"The question of causation lies outside of statistics." -- Michael Starbird
Contra Hume, our idea of causation stems directly from our experience of acting in the world. Look at the monkey above: he is not puzzling over causation. He knows that if he smashes the nut with the rock, he will cause it to yield its delectable innards.
The problems of causation dealt with in statistics are problems of detecting causation when the link between cause and effect is obscure. And then statistics can only provide evidence of causation, and never demonstrate it. There has been a strong correlation between which conference wins the Super Bowl and how stocks do that year. But nobody whatsoever believed for a minute that Super Bowl results were causing stock price movements, despite an 80% success rate in prediction.
We only feel confident we really have identified "the cause" of something when we can grasp the causal mechanism involved. And causal mechanisms are something we can directly perceive. (Again, see the monkey above.)