English

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

History and Philosophy of Physics 2025-12-16 v1

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.

Keywords

Cite

@article{arxiv.2512.11807,
  title  = {Provability vs. Execution: A Comment on "Consequences of Undecidability in Physics on the Theory of Everything"},
  author = {Evan Redden},
  journal= {arXiv preprint arXiv:2512.11807},
  year   = {2025}
}

Comments

3 pages, 0 figures. Comment on arXiv:2507.22950v1