The God of the Mathematicians

By Goldman, David P. | First Things; A Monthly Journal of Religion and Public Life, August/September 2010 | Go to article overview

The God of the Mathematicians


Goldman, David P., First Things; A Monthly Journal of Religion and Public Life


Kurt Gödel was a believer - or, at least, a knower - whose engagement with God included a reworking of the ontological proof of God's existence. Born in 1906, Gödel was arguably the great mathematician of his time. Certainly no twentieth-century thinker did more to show that the human mind cannot be reduced to a machine. At twenty-five he ruined the positivist hope of making mathematics into a self-contained formal system with his incompleteness theorems, implying, as he noted, that machines never will be able to think, and computer algorithms never will replace intuition. To Godel this implies that we cannot give a credible account of reality without God. But Gödel's God is not the well-behaved deity of the old natural theology, or the happy harmonizer of the intelligent-design subculture. Gödel's God hides his countenance and can be glimpsed only in paradox and intuition. God is not an abstraction but "can act as a person," as Gödel once wrote, confronting those who seek him with paradox, uplifting man through glorious insights while guarding his infinitude from human grasp. Gödel's investigations in number theory and general relativity suggest a similar theological result: that God cannot be reduced to a mere principle of the natural world. Gödel may have seen himself as a successor to Leibniz, whose critique of Spinoza's atheism set a precedent for much of Gödel's work. When we try to ascertain the theological intent underlying Gödel's mathematical investigations, though, several difficulties arise.

The first is Gödel's reticence. "Although he did not go to church," his wife Adele told the logician Hao Wang shortly after Gödel's death in 1978, he "was religious and read the Bible in bed every Sunday morning." But fear of ridicule and professional isolation made him reluctant to talk about his faith. "Ninety percent of contemporary philosophers see their principal task to be that of beating religion out of men's heads," he wrote to his mother in 1961.

A two-page draft of an ontological proof for God's existence forms the whole of Gödel's explicitly theological output. He showed his paper only to close friends, but word got out, and the clever young things on campus giggled behind his back. His biographer Rebecca Goldstein, who was a graduate student at Princeton during Gödel's last years, snickers that she and her peers "found it hilarious" that Godei "deluded himself into believing that God's existence could be proved a priori." The ambient hostility drove some of his best students out of the profession and may have worsened the eating disorder that hastened his death.

Another difficulty is that Gödel's work extends across several demanding fields, each with a high threshold of preparation.

There is also the problem that scavengers have been at work on his legacy for decades. The postmodernists have tried to claim him as an irrationalist who proved that nothing can be proved - just the opposite of what he intended. Rebecca Goldstein rightly debunks the postmodern claim, but her biography of the great mathematician makes no mention of his religious faith except to ridicule it, ignoring key facets of his work with theological implications.

Nonetheless, the ontological proof provides a point of entry into Gödel's work, linking intuitive theology with his mathematical investigation. The proof, in one form or another, has been known at least since the eleventh century, when St. Anselm of Canterbury paused to ask: If God is greater than we possibly can conceive, then how could God not exist?

In the best-known version of the argument, Anselm noted:

1. The definition of the word God is "that than which nothing greater can be conceived."

2. God exists in the understanding, since we understand the word with that definition.

3. To exist in reality and in the understanding is greater than to exist in the understanding alone.

4. Therefore, God must exist in reality.

Versions of the argument, with key twists and turns, have been introduced in Western philosophy through the centuries by thinkers from Descartes and Leibniz down to the twentieth-century American philosopher Charles Hartshorne. …

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