In the fallout of the replication crisis, several authors have pointed to an underlying "theory crisis" in the cognitive sciences, which are argued to lack a core set of shared principles, assumptions, and methodologies. In this essay, I contend that one major barrier to an integrated field stems from a widespread, often implicit ontological commitment among scientists to substance ontology: the metaphysical view that reality is composed of one or more fundamental, static, independent entities. I argue that this metaphysical assumption contributes to the impression that alternative theoretical decompositions of systems are logically incompatible. I consider cognitive, cultural, and historical reasons for the little-challenged dominance of substance thinking in scientific thought, but suggest that the philosophical foundations are shaky. As such, the field may benefit from engaging more deeply with alternative metaphysical traditions that can be grouped as "process ontologies": the family of views that tend to deny the idea of a fundamental level, take existence to be inherently relational, and emphasize that nature is inherently dynamic. I offer a brief survey of Western philosophical traditions that speak to one or more aspects of process thought, but shine a spotlight in particular on useful concepts from Buddhist and Daoist philosophical traditions. I consider three necessary aspects of all living systems that cannot be accounted for within substance ontology, but can by process: (1) fuzzy boundaries, (2) causal loops, and (3) change. I conclude by suggesting that process ontology may help the field of cognitive science progress by dissolving ill-founded debates regarding the fundamental level of analysis, opening a path for a rigorous meta-theory of cognition.