Re: The philosophy of logic reformulates existing ideas on a new basis ---

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.