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From: dbush <dbush.mobile@gmail.com>
Newsgroups: sci.logic
Subject: Re: The key undecidable instance that I know about --- Truth-bearers
 ONLY
Date: Sat, 15 Mar 2025 21:27:06 -0400
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On 3/15/2025 9:03 PM, olcott wrote:
> On 3/15/2025 2:25 PM, dbush wrote:
>> On 3/15/2025 3:16 PM, olcott wrote:
>>> On 3/15/2025 2:05 PM, dbush wrote:
>>>> On 3/15/2025 2:55 PM, olcott wrote:
>>>>> On 3/15/2025 12:39 PM, dbush wrote:
>>>>>> On 3/15/2025 1:08 PM, olcott wrote:
>>>>>>> On 3/10/2025 9:49 PM, dbush wrote:
>>>>>>>> On 3/10/2025 10:39 PM, olcott wrote:
>>>>>>>>> On 3/10/2025 9:21 PM, Richard Damon wrote:
>>>>>>>>>> On 3/10/25 9:45 PM, olcott wrote:
>>>>>>>>>>> On 3/10/2025 5:45 PM, Richard Damon wrote:
>>>>>>>>>>>> On 3/9/25 11:39 PM, olcott wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>> LP := ~True(LP)  DOES SPECIFY INFINITE RECURSION.
>>>>>>>>>>>>
>>>>>>>>>>>> WHich is irrelevent, as that isn't the statement in view, 
>>>>>>>>>>>> only what could be shown to be a meaning of the actual 
>>>>>>>>>>>> statement.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> The Liar Paradox PROPERLY FORMALIZED <is> Infinitely recursive
>>>>>>>>>>> thus semantically incorrect.
>>>>>>>>>>
>>>>>>>>>> But is irrelevent to your arguement.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> "It would then be possible to reconstruct the antinomy of the 
>>>>>>>>>>> liar
>>>>>>>>>>>   in the metalanguage, by forming in the language itself a 
>>>>>>>>>>> sentence"
>>>>>>>>>>
>>>>>>>>>> Right, the "Liar" is in the METALANGUAGE, not the LANGUAGE 
>>>>>>>>>> where the predicate is defined.
>>>>>>>>>>
>>>>>>>>>> You are just showing you don't understand the concept of 
>>>>>>>>>> Metalanguage.
>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Thus anchoring his whole proof in the Liar Paradox even if
>>>>>>>>>>> you do not understand the term "metalanguage" well enough
>>>>>>>>>>> to know this.
>>>>>>>>>>
>>>>>>>>>> Yes, there is a connection to the liar's paradox, and that is 
>>>>>>>>>> that he shows that the presumed existance of a Truth Predicate 
>>>>>>>>>> forces the logic system to have to resolve the liar's paradox.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> bool True(X)
>>>>>>>>> {
>>>>>>>>>    if (~unify_with_occurs_check(X))
>>>>>>>>>      return false;
>>>>>>>>>    else if (~Truth_Bearer(X))
>>>>>>>>>     return false;
>>>>>>>>>    else
>>>>>>>>>     return IsTrue(X);
>>>>>>>>> }
>>>>>>>>>
>>>>>>>>> LP := ~True(LP)
>>>>>>>>> True(LP) resolves to false.
>>>>>>>>
>>>>>>>> ~True(LP) resolves to true
>>>>>>>> LP := ~True(LP) resolves to true
>>>>>>>>
>>>>>>>> Therefore the assumption that a correct True() predicate exists 
>>>>>>>> is proven false.
>>>>>>>
>>>>>>> When you stupidly ignore Prolog and MTT that
>>>>>>> both prove there is a cycle in the directed graph
>>>>>>> of their evaluation sequence. If you have no idea
>>>>>>> what "cycle", "directed graph" and "evaluation sequence"
>>>>>>> means then this mistake is easy to make.
>>>>>>>
>>>>>>
>>>>>> That doesn't change the fact that 
>>>>>
>>>>> You have just proven you are clueless about these things
>>>>> by your next statement.
>>>>>
>>>>>> that ~True(LP) evaluates to true.
>>>>>>
>>>>>
>>>>> When
>>>>> LP  := ~True(LP)  True_Bearer(LP) == FALSE
>>>>
>>>> And by the above function, because True_Bearer(LP) == FALSE:
>>>>
>>>
>>> Which means that LP cannot possibly be either TRUE or FALSE
>>> and instead must be rejected as invalid input to a True(X)
>>> predicate.
>>
>> False.  The True() predicate must return "true" for true statements 
>> and false for *all other statements*.
>>
>> The fact that the True() you've defined *does* accept non-truth 
>> bearers and returns false for them shows you know this, but are being 
>> deliberately deceptive.
>>
>>>
>>>> True(LP) == FALSE, then
>>>> ~True(LP) == TRUE, so
>>>> LP == TRUE
>>>>
>>>> Contradiction.  Therefore the assumption that a correct True() 
>>>> predicate exists is proven false
>>>>
>>>
>>> Likewise Truth_Bearer("ksdnf34589jknsdf34r87&%78^%78") == FALSE
>>> <sarcasm>
>>> and on that basis we know that True(X) predicates cannot
>>> exist because True(X) predicates must correctly determine
>>> whether random gibberish is true or false.
>>> </sarcasm>
>>>
>>
>> True(X) predicates must correctly determine
>> whether random gibberish is true or *not true*.  And because random 
>> gibberish is not true, True("ksdnf34589jknsdf34r87&%78^%78") must 
>> return false
>>
> 
> That is fine, and makes Tarski wrong.
> 

Nope.  Tarski uses a proof by contradiction.  You know, that type of 
proof you still don't understand 50 years after learning it.

He starts by assuming that a True() predicate exists in a system that 
can express the full properties of natural numbers.

He then shows that it's possible to create in the system that can be 
shown in a meta system to effectively mean:

LP  := ~True(LP)

Given that True(LP) == false, we then have ~True(LP) == true.  And since 
~True(LP) is the same as LP, that gives us LP == true.

Contradiction.  Therefore the assumption that a True() predicate exists 
is proven false.