Gödel’s Ontological Proof and its Consistency Consequences
Abstract
Abstract This paper examines the ultrafilter interpretation of Kurt Gödel’s ontological argument and explores its philosophical and mathematical consequences. After reviewing the formulations of Anselm of Canterbury, Gottfried Wilhelm Leibniz, and Gödel, we show how Gödel’s positivity axioms can be understood extensionally as defining an ultrafilter over the domain of individuals. We argue that this perspective sheds new light on the modal collapse, suggesting that it reflects not merely features of the modal framework, but deeper structural properties of the underlying ultrafilter. We then relate this interpretation to the work of Harvey Friedman, where non-principal ultrafilters and divine objects are used to obtain relative consistency results in set theory.
Fields of Study & Subjects
Philosophy and Theoretical Science
Philosophy and History of Science
Embodied and Extended Cognition
Publication details
- Journal / source
- Logica Universalis
- Publisher
- Springer Science and Business Media LLC
- Volume
- 20
- Issue
- 1-2
- Pages
- 97–112
- Publication date
- 1 June 2026
- Language
- EN