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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception --- Tarski
Date: Wed, 12 Feb 2025 12:21:18 +0200
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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. 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.

-- 
Mikko