Understanding the neural basis of higher cognitive functions, such as those involved in language, requires a shift from mere localisation to an analysis of network operation. A recent proposal points at infinite recursion as the core of several higher functions, and thus challenges cortical network theorists to describe network behaviour that could subserve infinite recursion. I propose here that a capacity for infinite recursion may be associated with the natural adaptive dynamics of large semantic associative networks, once their connectivity becomes sufficiently extensive to support structured transition probabilities between global network states. The crucial development endowing a semantic system with a nonrandom dynamics would thus be an increase in connectivity, perhaps to be identified with the dramatic increase in spine numbers recently observed in the basal dendrites of pyramidal cells in Old World monkey and particularly in human frontal cortex.