I've always been told "correlation does not imply causation." However, I've never been told much about whether it can imply a probability of causation. Moreover, there seem to be competing and often misused definitions of "to cause", i.e., use in a syllogistic sense versus use in probabilistic sense. Please consider the following: Imagine we conduct a strictly controlled experiment only once, and it has one of two outcomes: (Outcome 1) Y is strongly correlated to X. (Outcome 2) Y is not correlated to X at all. Suppose the single experiment has outcome (1), and we call the probability that X causes Y, P1. Now let's go back in time, suppose it instead has outcome (2), and call the probability that X causes Y, P2. Is P1 > P2? Why? I realize this raises lots of questions: what do I mean by "cause"? What do we know about the experiment? What do we mean by strictly controlled? For the sake of my curiosity, I invite you to provide your own assumptions in answer to these questions. I apologize for the vagaries, but it's the vagaries of this question that have me scratching my head! Please, feel free to point out what must be clarified, and some possible clarifications in response (point out the blanks and fill them in). Thanks so much!