This is so great, thanks for doing this! The more people internalize this stuff the better -- this is "raising the sanity waterline."

Is there a reason you use superscripts for potential outcomes, and not e.g. Y(a), or Y_a which I see a lot more often?

We define a “Confounder” as anything you need to introduce behind the conditioning sign of the exchangeability assumption, in order to make the assumption “true”.

A slight technicality is that a "confounder" refers to individual variables, while "confounding" refers to a ternary relation between sets. "Confounding"(A,Y,C) just means adjusting for C gives a valid functional for Y(a), that is conditional ignorability holds: Y(a) independent of A | C. "Confounder"(A,Y,c) (for a singleton c) means ???. It's not so simple -- seemingly reasonable definitions can fail. Tyler wrote a paper with me about this.

Fun exercise: what is the smallest DAG where the definition of a confounder contained in the first sentence on the Wikipedia article on confounding fails.

I think the number of upvotes should count as feedback, and you should put up the entire sequence (if for no other reason than a very handy online reference for future discussions on this topic, and as a way to bridge inference gaps). Causal stuff comes up a fair bit here, and it would be good if we could say "read article X in this sequence to understand what I mean."

edit: may add more later.