is a Truth Beared.
>>>>>>>
>>>>>>> At a quick glance he seems to be working on logic that handles
>>>>>>> ill-defined statments with partial knowledge
>>>>>>>
>>>>>>>>
>>>>>>>>> Of course, those are probably the works that you can sort of
>>>>>>>>> understand, since they are at your level.
>>>>>>>>>
>>>>>>>>> And actually, MOST people just understand that non-truth of the
>>>>>>>>> Liar's Paradox and they leave it at that.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Tarski "proved" that truth cannot be specified and used the Liar
>>>>>>>> Paradox as the foundation of this proof.
>>>>>>>
>>>>>>> Not quite.
>>>>>>>
>>>>>>> He Showed that if you presume a complete specification for truth
>>>>>>> could exist in a system, that it is neccessarily possible to
>>>>>>> prove that the Liar's Paradox is True.
>>>>>>>
>>>>>>
>>>>>> Maybe Tarski made that same mistake you are are making.
>>>>>> If Tarski believed that he proved this sentence is true in his
>>>>>> meta-theory: "This sentence is not true" then Tarski made a
>>>>>> terrible mistake.
>>>>>>
>>>>>> {This sentence is not true: "This sentence is not true"} would be
>>>>>> true.
>>>>>> "This sentence is not true" is never true.
>>>>>>
>>>>>> My key skill from software engineering is to boil complex things
>>>>>> down to their barest possible essence. Tarski already mostly did
>>>>>> that for Gödel.
>>>>>>
>>>>>> Did you verify that his proof is only two pages yet?
>>>>>>
>>>>>> http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf
>>>>>>
>>>>>
>>>>> Where in those pages do you see your summary expressed?
>>>>>
>>>>> Note, the construction of the Meta Theory is such that any
>>>>> statement in the Theory means exactly the same thing in the Meta
>>>>> Theory, so it isn't the meta theory having a statement referencing
>>>>> the statement in the theory, but is a proof of the actual original
>>>>> statement.
>>>>>
>>>>
>>>> This sentence is not true: "This sentence is not true"
>>>> The outer-sentence has the same words as the inner sentence yet has a
>>>> different semantic meaning because the inner sentence is self-
>>>> referential and the outer sentence is not self-referential.
>>>
>>> And where are you getting these two sentences from?
>>>
>>
>> It is common knowledge that this is a version of the Liar Paradox:
>> "This sentence is not true".
>>
>
> so, what happened to the sentences:
>
>> This sentence is not true: "This sentence is not true"

The RHS is the Liar Paradox. The whole sentence is one sentence
referring to another sentence that refers to itself.

>> The outer-sentence has the same words as the inner sentence yet has a
>> different semantic meaning because the inner sentence is self-
>> referential and the outer sentence is not self-referential.
>
> You seem to like editing out the parts being refered to.
>
> Just shows how little you understand about what is True.
>
>
>> I discovered that when the pathological self-reference(Olcott 2004)
>> has been removed by applying the sentence to another instance of
>> itself, then this new sentence is true.
>>
>
> So? Since this isn't what the Theories are doing, it doesn't matter.
>
>>>>
>>>>> The proof you reference on pages 275-276 is just a simple proof
>>>>> that it is possible to construct in the Theory a statement that
>>>>> says, in effect, that statement x is not provable in the Theory if
>>>>> and only if p is True. With p being a reference to the whole
>>>>> sentence (Which is sort of Godels statement in the Meta-theory),
>>>>>
>>>>
>>>> LP := "this sentence is not true" // theory
>>>> ~True(LP) // meta-theory
>>>
>>> Nope, you apperently don't understand the concept of a Meta Theory.
>>>
>>
>> A meta-theory merely has an additional level of indirection when
>> referring to expression in the theory.
>
> Nope, says you don't understand the concept of the Meta-Theory,

What do you think it means?

