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

TL;DR

This paper distinguishes between limits of proof and limits of computation, arguing that undecidability affects what can be proven but not what can be computed or simulated, challenging claims about the universe's simulatability.

Contribution

It clarifies the difference between epistemic and ontological incompleteness and shows that undecidability does not necessarily prevent physical simulation or computation.

Findings

Undecidability constrains provability but not computability.

Simulation of the universe is not ruled out by undecidability.

Incompleteness alone does not imply failure of physical execution.

Abstract

Recent work by Faizal et al. (2025) claims that G\"odelian 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.