Applying Second-Order Quantifier Elimination in Inspecting Gödel's Ontological Proof
This work provides incremental insights for researchers in automated reasoning and formal logic by applying existing methods to a well-known philosophical proof.
The authors tackled the analysis of Gödel's ontological proof by applying second-order quantifier elimination in an automated logic environment, revealing previously unnoticed details and aspects of the proof.
In recent years, Gödel's ontological proof and variations of it were formalized and analyzed with automated tools in various ways. We supplement these analyses with a modeling in an automated environment based on first-order logic extended by predicate quantification. Formula macros are used to structure complex formulas and tasks. The analysis is presented as a generated type-set document where informal explanations are interspersed with pretty-printed formulas and outputs of reasoners for first-order theorem proving and second-order quantifier elimination. Previously unnoticed or obscured aspects and details of Gödel's proof become apparent. Practical application possibilities of second-order quantifier elimination are shown and the encountered elimination tasks may serve as benchmarks.