>>
>> LP := "This sentence is not true" // LP in the theory
>> ~True(LP) // LP in the meta-theory
>
> Nope. You aren't understanding the Meta Theory. I guess you mind is just
> too week.
>
>>
>>> Sentence x exists in the domain of the Theory.
>>>
>>> That exact same Sentence exist in the Meta-Theory, not a sentence
>>
>> Not, not at all, this is incorrect. The sentence in the meta-theory has
>> exactly one level of indirect reference to the sentence in the theory.
>
> Nope, because the statement in the Theory is ALSO a statement in the
> Meta-Theory, because of the rules used to create the Meta-Theory.
>


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Re: Tarski Undefinability Theorem is refuted [also Gödel]

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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Mon, 2 Jan 2023 20:45 UTC

On 1/2/23 3:21 PM, olcott wrote:
> On 1/2/2023 10:25 AM, Richard Damon wrote:
>> On 1/2/23 10:46 AM, olcott wrote:
>>> On 1/2/2023 8:52 AM, Richard Damon wrote:
>>>> On 1/2/23 9:30 AM, olcott wrote:
>>>>> On 1/2/2023 12:07 AM, Richard Damon wrote:
>>>>>> On 1/2/23 12:51 AM, olcott wrote:
>>>>>>> On 1/1/2023 11:07 PM, Richard Damon wrote:
>>>>>>>> On 1/1/23 11:20 PM, olcott wrote:
>>>>>>>>> On 1/1/2023 9:14 PM, Richard Damon wrote:
>>>>>>>>>> On 1/1/23 9:47 PM, olcott wrote:
>>>>>>>>>>
>>>>>>>>>>> I don't believe that you have an IQ anywhere near the top 1%
>>>>>>>>>>> much less
>>>>>>>>>>> than the 185 IQ of top 2 in a billion. I could easily believe
>>>>>>>>>>> the top
>>>>>>>>>>> 5%, most everyone here is in the top 5%.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Doesn't matter what you believe, as you have demonstrated that
>>>>>>>>>> you don't understand what is actually Truth.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> You have not demonstrated any very significant understanding of
>>>>>>>>> these
>>>>>>>>> things. It does seem that you have demonstrated key
>>>>>>>>> misunderstandings of
>>>>>>>>> Tarski. I guy with a 2 in one billion IQ would not make these
>>>>>>>>> mistakes.
>>>>>>>>> A guy with a top 1% IQ might make these mistakes if they barely
>>>>>>>>> skimmed
>>>>>>>>> the material.
>>>>>>>>>
>>>>>>>>> You can see that the proof is only two pages long, not too much
>>>>>>>>> to carefully study.
>>>>>>>>>
>>>>>>>>> http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf
>>>>>>>>>
>>>>>>>>
>>>>>>>> First, you confuse Intelgence with Knowledge.
>>>>>>>>
>>>>>>>> As I have mentioned before, this is an area that I admit I
>>>>>>>> haven't studied in great detail (but it seems I still understand
>>>>>>>> some of the point better than you, which shows your lack of
>>>>>>>> intelegence).
>>>>>>>>
>>>>>>>> You claim Tarski bases his proof on the Liar needing a Truth Value.
>>>>>>>>
>>>>>>>> In fact, a simple reading of the text shows that he is using the
>>>>>>>> standard Proof by Contradiction to show that IF the "Thesis A"
>>>>>>>> which resumes a definition of Truth was actually True, then we
>>>>>>>> can prove that the Liar's Paradox is True.
>>>>>>>>
>>>>>>>> Since we know the Liar's Paradox is not a Truth Bearer, and thus
>>>>>>>> not True, the Thesis can not be true.
>>>>>>>>
>>>>>>>> IF I find the time, I might put the effort to read the papers
>>>>>>>> you have linked to and see if I can make some more detailed
>>>>>>>> comments on them.
>>>>>>>>
>>>>>>>> My first guess is a few days effort would probably be sufficent,
>>>>>>>> which compared to your decades, seems a reasonable ratio
>>>>>>>> considering our comparative intelegence.
>>>>>>>
>>>>>>> Finite Truth is all about showing that a truth maker semantic
>>>>>>> connection exists. If exists then true else untrue.
>>>>>>>
>>>>>>
>>>>>> Where are you getting the term "Finite Truth".
>>>>>>
>>>>>
>>>>> Even a guy with a top 1% IQ would be able to figure out from our prior
>>>>> context that I must mean expressions of language that have finite
>>>>> semantic connections to their truth maker.
>>>>
>>>> Which means you aren't talking about ANYTHING that anyone else we
>>>> have been talking about would call "True", and thus meaningless for
>>>> this conversation.
>>>>
>>>
>>> The subset of expressions of language that have finite semantic
>>> connections to their truth maker is not an entirely different subject
>>> than the set of expressions of language having semantic connections
>>> to their truth maker.
>>>
>>>> Limiting your definition of "True" to finite connections is the
>>>> equivalent of limiting it to Provable, which has been shown (though
>>>> you don't understand it) to leads either logic system that are
>>>> constrained in what they can handle, or they become inconsistent.
>>>>
>>>
>>> Not at all. It leads to rejecting expressions of language that have
>>> no possible connection to any truth maker. Prolog can already do this.
>>
>> Bo, it leads to rejecting expression of language that DO have a
>> connection to a truth maker, because such a connect is infinite.
>>
>
> You and I and the set of human knowledge can all see that
> epistemological antinomies have no finite or infinite semantic
> connection to any truth maker, thus are not truth bearers.

