Computational Irreducibility as the Foundation of Agency: A Formal Model Connecting Undecidability to Autonomous Behavior in Complex Systems

The concepts of agency and autonomy, pertaining to a system's ability to function effectively, pursue objectives, and self-regulate, are central inquiries across biology, cognitive science, artificial intelligence, and philosophy [1, 2]. Furthermore, previous formalization attempts, largely focused on logical or probabilistic frameworks, have frequently overlooked the inherent limitations imposed by computational constraints on a system's capacity to process information and forecast its environment [6, 7]. This article posits that a deeper understanding of agency can be achieved by examining the fundamental constraints of computation and logic within complex systems. Building upon insights from G odel's incompleteness theorems [8], T uring's work on decidability and com-putability [9], and concepts from thermodynamics and information theory, we formulate a novel explanation. Our core thesis is that genuine autonomy necessarily implies unpredictability from an external perspective: for any truly autonomous system, there exist questions about its future behavior that are fundamentally undecidable. This provides a principled distinction between autonomous and non-autonomous systems without appealing to non-physical properties. We contend that agency specifically emerges in systems operating at the threshold of decidability. Here, G odel-like constraints manifest as the system's inability to internally represent complete 1