I just started doing logic and everything is going fine. But we just got to Material Implication and I don't really understand it. From for example $q$, we can get $q \lor \lnot p$ by Disjunction, and from there, using Material Implication, we can get $p \to q$.
The thing I don't understand is how is this valid. Let's say
- $p$ is "it's raining", and
- $q$ is "the floor is wet",
and $p \to q$ holds. But just because the floor is wet, doesn't mean that it's raining. So how can we conclude that $p \to q$ just from $q$? I'm sorry if it's confusing.