Comment by zozbot234

You could argue that the early constructivists' notions of "paradoxes" included things such as "statements about the existence of things that we don't know how to explicitly construct, and that may be even impossible to explicitly construct in the general case". Under Gödel's argument, these statements (like other classical statements) become mere negative statements asserting the non-existence of anything that might contradict the aforementioned non-constructive objects. So, they're no longer "paradoxical" in that sense. Stated another way, decidability/computability (perhaps relative to some appropriate oracle, to fully account for the surprising strength of some loosely-"constructive" principles) is not quite the same concern as consistency. Of course, this was all stated in very fuzzy and imprecise terms to begin with (no real notion back then of what "decidable" and "computable" might mean), so there's that.