> when you drill down to first principles

It is a trap to consider that first principles perspective is sufficient. Like, if I tell you before 1980: "iterate over f(z) = z^2 + c" there is no way you are going to guess fractals emerge. Same with the rules for Conway's Game of Life - seeing the code you won't guess it makes gliders and guns.

My point is that recursion creates its own inner opacity, it is irreducible, so knowing a recursive system behavior from its iteration code alone is insufficient. It is a becoming not a static thing. That's also why we have the halting problem - recursion.

Reasoning is a recursive process too, you can't understand it from analyzing its parts.