[yobbo]

If you want to talk about bayes, you could think about causation as a prior for correlation. We can measure correlation (variates), and then we can infer something about the causation (independent variables).

"Inference to the best explanation" could mean we accept any explanation regardless of how improbable it is - as long as it best explains the data.

The bayesian idea is that we can learn something about causation if we accept uncertainty and impose "sanity constraints" (priors) on the explanation.

Without knowing the real-world mechanics of Y, we can say something like "setting X to 0.33 will increase Y, with 60% probability." It maybe impossible to learn anything else from the data.