Comment by zmgsabst

You’d know the value in a more powerful system than ZFC (as it includes such an oracle) — but you can already reason about ZFC in a more powerful system.

We already have more powerful systems, but what causes the inability to self-reason is exactly that power: only first order logic can prove its own consistency. Once you get powerful enough to model arithmetic, you can build statements with self-referential weirdness.

I don’t see it as a paradox, but as growth: a sufficiently rich system can pose questions which suggest a richer system — and thereby scaffold up the universe hierarchy.