Understanding of Material Implication

Solution 1:

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.

Solution 2:

In your example, if the floor is wet, you are right that we cannot conclude it is raining. Neither can we conclude that rain will eventually cause the floor to be wet. Given that the floor is wet, we can conclude, however, that the implication "if it is raining then the floor is wet" is true.

Yes, it's a bit counter-intuitive, but, in general, if $P$ and $Q$ are logical propositions that are unambiguously either true or false in the moment, then we can easily prove that $Q\implies [P \implies Q]$.

In words, that which is true follows from anything, be it true or false. Similarly, anything follows from a falsehood.

See my answer at: Arguments pro material implication