Monday Musing: Replying to Euler

Review of Irreligion: A Mathematician Explains Why the Arguments for God Just Don't Add Up by John Allen Paulos

You may know the (almost certainly apocryphal) story of an 18th century encounter between the brilliant Swiss mathematician Leonhard Euler and the French freethinking encyclopaedist and philosopher Denis Diderot:

Diderot had been invited to the court by Catherine the Great, but then annoyed her by trying to convert everyone to atheism. Catherine asked Euler for help, and he informed Diderot, who was ignorant of mathematics, that he would present in court an algebraic proof of the existence of God, if Diderot wanted to hear it. Diderot was interested, and, according to De Morgan, Euler advanced toward Diderot, and said gravely, and in a tone of perfect conviction: "Sir, ( a + bn )/n = x , hence God exists; reply!" Diderot had no reply, and the court broke into laughter. Diderot immediately returned to France.

Not being ignorant of mathematics, had John Allen Paulos been in the place of Diderot, he would have had no trouble replying. He could just have presented Euler with a copy of his charming and brief book Irreligion. In Irreligion, Paulos provides (in the form of musings about them) refutations of twelve arguments for the existence of God which "range from what might be called the golden oldies of religious thought to those with a more contemporary beat," and he does so with verve, a robust prose, and a very welcome sense of humor. Along the way, we learn all sorts of interesting mathematical tidbits in short side-discussions of related issues. And there are delicious little anecdotes sprinkled throughout. I can't resist immediately providing an example of the latter:

[I am reminded] of a story related by Bertrand Russell about when he was entering jail as a conscientious objector during World War I. The admitting clerk asked him his religion, and when Russell responded that he was an agnostic, the clerk shook his head and said he'd never heard of that religion but that all of them worship the same God. [p. 79]

* * *

Let's get to the meat. To give a sense of Paulos's modus operandi, I'll present one of his refutations briefly here. This one, he calls The Argument from Prophecy (and the Bible Codes). For each of the arguments that he discusses, Paulos first distills them into a formal structure. Here's what that looks like for this argument:

1. A holy book makes prophesies.
2. The same book or adherents of it report that these prophesies have come true.
3. The book is indubitable and asserts that God exists.
4. Therefore God exists.

First, Paulos notes that in any narrative, the more details that are supplied, the more true it starts to seem. For example, if asked which of the following narratives is more likely to be true,

1. Congressman Smith took a bribe last year.
2. Congressman Smith took a bribe last year, took another one this year, used some of the money to rent a secret apartment for his young intern, and spent the rest on luxurious "fact-finding" trips with her.

many people will pick the second one even though mathematically speaking, any statement alone always has a higher probability of being true than its conjunction with any other statement(s):

Embedding God in a holy book's detailed narrative and building an entire culture around this narrative seem by themselves to confer a kind of existence on Him. Holidays, traditions, ideals, cultural identities, as valuable as they occasionally might be, all seem to add to the unwarranted presuppositions underlying them. Their familiarity also serves to inure us to the vindictive, petty, and repellent aspects of the God character. [p. 62]

Second, Paulos notes that people, even if they are deluded, often reinforce each others beliefs. A kind of "all-of-us-can't-be-wrong" thinking, and then he points to an interesting mathematical result:

note that testimony that someone is telling the truth is self-undermining if the likelihood of truth-telling is less than 1/2. If people are confused, lying, or otherwise deluded more often than not, than their expressions of support for each other are literally less than worthless.[p.64]

He goes on to give an example with two people who each get the truth right only 1/4 of the time. What is the probability if one of them makes an assertion and the other supports it as true, that it is actually true? Paulos shows with some simple mathematics that the probablity now drops to 1/10:

The Moral: Confirmation of a person's unreliable statement by another unreliable person makes the statement even less reliable. [p. 65]

The rest of the chapter is devoted to a probabilistic analysis showing that there is nothing unusual about the Bible Codes. Such codes could be extracted from any sufficiently large text, and they have been. For example, War and Peace has been shown to contain codes for "Jordan," "Chicago," and "Bulls" very close together, prompting Paulos to sarcastically declare Tolstoy a basketball clairvoyant!

* * *

The book is organized into three sections, each of which deals with four arguments. The first presents traditional ones, such as the ontological argument, and the argument from design. The second deals with subjective arguments such as the one I presented above. And the third section is on psycho-mathematical arguments such as Pascal's wager. Each section also contains short asides with commonsensical comments on various dubious assertions and practices in religion. For example, discussing Mel Gibson's movie The Passion of the Christ, Paulos writes:

Assume for the moment that compelling historical documents have just come to light establishing the movie's and the Bible's contentions that a group of Jews was instrumental in bringing about the death of Jesus; that Pilate, the Roman governor, was benign and ineffectual; and so on. Even if all this were the case, does it not seem hateful, not to mention un-Christian, to blame contemporary Jews? ...even if we give full credit to Plato's twenty-four-hundred-year-old account of Socrates' death, what zealous coterie of classicists or philosophers would hold today's Greeks responsible? [p.92-93]

Nowhere is Paulos preachy or condescending. His tone remains always detached and his humor dry. Paulos is not interested in engaging in polemics or spewing invective. This is a sincere, calm, humane and timely examination of a phenomenon nowadays much in the news, one we can benefit by reading regardless of our beliefs.

All my previous Monday Musings can be seen here.

Have a good week!