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Some remarks on the ontological arguments of Leibniz and Gödel

In Herbert Breger (ed.), Einheit in der Vielheit: Akten des VIII. Leibniz Kongresses. Hartmann. pp. 510-517 (2006)

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  1. 31 A Divine Consistency Proof for Mathematics. Friedman - 2024 - In Mirosław Szatkowski (ed.), Ontology of Divinity. De Gruyter. pp. 645-696.
    We present familiar principles involving objects and classes (of objects), pairing (on objects), choice (selecting elements from classes), positive classes (elements of an ultrafilter), and definable classes (definable using the preceding notions). We also postulate the existence of a divine object in the formalized sense of lying in every definable positive class. ZFC (even extended with certain hypotheses just shy of the existence of a measurable cardinal) is interpretable in the resulting system. This establishes the consistency of mathematics relative to (...)
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  • Ontology of Divinity.Mirosław Szatkowski (ed.) - 2024 - De Gruyter.
    This volume announces a new era in the philosophy of God. Many of its contributions work to create stronger links between the philosophy of God, on the one hand, and mathematics or metamathematics, on the other hand. It is about not only the possibilities of applying mathematics or metamathematics to questions about God, but also the reverse question: Does the philosophy of God have anything to offer mathematics or metamathematics? The remaining contributions tackle stereotypes in the philosophy of religion. The (...)
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