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Gödel's Ontological Argument Ported to Lean 4

By PulseAugur Editorial · [2 sources] ·

Researchers have successfully ported a dataset concerning Gödel's and Scott's ontological arguments from Isabelle/HOL to the Lean 4 programming language. This comprehensive port maintains the original structure, including 30 modules and the order of declarations, with a comparison tool verifying the identical nature of 548 statements. The project re-proves all results from the original study, such as the inconsistency of Gödel's 1970 axioms and the concept of modal collapse, and addresses statements that were previously refuted or left open. AI

IMPACT Formalization of philosophical arguments in programming languages may advance AI reasoning capabilities.

RANK_REASON The item is an academic paper published on arXiv detailing a formalization effort. [lever_c_demoted from research: ic=1 ai=0.4]

Read on arXiv cs.AI →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

Gödel's Ontological Argument Ported to Lean 4

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The item is an academic paper published on arXiv detailing a formalization effort. [lever_c_demoted from research: ic=1 ai=0.4]
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COVERAGE [2]

  1. arXiv cs.AI TIER_1 English(EN) · Christoph Benzm\"uller ·

    Proofs Without Nominals: G\"odel's Ontological Argument, its Shallow Embedding, and the Open Questions of the Monatshefte Notes

    arXiv:2609.36279v1 Announce Type: cross Abstract: The shallow embedding of higher-order modal logic in classical higher-order logic, used in Benzm\"uller and Scott's Notes on G\"odel's and Scott's variants of the ontological argument (2025), reaches beyond the modal object langua…

  2. arXiv cs.AI TIER_1 English(EN) · Christoph Benzm\"uller ·

    G\"odel's and Scott's Variants of the Ontological Argument in Lean 4 and TPTP THF

    arXiv:2609.26806v2 Announce Type: replace-cross Abstract: This paper presents a complete, structure-preserving port to Lean 4 of the Isabelle/HOL dataset accompanying Benzm\"uller and Scott's study of G\"odel's ontological argument and Scott's variant: 30 modules, one per theory,…

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