How intuitive a statement is is not generally taken as evidence to the truth of a statement. After all, it's a psychological state, and it makes no sense for a psychological state to influence the truth of something out there in the world such as whether the earth is flat or not.
But from an experiential point of view, how does one know if a belief is justified or if it "makes sense". Isn't a statement "making sense" usually correlated with a feeling, and thus a psychological state? The statements "2+2=4", "Most men have penises", etc etc, have a conscious signature attached to them, a psychological state where the statement "just feels right".
Without this psychological state occurring, how can one verify any belief?