Cognitive science is lacking conceptual tools to describe how an agent’s motivations, as such, can play a role in the generation of its behavior. The enactive approach has made progress by developing a relaxed naturalism, and by placing normativity at the core of life and mind; all cognitive activity is a kind of motivated activity. It has rejected representational architectures, especially their reification of the role of normativity into localized “value” functions, in favor of accounts that appeal to system-level properties of the organism. However, these accounts push the problem of reification to a higher level of description, given that the efficacy of agent-level normativity is completely identified with the efficacy of non-normative system-level activity, while assuming operational equivalency. To allow normativity to have its own efficacy, a new kind of nonreductive theory is proposed: irruption theory. The concept of irruption is introduced to indirectly operationalize an agent’s motivated involvement in its activity, specifically in terms of a corresponding underdetermination of its states by their material basis. This implies that irruptions are associated with increased unpredictability of (neuro)physiological activity, and they should, hence, be quantifiable in terms of information-theoretic entropy. Accordingly, evidence that action, cognition, and consciousness are linked to higher levels of neural entropy can be interpreted as indicating higher levels of motivated agential involvement. Counterintuitively, irruptions do not stand in contrast to adaptive behavior. Rather, as indicated by artificial life models of complex adaptive systems, bursts of arbitrary changes in neural activity can facilitate the self-organization of adaptivity. Irruption theory therefore, makes it intelligible how an agent’s motivations, as such, can make effective differences to their behavior, without requiring the agent to be able to directly control their body’s neurophysiological processes.