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

Evan Redden

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arXiv · 2512.11807

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

Evan Redden

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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.

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Evan Redden. 2025-11-14. Provability vs. Execution: A Comment on "Consequences of Undecidability in Physics on the Theory of Everything". https://arxiv.org/abs/2512.11807

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