Cultural evolutionary psychology (CEP) accounts for the cultural evolution of cognition. It is based on evolutionary psychology and cultural evolutionary theory and aims at a synthetic attempt which is achieved by what we want to call ‘generalization by recursion’. We argue in this paper that the evolutionary psychology program as a whole could greatly benefit from CEP’s generalization. As we will show, there is one theoretical element in particular, that CEP relevantly generalizes in contrast to its predecessors. It comes from (...) cultural evolutionary theory and has been referred to as the ‘dual inheritance argument’. CEP’s novelty consists in showing that not only cognitive products (‘grist’) but also cognitive mechanisms (‘mills’) are subject to cultural evolution and provides lots of empirical evidence for this claim. This account is ‘recursive’, because CEP’s generalization of the dual inheritance argument theoretically employs a recursive feedback-loop between cultural learning and cultural evolution. We also argue that this account might be considered to supersede unificatory and reductionistic efforts of its competitors, because it is stronger than purely structural or analogical unification while at the same time it is not too strong in order to fall prey to implausible reductionism. (shrink)