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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Every sufficiently competent C programmer knows --- Very Stupid
 Mistake and Liars
Date: Wed, 12 Mar 2025 23:55:59 -0400
Organization: i2pn2 (i2pn.org)
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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,