Science requires postformal capabilities to compare competing explanations and conceptualize how to coordinate or integrate them. With conflicts thus reconciled, science advances. The Model of Hierarchical Complexity facilitates the coordination of current arguments about intelligence. A cross-species measurement theory of comparative cognition is proposed. It has potential to overcome the lack of a general measurement theory for the science of comparative cognition, and the lack of domain-general mechanisms for evolutionary psychologists. The hierarchical complexity of concepts and debates as well as (...) the new theory are scored, and demonstrate the postformal hierarchical complexity of the proposed theory. (shrink)