[yorwba]

Syntax is usually used to describe those rules of a language that are easy to compute; so easy that you don't have to understand the meaning (semantics) to do it. E.g. you can point to a missing semicolon in a C program without understanding what the program does.

Of course you can call the rules of well-formedness "higher-order syntax" in the sense that the computation required to decide it is of a higher order than syntax, but the distinction between syntax and semantics is by no means unnatural. It has been discovered independently several times; some ancient studies of the syntax of Sanskrit have survived to this day.