Dual Computational Horizons: Incompleteness and Unpredictability in Intelligent Systems
This work addresses foundational constraints on reasoning and prediction in intelligent systems, but it is incremental as it builds on existing theories of incompleteness and unpredictability.
The paper formalizes two computational limitations—formal incompleteness and dynamical unpredictability—that constrain algorithmic intelligence, showing they prevent an agent from universally verifying its own maximal prediction horizon.
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.