Dual Computational Horizons: Incompleteness and Unpredictability in Intelligent Systems

TL;DR

This paper formalizes two fundamental computational limitations—formal incompleteness and unpredictability—that restrict an agent's reasoning and prediction abilities, revealing inherent trade-offs in intelligent systems.

Contribution

It introduces a formal framework for understanding how incompleteness and unpredictability jointly constrain self-reasoning and prediction in algorithms.

Findings

Agents cannot verify their own maximal prediction horizon universally.

Structural bounds limit reasoning about predictive capabilities.

The framework clarifies trade-offs between reasoning, prediction, and self-analysis.

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 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.