I still think what I said was correct.
> On the other hand, undecidable has a sharper meaning in computation contexts as well as constructive logics without excluded middle. In these cases we can comprehend the “reachability” of propositions. A proposition is not true or false, but may instead be “constructively true”, “constructively false”, or “undecidable”.
Yes, but that just means that independence/undecidability depend on the proof system, as I said before. So when using a constructive proof system, more statements will turn out to be undecidable/independent of a theory than with a classical one, since the constructive proof system doesn't allow non-constructive proofs, but the classical one does.
Yeah, I agree. "Independence" is fundamentally a property of the formal system you're working within (or really, it's a property of the system you're using and of the axiomatic system under test, the system a proposition would be independent from). I'm holding out a bit to unify that with "undecidability" because undecidability takes on a particular character in constructive systems that happens to align with Turing's notion.
So at some level, this was just an acknowledgement that "undecidability" in this form is well represented in formal logic. In that sense, at least in constructive logics, it's not just a synonym for "independence".