Though not implication, there is some reasoning to some other vacuously true statements. Take for example: All purple cows are smart. This statement is true,

Though not implication, there is some reasoning to some other vacuously true statements. Take for example: All purple cows are smart. This statement is true, because the set of purple cows is empty. It might seem, odd, but it's because we can rephrase it as: There does not exist a purple cow that is not smart. When you phrase it like that, I think most people would intuitively agree that it should evaluate to true. In other words, to preserve symmetry between the universal and existential qualifiers, you need the first statement to also be true. Without the ability to transform "exists" into "foralls" would make first order predicate logic pretty much useless. In addition, if the emptiness of a set actually changed how the quantifiers worked, it would be a big problem: breaking referential transparency, if you will. I don't recall there being a similar justification for implication in boolean logic, but I think the reasoning is similar. Hope that helps!