The Setup
The attempt here is to explain to myself the problem(s), notation, the dumbfuck/naive approach and what’s wrong/impossible with it, and how we fix these with our assumptions.
This stuff is pretty deep philosophically (to me at least) and can be logically tortuous. But it shows Science at its best ✨
Potential Outcomes
You're used to seeing $Y$. What happens. That's very nice. For example, you give someone Aspirin and say:
Effects, Causation, and Association
Effect = "What Happened?" We assign numbers to things that can happen. Some are binary (e.g. 0 = didn't work, 1 = worked), some are categorical, some are continuous.
The Game
The Game here is to see if and how the Observed Association can be used to recover the Average Causal Effect.
Estimands et al
There's the Average/Individual/Population Causal Effect as these vaunted things we want. These are estimands. You are going to use estimators to try and estimate them. Yeah quite the mouthful.