But how does that show that we do not infer causation from correlation? The inference, of course, need not always be a valid inference. We require more than mere correlation for a valid inference to causation, since although correlation is a necessary condition of causation, it is not a sufficient condition. We require controlled studies to determine that the correlation is not just accidental correlation, and, finally, some causal nexus between the cause and the effect that explains the correlation. But, correlation is a sign of causations, and a necessary condition of causation. No one claimed that correlation and causation should be identified. Even if the two clocks strike the hour simultaneously, there need be no causation, and in fact, there is none, since the striking of the two clocks is not causally connected, but they both strike the same hour because of a common cause. The same is true of night and day. Night does not cause day, nor day, night. But they are both the effects of a common cause.

Yes, I entirely agree. I was just qualifying prothero's post #418. Sometimes we infer causation, sometimes we don't.