Just to be clear, although we sometimes read \(P \imp Q\) as “\(P\) implies \(Q\)”, we are not insisting that there is some causal relationship between the statements \(P\) and \(Q\text{.}\) In particular, if you claim that \(P \imp Q\) is false, you are not saying that \(P\) does not imply \(Q\text{,}\) but rather that \(P\) is true and \(Q\) is false.
in-context