Potential Outcomes — Defining a Causal Effect Precisely
To reason about causation rigorously, you first need to define what a "causal effect" even is — and the answer is more subtle than it looks. The potential-outcomes framework defines it through a counterfactual: the difference between what happened and what would have happened otherwise. That single idea, and the "fundamental problem" that you can never observe both, is the foundation on which all of causal inference is built.
To reason about causation you must define a causal effect: the counterfactual difference between what happened and what would have happened otherwise. The potential-outcomes framework, the fundamental problem (you can never observe both), and why everything reduces to making treated and untreated groups comparable.