There is an interesting, if quite technical, answer here about Goodstein's Theorem which is a very reasonable number theory theorem which cannot be proven in first order logic.
So questions around statements which are true but not provable in certain logical systems do have concrete examples and are interesting imo.
So questions around statements which are true but not provable in certain logical systems do have concrete examples and are interesting imo.
https://math.stackexchange.com/questions/625223/do-we-know-i...