Amazingly, it’s now been 3 years since my post titled Singular Proof, for which I’d intended to write a followup almost since the beginning. The reason for that plan is that some readers seem to have misunderstood its intents — though frankly it appears that they were trying very hard to misunderstand. In any case, the sequel kept getting pushed to the back burner, because it seems I always had meatier matters to cover. But now, here at last is round two.

First, let me make it clear (in case I didn’t the first time) what the central thesis was: a single event — any single event — always proves at least one thing: namely, that such an occurrence is possible. One would think that such a truth would be self-evident. But apparently it isn’t. Because when I offered the illustration of Roger Bannister running the 4-minute mile for the first time, someone commented that his feat didn’t really prove anything, because it could have been just luck.

Well, sure. It could have been just luck. Or it could have been drugs. Or it could have been that he was mesmerized. Or it could have been divine intervention. Or he could have been guided by a cosmic beam projected from the mother ship hovering overhead. Or maybe some combination of the above. But guess what? Doesn’t matter one bit. Because Bannister’s run still proves that, one way or another, such a thing can be done.

It’s related to something called the law of the excluded middle. Which means basically that some propositions are either true or they are not — there is no middle ground. (This obviously does not include value judgments like “St. Louis is a big city”.  St. Louis certainly would appear enormous to someone coming there from a town of 2000, but to a visitor from Istanbul, it would appear to be just a quaint little village.) Propositions of possibility, however, do fall under that heading; either a thing is possible, or it is not.  If it is impossible, then by definition, it cannot happen. So if it does happen, that disproves its impossibility and, concurrently, proves its possibility. Every event is both a negation of an impossibility and an affirmation of possibility.

And it takes only a single instance to refute not only a presumption of impossibility, but any absolutism. Philosophers have famously noted, for instance, that the proposition “All swans are white” can be refuted by the observance of a single black swan. But such a single occurrence, though it clearly establishes possibility, says nothing about probability. It proves that some swans are black, but it gives no indication of how many.

Suppose your mother tells you that if you walk on the railroad tracks, you will get killed. But you decide, just once, to ignore her warning and walk down a railroad track for a hundred yards. And lo and behold, you live to tell about it. This single act of yours has discredited her belief that walking on railroad tracks inevitably leads to demise. But it does not establish that this is a safe practice.  It does not mean that in general, people should walk on railroad tracks.  It does not even guarantee that you will survive your second defiance of her admonition.

A single instance, then, is enough to disprove an absolute (walking on the tracks will get you killed); it’s enough to discredit an impossibility (you cannot walk on the tracks without getting killed); and it’s enough to establish a possibility (you can walk on the tracks and survive). But it does not establish a certainty (if you walk on the tracks, you’ll survive) nor even a probability (if you walk on the tracks, you’ll probably be safe). The latter proposition is where methodical investigation (science) comes in. In order to know whether it’s likely that you can walk on railroad tracks safely — and just how safe it would or wouldn’t be — we would need to compile some accurate statistics on the matter.

And of course the fact that you survive a single act of defying your mum does not mean that you made it through the day because you walked on the railroad tracks. In addition to falsely extrapolating a general conclusion from isolated incidents, one of the biggest mistakes people make is confusing correlation with causation: the telephone rings when you get into the bathtub, so it must be the act of getting into the bathtub that causes the telephone to ring; the leaves rustle when the wind blows, so it must be the movement of the leaves that stirs up wind; Roger Bannister ran the 4-minute mile wearing white socks, so the socks must have been the source of his superior speed.

Even rational interpreters of scientific data are not totally immune to this error. Years ago, research indicated that married people tend to be happier than unmarried people. And for a time, the conclusion many people drew from this was that there was something about marriage itself that made people happier; that a single person could become happier just by getting married. But finally, someone realized that this was putting the cart before the horse. It wasn’t that marriage made people happier; it was just that happier people were more likely to get married in the first place. (For, as someone astutely asked, “Who would want to marry a grouch?”)

I suppose to be generous I could assume that my critic wrongly concluded that I was conflating anecdotal evidence and anecdotal proof myself; but that would be extending a great deal of grace, since I made it clear that I was not doing any such thing. And anyone who’s read this blog very much at all knows that I’ve repeatedly not done it; I’ve stressed several times, to name just one example, that even though there are isolated incidents of an “armed good guy” stopping an “armed bad guy” that does not mean that in general guns make us safer — indeed, the evidence strongly indicates just the opposite.

