In their 2002 seminal paper Hauser, Chomsky and Fitch hypothesize that recursion is the only human-specific and language-specific mechanism of the faculty of language. While debate focused primarily on the meaning of recursion in the hypothesis and on the human-specific and syntax-specific character of recursion, the present work focuses on the claim that recursion is language-specific. We argue that there are recursive structures in the domain of motor intentionality by way of extending John R. Searle's analysis of intentional action. We then discuss evidence from cognitive science and neuroscience supporting the claim that motor-intentional recursion is language-independent and suggest some explanatory hypotheses: (1) linguistic recursion is embodied in sensory-motor processing; (2) linguistic and motor-intentional recursions are distinct and mutually independent mechanisms. Finally, we propose some reflections about the epistemic status of HCF as presenting an empirically falsifiable hypothesis, and on the possibility of testing recursion in different cognitive domains.