Mathematical Proof for the Existence of God

Claude Mariottini
Emeritus Professor
of Old Testament
Northern Baptist Seminary

Kurt Friedrich Gödel “was a logician, mathematician, and philosopher.” Gödel is considered “to be one of the most significant logicians in history.” Gödel made important contributions to proof theory. “Proof theory is a major branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques.” Gödel made an attempt at using mathematics to prove the existence of God.

In an article published in Spektrum der Wissenschaft titled “Lässt sich Gott mathematisch beweisen?” and republished in the Scientific American under the title “Can God Be Proved Mathematically?,” Manon Bischoff mentions “a preprint study first posted in 2013” in which “an algorithmic proof wizard checked Gödel’s logical chain of reasoning—and found it to be undoubtedly correct.”

Gödel used logic to prove the existence of God. In the diagram below, where Ax stands for axioms, Th stands for theorems, and Df stands for definitions, Gödel proved that God exists:

After evaluating the twelve steps in the diagram above, Bischoff concludes:

“From this one can now conclude that God exists because this being possesses every positive property, and existence is positive.”

“As it turns out, Gödel’s logical inferences are all correct—even computers have been able to prove that.”

So, according to Gödel’s logic, the existence of God can be proven mathematically.

However, Bischoff writes that Gödel’s logic, although correct, does not prove the existence of the God of the Bible. Bischoff writes,

“But all of this does not ensure that this set is unique. There could be multiple collections that satisfy the requirements. For example, as logicians have shown, it is possible to construct cases where, by Gödel’s definition, there are more than 700 divine entities that differ in essence.”

“This does not settle the final question of the existence of one (or more) divine beings. Whether mathematics is really the right way to answer this question is itself questionable—even if thinking about it is quite exciting.”

For people of faith, the God of mathematics is not the God of revelation. The God who reveals himself in the history of Israel and in the person of Christ is a God who is known by faith.

As Emil Brunner wrote, “Through the Biblical revelation we discover that what we can ‘learn’ to know as ‘God’ by our own unaided efforts is not the True God, precisely because we acquire this ‘knowledge’ by our own efforts. . . . It does not bring us fulfilment. It does not bring us to our knees, and it moves neither heart nor will” (Brunner 1950:118).

Paraphrasing Hebrews 11:6: “It is impossible to believe that God exists without faith. Anyone who wants to come to him must believe that God exists and that he rewards those who sincerely seek him.”

Mathematics can prove that God exists, but it cannot prove that this God is “a God merciful and gracious, slow to anger, and abounding in steadfast love and faithfulness, keeping steadfast love for the thousandth generation, forgiving iniquity and transgression and sin” (Exodus 34:6–7). Only faith can prove what kind of God God is.

BIBLIOGRAPHY:

Brunner, Emil. The Christian Doctrine of God. Volume 1. Philadelphia: The Westminster Press, 1950.

Claude Mariottini
Emeritus Professor of Old Testament
Northern Baptist Seminary

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2 Responses to Mathematical Proof for the Existence of God

  1. llamapacker says:

    I passed this along to my professor son (theoretical chemistry professor and math buff). He responded: My knee-jerk reaction to any claim such as a “mathematical proof for the existence of god” would be immediate dismissal. However, Gödel is not a logician to be dismissed lightly. As a mere dabbler in mathematics, in my opinion, Gödel had one of the greatest minds of the 20th century – an intellectual talent comparable to Einstein. There is an interesting Wikipedia page on this particular proof. While it appears to be valid in some sense, I simply lack the training to unpack its actual meaning…

    Like

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