If there was one passage in my post that might possibly, even by a huge stretch, have given someone the wrong impression, perhaps it was this:

Scientists, however, are sometimes scornful of anecdotal evidence, declaring it to be totally worthless. Which is ironic, given how dependent they are on it. A scientific experiment is preceded by a hypothesis. And where does the hypothesis come from? Anecdotal evidence, quite often. Like the rest of us, scientists exercise inductive reasoning: they notice specific events and extrapolate from them that there might be a general pattern. Unlike the rest of us, they undertake methodical tests in an effort to prove this hypothesis — or hopefully, an effort to disprove it, since that’s really the only way to accomplish either proof or disproof. And how do they do this? By collecting more anecdotes, either in a laboratory or in the wild. But this isn’t considered anecdotal evidence, since the events are collected systematically rather than haphazardly.

A reader purporting to be a scientist himself declared that I was quite mistaken about where a hypothesis comes from. It derives, said he, from a case study, and not merely from an isolated incident. Well, this is often true (especially in the social sciences), but so what? Don’t look now, but a case study is a collection of separate incidents. And some of the greatest scientific discoveries in history (microwaves, x-rays, and penicillin, to name just a few) sprang from observation of phenomena that were not only singular but accidental. Furthermore, even the most coldly calculated of laboratory experiments consists of a series of individual trials — each of which, as I meant to suggest, can be thought of as a narrative in its own right.

And just where do you suppose the concept for a case study comes from, anyway? Could it be from… an anecdote? Or two or three? Unless of course, it comes from a dream or a divine message delivered via burning bush. But wait, those are anecdotes too, aren’t they? When you get right down to it, all the wisdom the human race has accumulated in any field of endeavor — whether scientific, artistic, philosophical, athletic, or whatever — has depended upon the observance of single incidents. Such wisdom is expressed in generalities (It’s better to give than to receive; two times two is four; the days are longer in the summer and shorter in the winter; etc.) but such generalities are constructed of a series of singular instances.

This (supposed) scientist, by the way, also seized upon my mention that being a healthy vegetarian for several decades discredits the absolutism that eating meat is required to live a long and healthy life. This, he proclaimed, constituted a “claim” about the benefits of vegetarianism, which he in turn suggested was akin to claims about faith healing and communicating with the dead. If this really was a scientist speaking, it makes one really shudder to think what kind of illogic and irrationality must prevail among the lay masses.

One comment was to the effect that anecdotal evidence carries no weight even if it occurs a million times over. It’s hard to imagine anything more absurd. Suppose you have a city of a million residents, and the entire million die on the same day. Then you learn that the entire million ate shellfish from local waters on the day before their deaths. Wouldn’t you be just slightly inclined to be more wary of local shellfish than you would have been had there been only one such death? Of course, a million-fold unanimity is still not proof that the shellfish actually caused the deaths; it is, however — in the absence of comprehensive testing — a damn good indication that you would be prudent to avoid eating the stuff until you find out for certain.

A would-be assassin characterized my observations as “pseudoscientific nonsense” —  which in terms of substance is no more noteworthy than any of the other attacks leveled against me.  What is worth remarking about, however, is the commentator’s choice of vocabulary. He seems to be quite confused about the distinctions between unscientific, nonscientific and pseudoscientific (which is quite ironic given that the major linchpin of his attack was my unorthodox use of labels). So even though it’s a bit of a diversion, let’s take a moment to clarify these distinctions.

Unscientific means that something directly contradicts scientific fact — e.g., saying that the earth is flat or that men have fewer ribs than women, or that the earth is not getting warmer. Pseudoscientific is something that is not only unsupported by science, but is masquerading as science (we often call it quackery) — e.g., phrenology, snake oil remedies, and the anti-vax movement.

But there is another class of propositions that are unsupported by science, yet neither contradict nor pose as science; they are propositions that belong in another cognitive sphere altogether. For example: “In the beginning, God created the heavens and the earth.” This statement does not contradict science — it is, in fact, essentially meaningless. And it’s also, in itself, quite harmless; the problem arises when people try to substitute it for scientific fact. Even then, it is not pseudoscientific, because it is not posing as science; it is posing as something superior to science.

Like the author of Genesis, or the individual who coined the phrase “It’s raining cats and dogs”, I was being nonscientific — but not unscientific or pseudoscientific, and most certainly not antiscientific.  In asserting that scientific research is indebted to anecdotes, I was using a broad definition of anecdote, and perhaps indulging in a wee bit of poetic license. But not very much.