Counterfactuals and Potential Outcomes

Counterfactuals are outcomes that would have occurred under conditions that did not actually happen. The word itself comes from Latin: "contra factum" meaning "against the fact." Counterfactual reasoning is the intellectual engine that powers causal inference.

What If?

At its heart, counterfactual reasoning asks: "What would have happened if things had been different?" This seemingly simple question is profound because it forces us to think about alternative realities—worlds that could have existed but did not.

Consider a patient who took a medication and recovered from illness. Did the medication cause the recovery? To answer this, we must ask: What would have happened if the patient had NOT taken the medication? If they would have recovered anyway, the medication did not cause the recovery. If they would have remained ill, the medication was causally responsible.

"Causal inference requires thinking about what would have happened under conditions that may not have actually occurred." — What If, Chapter 1

The Two Worlds

For any decision or treatment, we can conceptualize two parallel worlds:

World	Description
Factual World	The world that actually occurred—with the treatment actually received
Counterfactual World	The world that did not occur—with the alternative treatment

The causal effect is the difference between outcomes in these two worlds. The fundamental challenge is that we can only ever observe the factual world; the counterfactual world remains forever hidden.

Counterfactuals in Clinical Medicine

Every clinical decision involves implicit counterfactual reasoning:

• Diagnosis: "If this patient had disease X, we would expect to see symptom pattern Y"
• Treatment: "If we administer this therapy, what outcome should we expect?"
• Prognosis: "If the patient continues this behavior, what will their health trajectory be?"

The methods of causal inference formalize this intuitive reasoning, making our assumptions explicit and our conclusions more rigorous.