An influential line of thought claims that natural language and arithmetic processing require recursion, a putative hallmark of human cognitive processing (Chomsky in Evolution of human language: biolinguistic perspectives. Cambridge University Press, Cambridge, pp 45-61, 2010; Fitch et al. in Cognition 97(2):179-210, 2005; Hauser et al. in Science 298(5598):1569-1579, 2002). First, 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 argue 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 processing, and thus, independent from both recursion and iteration. Furthermore, we claim that a property of natural language is physically uncountable finity and not discrete infinity.