Brian: I’m not the messiah.
Acolyte: Only the true messiah would deny that he was the messiah!
Brian: OK. I’m the messiah.
Mob: He’s the messiah! He’s the messiah!
—Life of Brian

Guy’s out walking in Manhattan when he sees a street vendor selling unmarked aerosol cans. He’s curious and asks what’s in them, and the vendor says, “Tiger repellent.” The guy points out that there are no tigers in New York City, and the vendor replies, “See how well it works?”

Certain ideas enter the world, like Athena, fully armed. Most of these are disreputable. Conspiracy theorists frequently insist that the absence of evidence for their theory constitutes proof of the power of the conspiracy; otherwise how could they cover it all up? Child “therapists” invoke the absence of any memory of sexual abuse as proof of the same; the horrific experience has been repressed. As Renee Fredrickson puts it, with all seriousness, in Repressed Memories: A Journey to Recovery from Sexual Abuse, “The existence of profound disbelief is an indication that the memories are real.” The major religions, of course, are the greatest tiger repellent of all. Good is proof of God’s wisdom and mercy; evil of his subtlety and inscrutability. Throw in a sacred text that it is blasphemy even to translate, and a standing order to slaughter the infidels, and you’ve really built something to last.

Tiger repellent also insinuates itself into more respectable precincts. In 1903 a well-known French physicist named Rene Blondlot announced the discovery of N-rays. Over the next three years more than 300 papers, published by 120 different scientists, enumerated some of the remarkable properties of these rays. They passed through platinum but not rock, dry cigarette paper but not wet. Rabbits and frogs emitted them. They could be conducted along wires. They strengthened faint luminosity, with the aid of a steel file.

N-rays, however, turned out to be highly temperamental. You could produce only so much of them, no matter how many rabbits or frogs you lined up. Noise would spoil their effect. Your instruments had to be tuned just so. Blondlot gave complex instructions for observing them, and still numerous physicists failed, for the excellent reason that N-rays do not exist. The American prankster physicist Robert Wood finally settled the matter by visiting Blondlot’s lab in 1906 and playing several cruel tricks on him. Wood surreptitiously removed the dispersing prism that was supposed to be indispensable to the observation of the rays. Blondlot claimed to see them anyway, and when he died thirty years later he was still firmly convinced of their existence.

It is easy to laugh at Blondlot from a century’s distance. But he was not dishonest, and many of the scientists who replicated his results were highly competent. N-rays were, on the face of it, no more improbable than X-rays, discovered a few years earlier. But a phenomenon so faint, so susceptible to external conditions, so difficult to reproduce, is tiger repellent.

All of this struck Karl Popper with such force that he attempted to erect an entire philosophy of science upon it. One sympathizes. Popper began to formulate his philosophy in the 1920s, when psychology, the largest tiger repellent manufacturer of the 20th century, was coming of age. Popper also, unlike most of his colleagues, does not give the impression of squinting at his subject through binoculars from a distant hill. He knows something of math and science and incorporates examples from them liberally. It is no surprise that of all philosophers of science only Popper, Kuhn possibly excepted, has a significant following among actual scientists.

For Popper a scientific theory must be falsifiable, by which he means that one could imagine an experimental result that would refute it. Scientific theories, it follows, are not verifiable either. No matter how many times a theory has been confirmed, no matter what its explanatory or predictive value, it is on probation, permanently. The very next experiment may blow it all to pieces.

Popper’s imaginary experimental result need not exist in our universe — some theories are true — but merely in some other possible universe far, far away. This possible universe may, indeed must, differ from ours in its particulars but may not violate the laws of logic. That 2 + 2 = 4 is necessary, true in all possible universes; that water boils at 100°C at sea level is contingent, true in ours. Science deals only in the contingent.

This distinction is essential to falsifiability. Some imaginary experimental results are valid, some are not, and this is how you tell the difference. In philosophy it has been formally known, since Kant, as the analytic/synthetic dichotomy. Analytic truths are tautologies; they are necessary; all of the information is contained in the premises. The locus classicus of the analytic is mathematics. Following Wittgenstein, Popper views math as “unpacking tautologies,” and therefore excludes it from science. It is, for him, a form of tiger repellent — useful to be sure, but tiger repellent just the same.

Trouble is, there’s no such distinction, at least not as Popper conceives it. Quine’s refutation in “Two Dogmas of Empiricism” is decisive. His arguments are well-known, if technical, and I will not recount them here. They amount to the contention that the analytic always bleeds into the synthetic and vice versa. Even mathematics turns out not to be strictly analytic, to Wittgenstein’s chagrin. If, as Gödel demonstrated, there are true statements in any formal system that cannot be reached from its axioms, how do we classify them? Are they analytic, or synthetic, or what? When Popper first published The Logic of Scientific Discovery, in 1934, Gödel was already internationally famous. Its index is replete with the names of contemporary scientists and mathematicians. Gödel’s does not appear.

The analytic/synthetic dichotomy has shown considerable staying power, its flaws notwithstanding, because it resembles the way people really think. Gerald Edelman’s theory of consciousness, for one, with its modes of “logic” and “selectionism,” maps quite well to analytic and synthetic. But the philosopher, in his hubris, elevates ways of thinking to categories of knowledge. Matt McIntosh, a convinced Popperian who rejects the analytic/synthetic dichotomy, has promised to salvage falsifiability notwithstanding. He assures me that this post will be coming, as we say in software, real soon now. (Note to Matt: I haven’t grown a beard while waiting, but I could have. Easily.)

The laws of thermodynamics, science by anyone’s standard, are probabilistic. It is not impossible for a stone to roll uphill, merely so unlikely that the contingency can be safely disregarded. Modern physics is statistical, and was in Popper’s day too. Popper acknowledges that respectable science employs probability statements all the time, which leaves him with two choices. He can admit what inituition would say, and what the Law of Large Numbers does say, that probability statements are falsifiable, to any desired degree of certainty, given sufficient trials. But then he would have to abandon his theory. By this same logic probability statements are also verifiable, and verifiability, in science, is what Popper is concerned to deny.

Hence he takes the opposite view: he denies that probability statements are falsifiable. More precisely, he denies it, and then admits it, and then denies it, and then admits it again. The lengthy section on probability in The Logic of Scientific Discovery twists and turns hideously, finally concluding that probability statements, though not falsifiable themselves, can be used as if they were falsifiable. No, really:

Following [the physicist] I shall disallow the unlimited application of probability hypotheses: I propose that we take the methodological decision never to explain physical effects, i.e. reproducible regularities, as accumulation of accidents. [Sec. 67, italics his.]

In other words, let’s pretend that the obvious — probability statements are falsifiable — is, in fact, true. Well, as long as we’re playing Let’s Pretend, I have a better idea: let’s pretend that Popper’s philosophy is true. We can, and should, admit that “what would prove it wrong?” remains an excellent question for any theory, and credit Popper for insisting so strenuously on it. We can, and should, deny that falsifiability demarcates science from non-science absolutely. Falsifiability is a superb heuristic, which is not be confused with a philosophy.

(Update: Matt came through with his post after all, which is well worth reading, along with the rest of his “Knowledge and Information” series. Billy Beck comments. He seems to think I play on Popper’s team.)