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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception
Date: Mon, 3 Feb 2025 19:39:38 -0500
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On 2/2/25 10:30 PM, olcott wrote:
> 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.
> 
> There is no Truth[0] anchoring in meaning that is not Provable[0].
> Any expression lacking a connection to its truthmaker remains
> impossibly true.

Of course there is, as Truth allows for an infinite chain, while 
Provable requires a finite chain.

All you are doing is proving you don't understand the differnence 
between the finite and the infinite.

> 
>> that the same word is not used for any other meaning. Dictionaries that
>> are not deictionaries of the particular art are not relevant.
>>
>> Consequently, there is no reason to revise my initial comment.
>>
> 
>