The "obvious" observation from the article is: > Obviously, λx.M should be seen as a sort of function The fact that lambdas can be seen as a syntax for descri

The "obvious" observation from the article is: > Obviously, λx.M should be seen as a sort of function The fact that lambdas can be seen as a syntax for describing functions (or function-like things) is kind of obvious to anyone who knows basic programming language theory (and many software engineers who use lambdas when they map over a list, for example). The sentence before it about β-reduction is describing the rule for how to call a function, which we learned in high school as "plug-and-chug". I think the confusion here might just be that the syntax is unfamiliar. You have probably seen these concepts before.