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

arXiv:2609.36279v4 Announce Type: replace-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, reaches beyond the modal object language: its quantifiers range over domains containing the nominals and satisfaction operators of hybrid logic. A proof using one proves a theorem of the embedding, not necessarily of the modal logic. Whether a result is one of the modal logic can be settled by replaying it in an explicit calculus, or, more cheaply and for

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