This is more of a linguistics topic, however it is interesting. Noam Chomsky argues that “recursion” is inherent in any language. However this has been challenged by Daniel Everett and his study on the Piraha language in the Brazilian Amazon.
“Linguist Noam Chomsky theorizes that unlimited extension of any natural language is possible using the recursive device of embedding clauses within sentences (Aspects of the Theory of Syntax. 1965). For example, two simple sentences—”Dorothy met the Wicked Witch of the West in Munchkin Land” and “The Wicked Witch’s sister was killed in Munchkin Land”—can be embedded in a third sentence, “Dorothy liquidated the Wicked Witch with a pail of water,” to obtain a recursive sentence: “Dorothy, who met the Wicked Witch of the West in Munchkin Land where her sister was killed, liquidated her with a pail of water.”
The idea that recursion is an essential property of human language (as Chomsky suggests) is challenged by linguist Daniel Everett in his work Cultural Constraints on Grammar and Cognition in Pirahã: Another Look at the Design Features of Human Language, in which he hypothesizes that cultural factors made recursion unnecessary in the development of the Pirahã language. This concept, which challenges Chomsky’s idea that recursion is the only trait that differentiates human and animal communication, is currently under debate. Andrew Nevins, David Pesetsky and Cilene Rodrigues provide a debate against this proposal.
Recursion in linguistics enables ‘discrete infinity’ by embedding phrases within phrases of the same type in a hierarchical structure. Without recursion, language does not have ‘discrete infinity’ and cannot embed sentences into infinity (with a ‘Russian nesting doll’ effect). Everett contests that language must have discrete infinity, and asserts that the Pirahã language—which he claims lacks recursion—is in fact finite. He likens it to the finite game of chess, which has a finite number of moves but is nevertheless very productive, with novel moves being discovered throughout history.”
An article on this: