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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2512.11807 |
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| _version_ | 1866911316462010368 |
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| author | Redden, Evan |
| author_facet | Redden, Evan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11807 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Provability vs. Execution: A Comment on "Consequences of Undecidability in Physics on the Theory of Everything" Redden, Evan History and Philosophy of Physics 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. |
| title | Provability vs. Execution: A Comment on "Consequences of Undecidability in Physics on the Theory of Everything" |
| topic | History and Philosophy of Physics |
| url | https://arxiv.org/abs/2512.11807 |