From the earliest history of mathematics and physics, there have been some who have tried to develop a formula to prove the existence of God, as well as to address other metaphysical questions. Some mathematicians try to demonstrate that belief in God is logical using various arguments, primarily ontological ones, that is, those based on the characteristics of God. Several of these have provided clear reasoning, yet we must conclude that faith is still necessary to believe.

The first to develop a mathematical formula about the existence of God was John Philoponus (d. 570), who desired to defend the logical consistency of the Christian faith against pagan philosophers. Using deductive logic, he argued that a) all material objects are caused by something, b) the universe is a material object, therefore, c) the universe has a cause, which he argued was God. In essence he argued for the necessity of a transcendent cause of the universe, which is someone outside of the material world. Of course, Aristotle had also argued for a belief in a “Prime Mover,” unlike Platonists who believed a perfect God could not interact with the imperfect material world, but Philoponus added mathematical proofs for each of the premises of his syllogism.

In the Middle Ages, several churchmen published other arguments for God. For example, Anselm of Canterbury (d. 1109) argued that, since varying degrees of goodness exist, there must be a supreme goodness, which is God. He neatly avoided the Euthyphro dilemma – whether God is good because God decides it or because He adheres to a standard of good – by arguing that God embodies all that is good. Thomas Aquinas (d. 1274) gave five proofs for the existence of God. These were: Motion – since there cannot be an indefinite chain of movement, there has to be a First Mover; Causation – since everything has a cause, there has to be a First Cause; Necessity – since all things whether necessary or unnecessary originate in something else that is necessary, there must be something that is necessary only within itself; Gradation – since all things come in a gradation of good to bad, or hot to cold, there must be something that is the superlative noble and good; Order – since nature follows laws, there must be something that establishes order. Although not one of his proofs, he also argued that we derive our reason from God, which is in essence the argument from reason, that reason proves there must be an intelligence behind creation rather than random events.

While these men discussed the rationality of God, they did not advance the mathematical proof. That was taken up by men such as Johannes Keppler (d. 1630), Isaac Newton (d. 1727), Renee Descartes (d. 1650) and Gottfried Leibniz (d. 1716). While Keppler and Newton argued for the existence of God based on the mathematical rationality of physics, Descartes more extensively developed the arguments of Anselm and Aquinas: the argument from reason (that reason proves the existence of God), the ontological argument (that there must be a perfect God who exists), and the causal argument (that nothing comes from nothing). He nevertheless used his own terminology. He argued the existence of finite substances independent of each other required the existence of an infinite substance on which all other substances depend. Leibniz also developed mathematical proofs for an ontological argument, in essence, that there must be a Perfect Being, that is, one that cannot act with less perfection than He is capable. From this, he argued for the need to attain to moral perfection and that the world he created was “the best of all possible worlds.”

The most recent mathematician to try to develop a God formula was Kurt Godel. I’ve discussed in past articles the importance of Godel’s “incompleteness theorems” in discussing the existence of God. In essence, he argued that all complete mathematical systems contain at least one assumption that cannot be proved without referring to something outside that system. Late in life, he sought to complete the work of Leibniz, although he never published his views due to fears of persecution. Instead, he gave them to a colleague shortly before his death. His proof focuses on the ontological argument of the necessity of the existence of a “God-like object” that possesses every good or positive property. Later scientists have tested out his formula with computers and found that it held up under analysis, although like all such theorems, it relies on the fundamental assumptions placed within it. Nevertheless, that a perfect being exists appears a mathematical certainty.

Despite the positive result of this verification, we must recall Godel’s incompleteness theorems, which are the only weak point in his ontological proof. Since all closed systems must contain an unprovable premise, so also did the ontological proof, which Godel no doubt recognized. All proof for God or against Him necessarily relies on assumptions at some point. Whether we believe in God or not has always come down to faith, though we can and should base our faith on logic or other evidence. When we do, we find it reasonable to believe in God.

© 2022 J.D. Manders