Dual Computational Horizons: Incompleteness and Unpredictability in Intelligent Systems

Abstract: We formalize two independent computational limitations that constrain algorithmic intelligence: formal incompleteness and dynamical unpredictability. The former limits the deductive power of consistent reasoning systems while the later bounds long-term prediction under finite precision. We show that these two extrema together impose structural bounds on an agent's ability to reason about its own predictive capabilities. In particular, an algorithmic agent cannot compute its own maximal prediction horizon generally. This perspective clarifies inherent trade-offs between reasoning, prediction, and self-analysis in intelligent systems.