Author: Tomás Bogardus
Category: Philosophy of Religion
Word Count: 1000
True story: My friend’s daughter failed a hearing test when she was two years old, and was subsequently diagnosed with a rare hearing disorder. The doctors recommended a battery of follow-up tests and procedures, both expensive and invasive. My friend was, of course, crushed by the news. I suspect most parents would grimly set their teeth and proceed with the doctors’ orders for the child’s sake. Fortunately, my friend was a philosophy student in those days, studying probability theory. What he learned allowed him to decline further treatment and still sleep in peace. For he knew that, though this test was highly reliable, it was not infallible. It occasionally, though rarely, issued false positives. And he knew that the incidence of this hearing disorder—its base rate, its frequency in the general population, the prior probability that his child had the disease, before the test—was low enough to de-claw the test’s result.
Just how low is low enough? Suppose the disease is as common as the test’s failure rate: One in a thousand. Now picture my friend’s child standing last in a line of one thousand anxious children waiting to take this hearing test. Let’s say every child before my friend’s gets a true negative result from the test; they all check out fine. Now my friend’s child steps up and receives the dreaded positive result. On the one hand, we feel cause for concern: This test fails only 0.1% of the time, so isn’t the diagnosis overwhelmingly likely to be accurate? But, on the other hand, we know that, after 999 true results, this test was “due” to fail, like a bald tire approaching its last mile. So, should we be concerned? The correct answer is that, given the low base rate of the disease—and despite the test’s very low failure rate—there is only a 50% chance that the child who tested positive actually has the disease. Maybe it’s the real deal, but just as likely it’s a false positive. And, of course, the rarer the disease—the lower its base rate—the more likely it is that this child pulled the “false positive” card rather than the “rare disease” card. If the base rate of the disease is vanishingly small—as it was in the case of my friend and his daughter—a positive result from a test that rarely fails can, paradoxically, be almost certainly false.
Careful attention to probabilities might yield many more useful conclusions, beyond my friend’s. For example, philosopher Larry Shapiro believes that what we just learned should convince us that no one can justifiably believe in miracles, e.g., that God raised Jesus from the dead. His argument follows my friend’s right down the line. Shapiro generously grants to the miracle-believer that those who tell us about these miracles—St. Paul, say—are as reliable as the hearing test we discussed, falsely reporting miracles only 0.1% of the time. The problem, according to Shapiro, is that the base rate of miracles like resurrection of the dead—the frequency of resurrection, its “prior” probability, before the testimony—is vanishingly small. It’s a miracle, after all. And so, Shapiro says, any testimony of a miracle, even from a highly reliable source, is almost certainly false. So much for Christianity, Shapiro concludes: It’s irrational. As is any other religion based on miracle reports.
Shapiro’s argument is as smooth as wind on ice, as menacing now as it was when David Hume premiered it back in 1748. But perhaps it’s too quick. Before you give up on miracles, let me develop a response to Hume offered by Peter van Inwagen. Try this colorful experiment for yourself. Find some lipstick and the nearest mirror. Pick an improbable string of numbers or letters—maybe, “Miracles do happen, Larry!”—and write them across your forehead. Stare into the mirror. Look at what you’ve become. Can you believe you wrote that message on your face just because the internet told you to?
Seriously. Can you? Yes, of course you can. In fact, you do and you should. That belief is highly rational, given the testimony of your eyes. But hold on: While your eyes are reliable, they’re not infallible. Occasionally they’ll issue false positives, reporting something’s there when it’s not. Presently, they’re reporting that message on your face. But what’s the base rate of that? Prior to reading this essay and watching it happen, how likely would you have thought it that you would be standing there with a lipstick message on your face? Nothing just like that has ever happened before in the history of the universe. So the base rate of that event—its prior probability—must be vanishingly small, right? But then doesn’t the general form of Shapiro’s argument lead us to the conclusion that it would be irrational to believe what’s staring you in the face?
Perhaps this shows that something’s wrong with Shapiro’s argument. Most likely it’s his assumption that, because something has never happened before, or only rarely, its base rate—its prior probability—must be low. The lipstick message on your face had never happened before. But we know of things like that, we know how such a thing easily might happen, so its prior probability need not be low. That would explain why the reliable albeit fallible testimony of our eyes convinces us that it’s happening. And, if that’s right, the miracle-believing Christian could reason this way: “Before Jesus, the dead rose rarely. Or maybe even never. It needn’t follow that the prior probability of God’s raising Jesus from the dead is small. For we know of things like that, how such a thing easily might happen. It’s God, after all, who can do as he likes, and he may like resurrecting people. And that’s why, contra Shapiro and Hume, it may be fully rational for the reliable albeit fallible testimony of St. Paul et al. to convince us that it happened.” So says the miracle believer. What do you say?
Take My Word for It: On Testimony by Spencer Case
Conspiracy Theories by Jared Millson
The Epistemology of Disagreement by Jonathan Matheson
About the Author
Tomás Bogardus is an Associate Professor of Philosophy at Pepperdine University in Malibu, California. https://sites.google.com/site/tbogardus