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 on…