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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception
Date: Tue, 4 Feb 2025 11:22:40 +0200
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On 2025-02-03 16:54:08 +0000, olcott said:

> On 2/3/2025 9:07 AM, Mikko wrote:
>> On 2025-02-03 03:30:46 +0000, olcott said:
>> 
>>> On 2/2/2025 3:27 AM, Mikko wrote:
>>>> On 2025-02-01 14:09:54 +0000, olcott said:
>>>> 
>>>>> On 2/1/2025 3:19 AM, Mikko wrote:
>>>>>> On 2025-01-31 13:57:02 +0000, olcott said:
>>>>>> 
>>>>>>> On 1/31/2025 3:24 AM, Mikko wrote:
>>>>>>>> On 2025-01-30 23:10:18 +0000, olcott said:
>>>>>>>> 
>>>>>>>>> Within the entire body of analytical truth any expression of language 
>>>>>>>>> that has no sequence of formalized semantic deductive inference steps 
>>>>>>>>> from the formalized semantic foundational truths of this system are 
>>>>>>>>> simply untrue in this system. (Isomorphic to provable from axioms).
>>>>>>>> 
>>>>>>>> If there is a misconception then you have misconceived something. It is well
>>>>>>>> known that it is possible to construct a formal theory where some formulas
>>>>>>>> are neither provble nor disprovable.
>>>>>>> 
>>>>>>> This is well known.
>>>>>> 
>>>>>> And well undeerstood. The claim on the subject line is false.
>>>>> 
>>>>> a fact or piece of information that shows that something
>>>>> exists or is true:
>>>>> https://dictionary.cambridge.org/us/dictionary/english/proof
>>>> 
>>>> We require that terms of art are used with their term-of-art meaning and
>>> 
>>> The fundamental base meaning of Truth[0] itself remains the same
>>> no matter what idiomatic meanings say.
>> 
>> Irrelevant as the subject line does not mention truth.
>> Therefore, no need to revise my initial comment.
> 
> The notion of truth is entailed by the subject line:
> misconception means ~True.

The title line means that something is misunderstood but that something
is not the meaning of "true". But the subject line is false. Mathematical
incompleteness is sometimes misunderstood but not always. Its definition
is clear but some people make invalid inferences.

-- 
Mikko