Systemic Constraints of Undecidability

Abstract

This paper presents a theory of systemic undecidability, reframing incomputability as a structural property of systems rather than a localized feature of specific functions or problems. We define a notion of causal embedding and prove a closure principle: any subsystem that participates functionally in the computation of an undecidable system inherits its undecidability. This result positions undecidability as a pervasive constraint on prediction, modeling, and epistemic access in both natural and artificial systems. Our framework disarms oracle mimicry and challenges the view that computational limits can be circumvented through architectural innovation. By generalizing classical results into a dynamic systems context, this work augments the logical trajectory of Gödel, Turing, and Chaitin, offering a new perspective of the topology of computability and its interrelation to the boundaries of scientific knowledge.