Dual Computational Horizons: Incompleteness and Unpredictability in Intelligent Systems

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 latter 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 verify its own maximal prediction horizon universally. This perspective clarifies inherent trade-offs between reasoning, prediction, and self-analysis in intelligent systems. The construction presented here constitutes one representative instance of a broader logical class of such limitations.