I discuss Aoki’s fundamental model of institutions in its most recent version, building on a comment that Aoki contributed to a paper by Hindriks and Guala (J Inst Econ 11(3):459–480, 2015). These authors advance a ‘rules in equilibrium’ approach to institutions that claims to reduce a Searlian social ontology of institutions to mere linguistic conventions and theoretical terms. Against this view, I posit ‘institutional naturalism’ and reinstate the analytical need for recognizing the ontological autonomy of institutions, reflected in their causal powers. I show how this follows from a proper reconstruction of the Aoki model, building on advanced cognitive sciences which are also deployed by Aoki. In this view, notions such as collective intentionality reflect the material embodiments of distributed cognition and distributed agency. This approach has been dubbed ‘Neo-Hegelian’ by Aoki in his comment.