I think the point is this is paradoxical. Everything must be proven by facts and we cannot trust any general, abstract statement of its own accord, then how can we prove “everything must be proven by facts and we cannot trust any general, abstract statement of its own accord”? What if that’s a wrong assumption?

Maybe the truth is we don’t always need to rely on observable facts, but we don’t know that because we’re making the aforementioned assumption without having any proof that it’s correct.