6 ideas
Causal reasoning operates at three distinct levels: association (seeing patterns, 'what if I see X'), intervention (doing, 'what if I do X'), and counterfactuals (imagining, 'what if I had done X instead'). Each rung requires more information than the one below it, and no amount of data at a lower rung can answer questions at a higher rung.
Statistics can only describe associations within data, never causal relationships, because correlation is symmetric while causation is directional. To extract causal conclusions you must supply a causal model — assumptions about how the world works — that lives outside the data itself.
A confounder is a common cause that influences both the supposed cause and the effect, producing a correlation between them that disappears once the confounder is held fixed. Controlling for the right confounders — not all variables — is what isolates the genuine causal effect.
The notation do(X) formalizes the difference between passively observing X and actively intervening to set X, because intervention severs all the arrows that normally cause X. This distinguishes P(Y|X) — the probability of Y given you observe X — from P(Y|do(X)) — the probability of Y if you force X to happen.
When two independent causes both influence a common effect (a collider), conditioning on that effect creates a false correlation between the causes that did not exist before. This means controlling for more variables can introduce bias rather than remove it — for instance, selecting on an outcome makes unrelated traits appear linked.
For decades the tobacco industry argued a genetic confounder might cause both smoking and lung cancer, and pure statistics could not refute this because the correlation was consistent with both stories. The dispute was only resolvable by reasoning about causal mechanisms and interventions, demonstrating why association alone left a deadly question paralyzed for years.