The term "formal logic" seems to be being used in several senses. I understand it refer to the branch of mathematics, but you seem to be using it to mean "rigorous reasoning". Most people would not understand a statement written in formal logic, according to the former definition, let alone find it convincing. And even with the latter meaning, there is much of formal logic that ordinary people find unconvincing, such as "The statement 'all crows are black' is logically equivalent to 'all non-black things are non-crows'; therefore, if I find something that isn't black, and it isn't a crow, that is support for the claim that all crows are black".