In the recent twenty-year retrospective issue of Animal Behavior and Cognition, Povinelli and Henley (2020) argue that a host of comparative studies into “complex cognition” suffer, fatally, from a theoretical confusion. To rectify the problem, they issue the following challenge: alongside specifications of the higher-order capacity to be tested, provide hypotheses of the mechanism(s) necessary to implement it. They spearhead this effort with a discussion of how the Relational Reinterpretation Hypothesis (RRH) provides just such an account. In the first part (...) of the paper, I argue that RRH is neither necessary nor sufficient to explain the second-order behavior in question. In part two, I describe an alternative hypothesis, externalism, that does sufficiently account for it. Further, it opens new avenues of comparative research. (shrink)