The first sentence of your first paragraph appears to appeal to experiment, while the first sentence of your second paragraph seems to boil down to “Classically, X causes Y if there is a significant statistical connection twixt X and Y.”
No. “Dependence” in that second sentence does not mean causation. It just means statistical dependence. The definition of dependence is important because an intervention must be statistically independent from things “before” the intervention.
None of these appear to involve intervention.
These are methods of causal inference. I’m talking about what causality is. As in, what is the difference between a mere correlation, and causation? The difference is that the second is robust to intervention: if X causes Y, then if I decide to do X, even in circumstances different from those where I’ve observed it before, Y will happen. If X only correlates with Y, it might not.
No. “Dependence” in that second sentence does not mean causation. It just means statistical dependence. The definition of dependence is important because an intervention must be statistically independent from things “before” the intervention.
These are methods of causal inference. I’m talking about what causality is. As in, what is the difference between a mere correlation, and causation? The difference is that the second is robust to intervention: if X causes Y, then if I decide to do X, even in circumstances different from those where I’ve observed it before, Y will happen. If X only correlates with Y, it might not.