Right, but Godel's G is NOT an epistemolgical antinomy, and neither is
the sentence Tarski uses on that page of proof.

>
> That Gödel and Tarski included expressions of language that cannot
> possibly have a correct Boolean value in their respective formal systems
> was their key mistake invalidating both of their proofs.

Nope, you just don't understand the sentences they give.

The fact that you can't even give a proper summary of Godel's G is very
telling.

>
>>>
>>> ?- LP = not(true(LP)).
>>> LP = not(true(LP)).
>>>
>>> ?- unify_with_occurs_check(LP, not(true(LP))).
>>> false.
>>
>> Fallacy of Proof by Example.
>>
>> Proving your Stupidity.
>
> Prolog correctly determines that LP is not a truth bearer because it
> correctly determines that is has no semantic connection to any truth
> maker.

The fact that Prolog can identify that one sentence is not a Truth
Bearer does not establish that Prolog is a complete logic system that
can handle the stuff you claim.

The fact you make the claim just proves you are incompetent to handle logic.

>
>>>
>>>> If that is the sort of logic system you want to talk about, ok, but
>>>> make it clear, and admit you aren't talking about fields like the
>>>> properties of the Natural Numbers.
>>>>
>>>
>>> Any expression of formal or natural language that cannot possibly have
>>> any connection to a truth maker is not true. Epistemological antinomies
>>> cannot possibly have a semantic connection to any truth maker, thus are
>>> always untrue.
>>
>> So? I haven't been talking about Epistemological antinomies having a
>> semantic connection to a truth maker,
>
> Then you have been dodging the key point because the Gödel and Tarski
> proofs require an epistemological antinomy or they fail.

Nope. You just don't seem to understand what an epistemological antinomy
actually is, or what the sentences that they use are.

G is NOT an epistemological antinomy, but a question about the existence
of a number define to have a specific property defined by a primitive
recursive relationship. Since Primative Recursive Relationships are
Computable, the existance or lack thereof of a number that meets that
relationship IS a Truth Bearer.

>
>> but that some actually TRUE statement, having an infinite set of
>> connections to a Truth Maker, actually ARE TRUE by definition, but are
>> also not provable, since a proof needs a FINITE connect.
>>
>> The fact you keep going to the antinomies shows you don't understand
>> this basic concept, because you are just too stupid,
>>
>
> Verbatim quote of Gödel anchoring his key mistake:
>   14 Every epistemological antinomy can likewise be used for a similar
>      undecidability proof.
>


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