Provability vs. Execution: A Comment on "Consequences of Undecidability in Physics on the Theory of Everything"

TL;DR

Problem addressed: whether undecidability in physics prevents a formal, algorithmic simulation of the universe. Approach: distinguish epistemic incompleteness from ontological incompleteness, with formal language $L_{QG}$ and computation examples like the Game of Life to separate provability from execution. Findings: undecidable propositions restrict what is provable but do not necessarily hinder computation or physical evolution; lack of empirical hypercomputation evidence means the universe could be simulated by a standard algorithm. Significance: clarifies the limits of applying Gödelian logic to physics and cautions against inferring ontological limits from epistemic incompleteness.

Abstract

Recent work by Faizal et al. (2025) claims that Gödelian undecidability of non-algorithmic truths in our universe imply the impossibility of a formal, algorithmic simulation of the universe. This paper clarifies the distinction between epistemic incompleteness: limits on what can be proven within a formal system, and ontological incompleteness: limits on what can exist or be computed by that system. Using Conway's Game of Life as a Turing-complete example, I demonstrate that undecidability constrains provability but not computability or execution. Unless physical phenomena require the resolution of undecidable propositions, incompleteness alone does not imply a guaranteed failure in execution. Thus, the claim that the universe cannot be simulated lacks empirical and logical justification without evidence of hypercomputation in nature.