🤖 AI Summary
This paper identifies two fundamental computational limitations inherent in intelligent systems: Gödelian incompleteness of formal systems—which constrains the deductive power of consistent reasoning—and finite-precision unpredictability in dynamical systems—which bounds long-term predictive accuracy. Methodologically, it integrates formal logic, computability theory, dynamical systems analysis, and algorithmic information theory to establish a unified framework. The key contribution is the first rigorous characterization of the intrinsic trade-off between inferential completeness and predictive stability, culminating in a proof that no algorithmic agent can *decidably* compute its own maximal prediction horizon. This result establishes an insurmountable theoretical limit on AI interpretability, autonomous reasoning, and long-horizon planning, thereby defining the intrinsic boundary of self-reflective capability for computational agents.
📝 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.