All models of reality rely on a core unprovable premise, which if proven false, would cause the entire model to be revamped. (In biology for example, the “dogma of biology” is that DNA transcribes to RNA transcribes to protein; if that were proven false, then all subsequent theories would need reworking).
So in light of unprovable premises, the importance of structure and logic becomes clear: Logic and structure are for navigation and guidance, not for proselytization.