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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: The philosophy of logic reformulates existing ideas on a new
 basis ---
Date: Fri, 8 Nov 2024 13:02:47 -0500
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On 11/8/24 12:25 PM, olcott wrote:

> 
> That formal systems that only apply truth preserving
> operations to expressions of their formal language
> that have been stipulated to be true cannot possibly
> be undecidable is proven to be over-your-head on the
> basis that you have no actual reasoning as a rebuttal.
> 

No, all you have done is shown that you don't undertstand what you are 
talking about.

Godel PROVED that the FORMAL SYSTEM that his proof started in, is unable 
to PROVE that the statement G, being "that no Natural Number g, that 
satifies a particularly designed Primitive Recursive Relationship" is 
true, but also shows (using the Meta-Mathematics that derived the PRR 
for the original Formal System) that no such number can exist.

He does it by showing that that particular PRR can be derived, using the 
mathematics available in the original formal system, that when 
interpreted by the semantics added in the Meta-Mathematics, can be 
interpreted as a "Proof Checker" for a proof encoded by the rules of the 
meta-math, for the statement of G.

Thus, if a number exists that satisfies that PRR, it also produces a 
valid proof that no such number can exist, and thus since that would be 
a contradiction, and the stated assumption was that the original formal 
system was non-contradictory, so no such number can exist.

It also shows that no proof can be formed in the original Formal System, 
as any such proof could be encoded into a number, that would satisfy the 
PRR, and thus show the proof could not be valid, as the statement was false.

Your failure to understand this just shows your ignorance of the 
subject. Admittedly, this is somewhat complicated, so ignorance of it 
isn't that bad, but when you claim that the logic is wrong, and do so 
asserting things that are just not true, just shows that you are REALLY 
ignorant of what you talk about, and nothing but a pathological liar.

Sorry, YOU are the one over-your-head, but are too stupid to understand 
it, and seem to have drowned and killed off your mental ability.