Here’s the bad
news: the reductio ad unlikely, unlike its Aristotelian ancestor, is
not logically sound in general. It leads us into its own absurdities. Joseph
Berkson, the longtime head of the medical statistics division at the Mayo
Clinic, who cultivated (and loudly broadcast) a vigorous skepticism about
methodology he thought shaky, offered a famous example demonstrating the
pitfalls of the method. Suppose you have a group of fifty experimental subjects,
who you hypothesize (H) are human beings. You observe (O) that one of them is
an albino. Now, albinism is extremely rare, affecting no more than one in
twenty thousand people. So given that H is correct, the chance you’d find an
albino among your fifty subjects is quite small, less than 1 in 400,* or
0.0025. So the p-value, the probability of observing O given H, is much lower
than .05.
We are inexorably
led to conclude, with a high degree of statistical confidence, that H is
incorrect: the subjects in the sample are not human beings.
It’s tempting to
think of “very improbable” as meaning “essentially impossible,” and, from
there, to utter the word “essentially” more and more quietly in our mind’s
voice until we stop paying attention to it. But impossible and improbable are
not the same—not even close. Impossible things never happen. But improbable
things happen a lot. That means we’re on quivery logical footing when we try to
make inferences from an improbable observation, as reductio ad unlikely asks us
to.
