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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception ---
 Tarski
Date: Sat, 22 Feb 2025 07:20:46 -0500
Organization: i2pn2 (i2pn.org)
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On 2/21/25 11:44 PM, olcott wrote:
> On 2/21/2025 7:05 PM, Richard Damon wrote:
>> On 2/21/25 6:19 PM, olcott wrote:
>>> On 2/20/2025 2:54 AM, Mikko wrote:
>>>> On 2025-02-18 03:59:08 +0000, olcott said:
>>>>
>>>>> On 2/12/2025 4:21 AM, Mikko wrote:
>>>>>> On 2025-02-11 14:07:11 +0000, olcott said:
>>>>>>
>>>>>>> On 2/11/2025 3:50 AM, Mikko wrote:
>>>>>>>> On 2025-02-10 11:48:16 +0000, olcott said:
>>>>>>>>
>>>>>>>>> On 2/10/2025 2:55 AM, Mikko wrote:
>>>>>>>>>> On 2025-02-09 13:10:37 +0000, Richard Damon said:
>>>>>>>>>>
>>>>>>>>>>> On 2/9/25 5:33 AM, Mikko wrote:
>>>>>>>>>>>> Of course, completness can be achieved if language is 
>>>>>>>>>>>> sufficiently
>>>>>>>>>>>> restricted so that sufficiently many arithemtic truths 
>>>>>>>>>>>> become inexpressible.
>>>>>>>>>>>>
>>>>>>>>>>>> It is far from clear that a theory of that kind can express 
>>>>>>>>>>>> all arithmetic
>>>>>>>>>>>> truths that Peano arithmetic can and avoid its incompletness.
>>>>>>>>>>>
>>>>>>>>>>> WHich, it seems, are the only type of logic system that Peter 
>>>>>>>>>>> can understand.
>>>>>>>>>>>
>>>>>>>>>>> He can only think in primitive logic systems that can't reach 
>>>>>>>>>>> the complexity needed for the proofs he talks about, but 
>>>>>>>>>>> can't see the problem, as he just doesn't understand the 
>>>>>>>>>>> needed concepts.
>>>>>>>>>>
>>>>>>>>>> That would be OK if he wouldn't try to solve problems that 
>>>>>>>>>> cannot even
>>>>>>>>>> exist in those systems.
>>>>>>>>>
>>>>>>>>> There are no problems than cannot be solved in a system
>>>>>>>>> that can also reject semantically incorrect expressions.
>>>>>>>>
>>>>>>>> The topic of the discussion is completeness. Is there a complete 
>>>>>>>> system
>>>>>>>> that can solve all solvable problems?
>>>>>>>
>>>>>>> When the essence of the change is to simply reject expressions
>>>>>>> that specify semantic nonsense there is no reduction in the
>>>>>>> expressive power of such a system.
>>>>>>
>>>>>> The essence of the change is not sufficient to determine that.
>>>>>
>>>>> In the same way that 3 > 2 is stipulated the essence of the
>>>>> change is that semantically incorrect expressions are rejected.
>>>>> Disagreeing with this is the same as disagreeing that 3 > 2.
>>>>
>>>> That 3 > 2 need not be (and therefore usually isn't) stripualted.
>>>
>>> The defintion of the set of natural numbers stipulates this.
>>>
>>>> It follows from the traditional meanings of "3", "2", and ">".
>>>> Therefore the above statement is meaningless.
>>>>
>>>>>> The
>>>>>> result depends on all of the change. But as long as we don't even
>>>>>> know whether that kind of change is possible at all the details are
>>>>>> impossible to determine.
>>>>>
>>>>> LP := ~True(LP) has never been more than nonsense.
>>>>
>>>> More specifically, your nonnsense. The symbol ":=" usually means 
>>>> definition
>>>> but requires that the symbol on the left side (in this case "LP") is 
>>>> not
>>>> used on the right side (and also that it is not used in the 
>>>> definition of
>>>> any of the symbols on the right side).
>>>>
>>>> Usually languages of formal logic are constructed so that symbol 
>>>> that is
>>>> defined with an expression that starts with a negation operator cannot
>>>> be used as an argument to a function or a predicate.
>>>>
>>>>> Tarski (although otherwise quite brilliant) had a blind spot.
>>>>
>>>> Tarski did not use your nonsense.
>>>>
>>>
>>> Tarski anchored his whole proof in the Liar Paradox.
>>>
>>
>> By showing that given the necessary prerequisites, The equivalent of 
>> the Liar Paradox was a statement that the Truth Predicate had to be 
>> able to handle, which it can't.
>>
> 
> It can be easily handled as ~True(LP) & ~True(~LP), Tarski just
> didn't think it through. The limitations of logic systems is that
> they try to unsuccessfully simply assume that every expression
> of language <is> a truth bearer. These systems cannot think outside
> of that box.
> 

Nope.

It is YOU that can't handle logic,

What VALUE does True(LP) have?

Your problem is you can't face the facts, so you go to your diversions, 
because all you are is a liar.

Remember, if True calls "LP" nonsense, it is calling itself nonsense, as 
LP is defined in relationship to True, and the relationship is shown to 
be a valid one by the earlier proof of Tarski, which you just ignore and 
call nonsense, which means you are just calling logic itself nonsense, 
because to you, it is, because EVERYTHING to you is nonsense as your 
brain is stuck in a broken logic system.