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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: Why Tarski is wrong
Date: Mon, 17 Mar 2025 21:19:07 -0400
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On 3/17/25 11:40 AM, olcott wrote:
> On 3/16/2025 9:51 PM, Richard Damon wrote:
>> On 3/16/25 9:50 PM, olcott wrote:
>>> On 3/16/2025 5:50 PM, Richard Damon wrote:
>>>> On 3/16/25 11:12 AM, olcott wrote:
>>>>> On 3/16/2025 7:36 AM, joes wrote:
>>>>>> Am Sat, 15 Mar 2025 20:43:11 -0500 schrieb olcott:
>>>>>>>
>>>>>>> We can define a correct True(X) predicate that always succeeds 
>>>>>>> except
>>>>>>> for unknowns and untruths, Tarski WAS WRONG !!!
>>>>>> That does not disprove Tarski.
>>>>>>
>>>>>
>>>>> He said that this is impossible and no
>>>>> counter-examples exists that shows that I am wrong.
>>>>> True(GC) == FALSE Cannot be proven true AKA unknown
>>>>> True(LP) == FALSE Not a truth-bearer
>>>>>
>>>>
>>>>
>>>> But if x is what you are saying is 
>>>
>>> A True(X) predicate can be defined and Tarski never
>>> showed that it cannot.
>>
>> Sure he did. Using a mathematical system like Godel, we can construct 
>> a statement x, which is only true it is the case that True(x) is 
>> false, but this interperetation can only be seen in the metalanguage 
>> created from the language in the proof, similar to Godel meta that 
>> generates the proof testing relationship that shows that G can only be 
>> true if it can not be proven as the existance of a number to make it 
>> false, becomes a proof that the statement is true and thus creates a 
>> contradiction in the system.
>>
>> That you can't understand that, or get confused by what is in the 
>> language, which your True predicate can look at, and in the 
>> metalanguage, which it can not, but still you make bold statements 
>> that you can not prove, and have been pointed out to be wrong, just 
>> shows how stupid you are.
>>
>>>
>>> True(X) only returns TRUE when a a sequence of truth
>>> preserving operations can derive X from the set of basic
>>> facts and returns false otherwise.
>>
>> Right, but needs to do so even if the path to x is infinite in length.
>>
>>>
>>> This never fails on the entire set of human general
>>> knowledge that can be expressed using language.
>>
>> But that isn't a logic system, so you are just proving your stupidity.
>>
>> Note, "The Entire set of Human General Knowledge" does not contain the 
>> contents of Meta-systems like Tarski uses, as there are an infinite 
>> number of them possible, and thus to even try to express them all 
>> requires an infinite number of axioms, and thus your system fails to 
>> meet the requirements. Once you don't have the meta-systems, Tarski 
>> proof can create a metasystem, that you system doesn't know about, 
>> which creates the problem statement.
>>
>>>
>>> It is not fooled by pathological self-reference or
>>> self-contradiction.
>>>
>>
>> Of course it is, because it can't detect all forms of such references.
>>
>> And, even if it does detect it, what answer does True(x) produce when 
>> we have designed (via a metalanguage) that the statement x in the 
>> language will be true if and only if !True(x), which he showed can be 
>> done in ANY system with sufficient power, which your universal system 
>> must have.
>>
>> Sorry, you are just showing how little you understand what you are 
>> talking about.
>>
> 
> We need no metalanguage. A single formalized natural
> language can express its own semantics as connections
> between expressions of this same language.

But it can't express all its properties and stay finite.

> 
> By the theory of simple types I mean the doctrine which says that the 
> objects of thought (or, in another interpretation, the symbolic 
> expressions) are divided into types, namely: individuals, properties of 
> individuals, relations between individuals, properties of such 
> relations, etc. (with a similar hierarchy for extensions), and that 
> sentences of the form: " a has the property φ ", " b bears the relation 
> R to c ", etc. are meaningless, if a, b, c, R, φ are not of types 
> fitting together.
> https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944

Which doesn't eliminate the ability (or the need) for metalanguages.



> 
> When True(X) only returns TRUE for contiguous sequences
> of truth preserving operations on the basis of basic
> facts expressed in formalized natural language then
> True(X) consistently works correctly for the entire
> set of general human knowledge that can be expressed
> using language.
> 

Nope, becuase it can't handle ALL statements, at least not if the 
language can handle the properties of the Natural Numbers.

Simple prove that you NEED the ability to have metalanguages, let us 
assume we don't need to have a metalanguage, but will have a system with 
two basic axioms, plus axioms to assign a number to each axiom to allow 
us to mathematize our language. So, our list of axioms are:

A
B
A is axiom 1
B is axion 2
"A is axiom 1" is axiom 3
"B is axiom 2" is axiom 4

and this will continue FOREVER and you will not have a finite system.

We need the metalanguage, so we can number the axioms in the language, 
and not need to number the numbering.

Note, this shows that *ANY* finite logic system could have a metasystem 
that numbers it, as it will have a finite number of axioms, so the 
metasystem will just have twice that number (the axioms of the system, 
plus the axioms of numbering those) and we have shown that such a 
numbering can not be done within the original system itself.