"A ⇒ B is true only in the case that either A is false or B is true, or both."
Material implication, in classical logic, is simply a binary operator, like AND or OR. It implies nothing about the relationship between A and B beyond their truth values.
I think you're trying to read more into it than is there.
![[Image: extraordinarywoo-sig.jpg?rlkey=x1nmxbwrp...pouidnfvtl]](https://dl.dropboxusercontent.com/scl/fi/a6a72vica8gsyddmkhtxp/extraordinarywoo-sig.jpg?rlkey=x1nmxbwrpk9dzrupouidnfvtl)


