Variables and scopes considered formally

We consider what natural language explanations are required to present a formalism. We desire to be as complete as possible, leaving nothing implicit, and yet to keep the natural language to a minimum, moving as quickly as possible away from informal explanations and into the formalism. We also try to keep the informal explanation as independent as possible of the formalism being presented. We pay particular attention to scope-ignoring and scope-respecting substitution. Variable renaming turns out to be a consequence of scope and extension. We speculate on the possibility of recursive variable introduction.