What is the intuition behind implication in logic?

however, I suspect that won't give you the intuition that you expected (though the table on the left will be helpful later). read more

The main point in my answer will be that there is, in fact, no intuition behind material implication. In fact, it was firstly introduced in systems like Boolean algebra where [math]A\supset B[/math] was a shortened version of [math]eg A\vee B[/math]. read more

In the field of logic,"or" has one and only one meaning, and that is that the option of both at the same time is considered valid. However, some times you need to express the idea of"either-or", where choosing one option excludes the other. Where the case of going with both is excluded. That is what exclusive or is for. read more

In logic, what we care about is preserving the truth value of statements that are true, such that we never have a valid argument that goes from true to false. But we care a lot less (at least in classical logic) about going from false to true. read more