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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception
Date: Fri, 31 Jan 2025 09:53:33 -0500
Organization: i2pn2 (i2pn.org)
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On 1/31/25 8:57 AM, olcott wrote:
> 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. What is not so widely known is that this
> is only possible because process defining what is referred to
> as a math proof intentionally leaves out key required elements
> that would otherwise make it complete.

What is a "proof" is a well defined definition, and based on what is 
required to make something knowable in the system.

> 
> Any expression of language that lacks a sequence of semantic
> deductive inference steps from the basic facts stipulated truths
> of this system to this expression is simply untrue in this system.

And if that sequence is infinite, the fact is true, but might not be 
provable, (or knowable through that system).

> 
> Using another more expressive system to show that the expression
> is true in this other system does not make the expression true in
> the original system.

Nor does it say that the infinte sequence shown in the original wasn't 
correct, and make the statement untrue.

> 
> 
>> Often that is done intentionally in
>> order to make the theory applicable to situations where some such 
>> sentence
>> is true as well as to situations where the same sentence is false.
>>
> 
> Thus incompleteness is intentional incoherence that can always be 
> prevented.
> 

Nope, your ideas are inherently, and perhaps intentionally, incoherent 
showing your stupidity and ignorance. Your failure to understand the 
nature of truth will be your demise.