Understanding of Material Implication 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.   

If you know $Q$ holds, then $P\to Q$ says nothing about $P$.
A perhaps better way of thinking about it is the following. Let's say that given $R$ you could prove $Q$. Then clearly if I give you both $R$ and $P$, you could still prove $Q$ by simply ignoring $P$. Since you're not actually "using" $P$, it doesn't matter whether it is true or not.
