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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 22:18:36 -0400
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On 3/15/2025 9:47 PM, olcott wrote:
> On 3/15/2025 8:27 PM, dbush wrote:
>> 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. 
> 
> True(LP) == FALSE 

And ~True(LP) == TRUE
Therefore LP == TRUE

Contradiction.

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