Human intelligence is commonly framed through dual process theory—fast, automatic System 1 and slow, deliberative System 2. Yet this individual-centered view overlooks two critical layers. Beneath System 1 lies System 0: the raw adaptive intelligence of the body itself, operating through physical dynamics and spinal reflexes without central neural control. Beyond System 2 lies System 3: the distributed symbolic intelligence of society, enacted through language, norms, and institutions via collective predictive coding. This three-layered model—or quad-process theory—situates symbol emergence systems within a multi-scale temporal framework, from the millisecond dynamics of embodied reflexes to the slow evolution of cultural symbol systems. The chapter argues that what distinguishes human intelligence is not any single cognitive layer but the interplay across all four systems, and that accounting for System 3 is essential to understanding both human cognition and the design of AI that can participate in our symbolic world.