But here is something you probably didn’t know. Most mathematicians believe in heaven. Not a heaven with angels, but one populated by the abstract objects they devote themselves to studying: perfect spheres, infinite numbers, the square root of minus one and the like.
Moreover, they believe they commune with this realm of timeless entities through a sort of extrasensory perception. Mathematicians who buy into this fantasy are called “Platonists,” since their mathematical heaven resembles the realm of the Good and the True described in Plato’s “Republic.” Some years ago, while giving a lecture to an international audience of elite mathematicians in Berkeley, I asked how many of them were Platonists. About three-quarters raised their hands. So you might say that mathematicians are no strangers to belief in the unseen. (Of course, mathematicians don’t drag their beliefs into the public square, let alone fly planes into buildings.)
John Allen Paulos is a mathematician who teaches at Temple University and also a talented popularizer. In previous books he has trained his mathematical eye on humor, the stock market and what he reads in the newspaper. Now he has taken on God. Paulos is not a credulous man. He sees things, he tells us, in the cold light of logic and probability. (His stock market book told how he was suckered into losing a bundle on WorldCom stock, but never mind.) In “Irreligion,” Paulos intends to expose the “inherent illogic” of arguments for the existence of God. He finds these supposed proofs to be, by and large, a load of tripe.
The classic arguments for the existence of God have few friends these days. Theologians scorn them, insisting that they “objectify” a Supreme Being that can be known only through self-revelation. Philosophers make a parlor game of dissecting their logic. (In the 1994 book “God and the Philosophers,” edited by Thomas V. Morris, none of the 20 philosophers who discussed their religious faith said they came to it through logic; typically, it was a matter of experiencing what they felt to be the love of God in their lives.) And ordinary believers have never heard of them.
Still, studying these arguments can pay big intellectual dividends. Take the cosmological argument, the first one Paulos considers. It goes something like this. The universe we live in seems contingent. Nothing about it suggests that it exists by its own nature. Therefore, if there is an explanation for the universe’s existence, that explanation must involve another kind of entity — one that does exist by its very nature. Call this entity “God.”
From that barest of sketches, it is obvious that the cosmological argument has some grave problems. For one thing, it takes for granted the dubious principle that everything has an explanation. For another, there is no reason to suppose that the self-existent entity it points to has any other divine attributes, like omniscience or benevolence. But grappling with its flawed logic has led to a deeper understanding of existence, causation, time and infinity.
Paulos misses most of that. Just when the going ought to get good, intellectually speaking, he bales out with a jokey allusion to self-fellating yogis. He has a similarly glib way with the other classic arguments for God’s existence. The ontological argument — which, in its most up-to-date version, involves a subtle analysis of how existence might be built into the very definition of being like a god — is “logical abracadabra.” The argument from design is a “creationist Ponzi scheme” that “quickly leads to metaphysical bankruptcy.” You wonder how such transparently silly arguments could have engaged serious thinkers from Descartes, Leibniz and Hegel to the present day.
Clearly, Paulos is innocent of theology, which he dismisses as a “verbal magic show.” Like other neo-atheist authors, his tone tends to the sophomoric, with references to flatulent dogs and the Flying Spaghetti Monster. Ann Coulter crops up in the index, but one looks in vain for the name of a great religious thinker like Karl Barth, who saw theology as an effort to understand what faith has given, not a quest for logical proof.
When Paulos is dealing with matters more familiar to him, however, he often lurches into sense, almost redeeming the book. In one bravura passage, he shows how a mathematical result called Ramsey’s theorem can account for the illusion of divine order arising from chaos. Yet there are also symptoms of hasty writing. At one point, Paulos claims that the computer scientist Gregory Chaitin’s work shows that a formal system can only generate information whose complexity is less than its own. A dozen or so pages later, Paulos says the mathematician John Horton Conway’s work shows that sources of complexity need not be complex. The reader might be forgiven for smelling a contradiction where none really exists.
Paulos concedes that, just as arguments for God’s existence are logically inconclusive, so too are arguments against God’s existence. That means that you can either believe or disbelieve without being convicted of stark irrationality. Similarly, Paulos’s fellow mathematicians can either believe that they are communing with a Platonic realm of perfect mathematical entities, or they can believe that they are playing a meaningless game with symbols on paper. Most mathematicians appear to be in the former camp. Is it wrong of them to hold this unexamined and (arguably) groundless faith if it helps them flourish in their mathematical lives?
The same pragmatic justification may apply to the many intellectuals I know who, despite the exertions of Paulos, Christopher Hitchens, Richard Dawkins et al., are serious about religion (usually, as it happens, either Catholicism or Judaism). But I sometimes wonder whether they’re not a little like the physicist Niels Bohr, who (the story goes) nailed a horseshoe above his office door for good luck. “You don’t really believe in that stuff, do you?” a colleague asked him one day. To which Bohr responded, “No, but I’ve heard it works even for people who don’t believe.”
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