A Computer-Assisted Proof of God’s Necessary and Unique Existence? The Leibniz–Gödel System

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Can a computer help prove God’s existence? In this video, I explore Gödel’s ontological argument, its formalization in higher-order logic, and the surprising use of computer-assisted proof systems to analyze its consistency.

This video promotes my book Gödel’s God Theorem, which presents four interlinking arguments for God’s necessary and unique existence:

The Gödel–Scott System (GSS) – a formalization of Leibniz’s Ontological Argument that axiomatizes a philosophical notion of positiveness, where a positive property appears to be a conjunction of Leibnizian perfections.

The ♦–Cosmological Argument (♦CA) – my streamlined version of Leibniz’s Cosmological Argument, avoiding the metaphysical baggage of the Kalam Argument.

A Possible Worlds Argument (PWA) – a straightforward yet ingenious contribution of Leibniz.

A Diagonal Eternal Truths Argument (DETA) – my attempt to use Gödel’s Incompleteness Theorems as evidence for mathematical Platonism, and then to use Platonism to reinforce a Leibniz-style eternal truths argument.

Part II of the book provides notes on higher-order logic (HOL), including:

Syntax via typed lambda calculus

Semantics under full and Henkin models

Proof systems and meta-theorems

Equality and extensionality

Modal extensions: base type for worlds, varying/constant domains, Kripke frames, Henkin/Kripke models

Rigidity and flexibility in designation

These chapters are not an exhaustive survey but rather a set of working notes in which I remain as much a student as a teacher. The aim is to equip readers with the tools to understand Gödel’s argument in the context of modern logic and computer verification.

If you’re interested in logic, philosophy, mathematics, theology, or computer-assisted proof, this video and book bring all these fields together.

References

Benzmüller, Christoph, and Bruno Woltzenlogel Paleo. The Inconsistency in Gödel’s Ontological Argument: A Success Story for AI in Metaphysics. In Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence (IJCAI-16), 936–942. AAAI Press, 2016.

Wang, Hao. A Logical Journey: From Gödel to Philosophy. MIT Press, 1996.

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Andrew M. Cavallo is a guitarist, composer, and self-produced musician who enjoys fusing early music—Medieval, Renaissance, and Baroque—with hard rock guitar.

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