Natural language - no infinity and probably no recursion

We question the need for recursion in human cognitive processing by arguing that a generally simpler and less resource demanding process – iteration – is sufficient to account for human natural language and arithmetic performance. We claim that the only motivation for recursion, the infinity in natural language and arithmetic competence, is equally approachable by iteration and recursion. Second, we submit that the infinity in natural language and arithmetic competence reduces to imagining infinite embedding or concatenation, which is completely independent from the ability to implement infinite computation, and thus, independent from both recursion and iteration. Furthermore, we show that natural language is a finite rather than infinite set.