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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Every sufficiently competent C programmer knows --- Very Stupid
 Mistake and Liars
Date: Wed, 12 Mar 2025 23:17:29 -0500
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On 3/12/2025 10:55 PM, Richard Damon wrote:
> On 3/12/25 8:28 PM, olcott wrote:
>> On 3/12/2025 5:46 PM, Richard Damon wrote:
>>> On 3/12/25 10:50 AM, olcott wrote:
>>>> On 3/12/2025 8:03 AM, André G. Isaak wrote:
>>>>> On 2025-03-11 20:29, Richard Heathfield wrote:
>>>>>
>>>>>> Look up "infinite". You keep using that word. I do not think it 
>>>>>> means what you think it means.
>>>>>
>>>>> If you continue to engage with Olcott, you will discover that a 
>>>>> great many words don't mean what he thinks they mean.
>>>>>
>>>>> André
>>>>>
>>>>
>>>> Incomplete[0] (base meaning)
>>>> Not having all the necessary or appropriate parts.
>>>>
>>>> Provable[0] (base meaning)
>>>> Can be shown to be definitely true by some means.
>>>>
>>>>
>>>>
>>>
>>> Right, and the appropriate part for logic that it is missing is the 
>>> proofs of some of the statements.
>>>
>>> Proofs, to SHOW something, must be finite, as we can not see 
>>> something that is infinite, as we are finite.
>>>
>>
>> So then we know that G <is> TRUE because meta-math proves this.
>> If we are stupid enough to define a system that does not know
>> this then we are stupid.
>>
>>
> 
> Yes, we know that G is true, as from the additional information provide 
> in the meta-system we can reduce the infinite sequence that can be built 
> in the base system to a finite proof.
> 
> Note, PROOF belong to a system, and if they try to use something not 
> known to be true in the system, they fail to be a proof, as they don't 
> SHOW the needed result.
> 
> Note, the "System" can't contain all of the Meta-System, as one 
> important added part of the meta-system, as a set of axioms, was an 
> enumeration of all axioms in the base system. If we try to put that 
> enumeration into the base system, it becomes self-referential and we 
> have an infinite set of axioms, something not allowed in normal formal 
> logic.
> 
> It is possible to do in a meta-system, as the system has a finite 
> axiomization, so we just need to develope a numbering of that list of 
> axioms.
> 
> This seems to be part of your problem of not understanding why meta- 
> systems can exist and not be part of the original system, but does 
> describe it,
> 
> 

The only reason why the meta-system and the system
cannot be the same system is that semantically incorrect
expressions are not rejected as not truth bearers in
the system.

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