[deeThrow94]

If you define recursion as a symbol referencing itself, either directly or indirectly, and if you define language as a system of relating symbols to each other, recursion is a linguistic concept, it is a concept that describes a relationship between symbols. There are good reasons to define each concept differently, but if you identify recursion empirically, recursion won't "actually" exist outside of the description of the process. It's our characterization of the process that reveals the recursive structure, even if that characterization doesn't actually exist outside of language.

[Jensson]

> If you define recursion as a symbol referencing itself, either directly or indirectly, and if you define language as a system of relating symbols to each other, recursion is a linguistic concept

But that isn't what we mean with recursive function. We don't call this recursive:

    x = x + 1

Its just incrementing x.

[deeThrow94]

> We don't call this recursive... it's just incrementing x

That's not a recursive function as it's written, but you could certainly consider it a form of symbolic recursion. This just isn't a very useful characterization in an iterative/imperative context. You could frame incrementing as recursive, though—this is just peano axioms/church encoding.