Two random independent variables ($P$: "two variables are independent") are uncorrelated ($Q$: "two variables - the same two involved in sentence $P$ - are uncorrelated"), or using the words of logic $P \rightarrow Q$.
Now, we can reverse the logical implication, negating both sentences as $\overline{Q} \rightarrow \overline{P}$, that can be written as "if two random variables are not uncorrelated (i.e. their correlation is not identically equal to zero), they are not independent".
The last sentence seems to contradict the more famous sentence "correlation is not causation".
What am I missing, or where is the mistake in this apparent contradiction? Is the exact correlation ($\rho_{PQ} = 1$) involved in the sentence "correlation is not causation"?
