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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception ---
 Tarski
Date: Fri, 21 Feb 2025 17:22:23 -0600
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On 2/20/2025 3:01 AM, Mikko wrote:
> On 2025-02-18 13:50:22 +0000, olcott said:
> 
>> On 2/18/2025 6:25 AM, Richard Damon wrote:
>>> On 2/17/25 10:59 PM, olcott wrote:
>>>> 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.
>>>
>>> But your logic needs to reject some of the results of your logic as 
>>> semantically incorrect, and thus your logic is itself semantically 
>>> incorrect.
>>>
>>
>> There is nothing like that in the following concrete example:
>> LP := ~True(LP)
>>
>> In other words you are saying the Prolog is incorrect
>> to reject the Liar Paradox.
>>
>> Above translated to Prolog
>>
>> ?- LP = not(true(LP)).
>> LP = not(true(LP)).
> 
> According to Prolog rules LP = not(true(LP)) is permitted to fail.
> If it succeeds the operations using LP may misbehave. A memory
> leak is also possible.
> 
>> ?- unify_with_occurs_check(LP, not(true(LP))).
>> false
> 
> This merely means that the result of unification would be that LP conains
> itself. It could be a selmantically valid result but is not in the scope
> of Prolog language.
> 

It does not mean that. You are wrong.
I  am not going bother to quote Clocksin and Mellish
proving that you are wrong.

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer