Gödel’s Ontological Proof of the Existence of God and its Consistency Consequences

Gödel’s ontological proof of God’s existence, finalized in 1970, constitutes one of the most ambitious attempts to formalize metaphysical theology using modern logic. Rooted in a tradition stretching from Anselm through Descartes and Leibniz, Gödel’s argument reformulates the classical ontological proof in higher-order modal logic. Yet its significance extends far beyond theology. When stripped of modalities, Gödel’s axioms define an ultrafilter, thereby connecting metaphysical reasoning with foundational set theory and strong axioms of infinity. This talk reconstructs the historical development of ontological arguments, analyzes Gödel’s formal system, examines the phenomenon of modal collapse, and explores the unexpected implications for mathematical foundations, showing that consistency of arithmetic and ZFC is a consequence of the ontological proof. It is argued that Gödel’s proof should be understood not primarily as a theological demonstration but as a profound structural experiment revealing deep connections between logic, metaphysics, and infinity.