Re: Every sufficiently competent C programmer knows --- Very Stupid Mistake and Liars

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:
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Look up "infinite". You keep using that word. I do not think it means what you think it means.

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If you continue to engage with Olcott, you will discover that a great many words don't mean what he thinks they mean.
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André
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Incomplete[0] (base meaning)
Not having all the necessary or appropriate parts.
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Provable[0] (base meaning)
Can be shown to be definitely true by some means.
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Right, and the appropriate part for logic that it is missing is the proofs of some of the statements.
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Proofs, to SHOW something, must be finite, as we can not see something that is infinite, as we are finite.
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 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,