Explanations, correlations, interventions, causal factors

Science explains. Modern fundamental science is embodied in a small number of fundamental laws. The behavior of specific systems is logically inferred from basic laws. This is scientific explanation. For instance, we can logically infer the trajectory of a projectile from basic laws of dynamics and gravitation plus initial conditions. Explanation is observational: basic laws are empirical hypotheses.

Two variables X and Y are said to be correlated if they move together. Correlation is an observational phenomenon: we passively observe the behavior of X and Y in their universe; we do not intervene. For example, X and Y can represent returns of two stocks.

Causation is a different concept. The variable X causes the variable Y if after an arbitrary change of X we find that Y has also changed. Causation is not simply observational. For example, changing interest rates has a causal effect on the economy. The causal link between X and Y is explained postulating an independent mechanism that makes Y change value if X changes value.

However, modern causal systems want to infer causation from correlation without making experiments. How do they do it? They assume that variables have causal links. If variables have causal links, then correlations have special properties, in particular conditional independence. For instance, we can assume factors are causal and test for these special properties. Then we conclude factors are causal factors. Bottom line: causal models require careful thinking, and additional research is probably needed.