I suggest folk re-read

It's a statement about provability for statements in a certain class of consistent systems (those than can encompass arithmetic) — Count Timothy von Icarus

Stop right there. It's about limitations in mathematics.

To talk about "certain classes of consistent system" can mislead someone to thinking Gödel is talking about something obscure. Yet it is the limited obscure fields in Mathematics which don't encompass arithmetic, which are the fields that need long descriptions to formalize them. And just what you can do with them (as they are likely to be extremely simplistic) more than give a theoretical description about them is usually even more difficult.

I proved above that when
"a proposition which asserts its own unprovability. (Gödel 1931:43-44)"

G := ¬(F ⊢ G) — PL Olcott

That this proposition is self-contradictory:
Proving G in F requires a sequence of inferences steps in F that proves there is no such sequence of inference steps in F.

thus the assessment that its formal system is incomplete is incorrect.

If the mathematical notion of incomplete is incorrect for one input then it
cannot be trusted for other inputs.

Copyright 2023 PL Olcott

Stop right there. It's about limitations in mathematics.

To talk about "certain classes of consistent system" can mislead someone to thinking Gödel is talking about something obscure. Yet it is the limited obscure fields in Mathematics which don't encompass arithmetic, which are the fields that need long descriptions to formalize them. And just what you can do with them (as they are likely to be extremely simplistic) more than give a theoretical description about them is usually even more difficult

I don't think anything I said gives the impression that the above is not the case. I was just thinking in terms of the ways that philosophers have attempted to generalize Godel (and Tarski's) findings beyond the scope of mathematics. Plus, more importantly, given the context of this thread's topic, that this doesn't hold the same way for paraconsistent systems (granted such systems won't be able to handle arithmetic and be consistent.)

See: my last post, TonesInDeepFreeze's post, etc.

I don't think anything I said gives the impression that the above is not the case. I was just thinking in terms of the ways that philosophers have attempted to generalize Godel (and Tarski's) findings beyond the scope of mathematics. — Count Timothy von Icarus

Fair enough. But usually there isn't much discussion of just what is the impact of this (or similar) findings.

I have never been able to grasp what it means to say "This statement is true"/ What statement?

How can 'This statement' be true or false?

Very naive thoughts I know, but I seem to have a mental block on this topic.

Many philosophers agree with you. Some say a statement like that isn't actually meaningful, it doesn't have any meaningful content, it doesn't refer to anything.

It's certainly a valid take on the subject, don't consider your intuition here naive. You're very possibly right to find it incomprehensible.

Thanks for the reassurance. .