Well, I don't share this insistence that natural language is somehow special or privileged. Natural language has a tree structure and nobody need to learn about

Well, I don't share this insistence that natural language is somehow special or privileged. Natural language has a tree structure and nobody need to learn about formal grammars to comprehend that. A schoolchild understands this much, without having to understand recursion in a rigorous way. Furthermore, as I mentioned before, formal grammars are artificial languages in their own right. The key thing is that the only way a human being can understand these languages (e.g., still at the level of syntax, independent of recursive computations like in functional programming which you did mention) is through some kind of recursive reasoning about their grammar. And to keep the discussion at the forest instead of the trees, it is weird that human cognition comprehends these tree structures, recursive structures, or fractal structures, relatively naturally and intuitively. If I had said fractal would you have argued that natural languages don't exhibit fractal properties? We are talking bird's-eye level view of things here. I also believe in the Church-Turing thesis plus the Chomsky hierarchy of computable languages (the idea that languages are models of computation, and that some language classes contain other classes in a hierarchy of what is computable -- see for instance the formal class of Recursive Languages), meaning that natural languages are not based on magical computations exceeding the power of universal computation; furthermore, as another subcommenter (see both users bbor and foobarqux) put it differently to you but if you are committed to a position that natural human language can only be approximated by artificial languages defined by formal grammars then you can never have a humanly intelligible account of the computational features of actual human language. It would be like arguing a laptop is not "meaningfully" like a Turing machine because a laptop has finite number of atoms as is thus really technically a finite state machine -- it's throwing the emergent/abstract baby out with the empirical bathwater. https://en.wikipedia.org/wiki/Recursively_enumerable_language https://en.wikipedia.org/wiki/Recursively_enumerable_languag...