The Holmesian Principle
“Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth.”
— Sherlock Holmes
There is a Rational Wiki article that describes this quote as the “Holmesian Fallacy” — an apparent mistake in reasoning that is destined to lead to spurious conclusions of deduction. It alleges the quote argues that, “when some explanation is believed to be true on the basis that alternate explanations are impossible, yet not all alternate explanations have been ruled out.” The article, somewhat ironically, is but a misunderstanding of the Arthur C. Doyle quote. The Rational Wiki article claims that this quote is a logical fallacy because it is used to justify paranormal explanations for inexplicable data. What the Holmes quote actually says is the opposite: that once you eliminate the set of impossible explanations (such as paranormal ones), you are left with a set of explanations which must include the true explanation.
Those who have read the Sherlock Holmes stories will know there is a repeating pattern in the stories which goes something like this: Holmes and Watson are called upon to investigate an inexplicable murder or disappearance, Watson is baffled because the evidence makes no sense, the reader is left concluding there can be no possible earthly explanation for the available data, and the story concludes with Sherlock Holmes explaining the idiosyncratic sequence of events precisely as they occurred to explain the seemingly inexplicable pattern of data. In fact, the lesson of Sherlock Holmes is precisely that data often appears inexplicable, and the human tendency to rely upon supernatural explanations is misguided, when in fact exceedingly complex and unusual explanations remain more likely than the supernatural, no matter how contrived or bizarre they may seem. Sherlock Holmes’ creator Arthur C. Doyle wrote the Sherlock Holmes stories to explore the limits of peculiarity in the ordinary. The Holmes quote therefore captures an important truth about reality, not a fallacy as the rationalist community has spuriously concluded, which I call the Holmesian Principle. The Holmesian Principle is twofold: 1) the inability to explain something does not justify the invocation of the supernatural or paranormal, 2) the subjective plausibility of an explanation has no bearing over whether or not it is true. Let’s dissect these two parts.
Part 1: Eliminating the impossible
It is true that for some people, the supernatural and paranormal exist within the realm of possible, but there is an important tool to escape the inclination to invoke the supernatural for the inexplicable: magic. No, not *real* Magic, but the art of illusion magic. The art of magic involves the deception of an audience to conceal any feasible explanation for a trick, such that the mind of the audience is left dumfounded and astonished. In magic, all tricks, no matter how inexplicable, do have an earthly (and often contrived) explanation. In a question and answer interview, famed magician Penn Jillette was asked, “a serious moral question for magicians. When a sick kid asks you is magic real do you tell them the truth or a lie?” to which Penn responded:
That is a serious moral question, there's a serious moral answer. There's no such thing as magic, there's no such thing as the supernatural. And I don't care if it's a sick child or a healthy adult, you do not lie. I never, ever, wanna leave someone believing that magic is real. That would be morally wrong.
Now that we have established that all magic is an illusion, and thus we can safely eliminate any supernatural trickery in explaining how any particular trick is done, the question becomes how good are we at deducing the explanation for any given magic trick? [As an aside: it is true, there are magicians that claim to be harnessing supernatural powers to perform their tricks, but they are quacks and have been debunked.]
Most people would not be able to deduce how even the simplest tricks are performed, and some of the best tricks have eluded explanation by anyone. Try, for instance, to deduce how this magic trick was done, and you will realize you could spend your entire life searching for an answer in vain. One must therefore submit to the following proposition: just because you cannot explain something does not mean it is inexplicable, nor does it justify the introduction of supernatural forces to explain it. Thus, the application of the first part of the Holmesian Principle can be practiced by observing good magic tricks. In Penn and Teller’s Fool Us, the judges, despite being experts well versed in illusions and magic techniques, are at times unable to explain the tricks being performed in front of them (the magician wins by “fooling” the judges). In the show, no one ever claims that “real magic” has occurred — the point of the show is to illustrate how possible it is to deceive one’s perceptions, even an expert’s.
Human perception and logic is fallible, and the inability to explain something does not warrant the invocation of the supernatural, for it is rather trivial to fool the human mind. Now to explore the second argument of the Holmesian Principle: accepting the truth even when it seems improbable.
Part 2: Rescuing the improbable
There is an implicit tendency to eliminate the improbable from a set of possibilities as a matter of “hedging one’s bets” on what will turn out to be true. It is an important heuristic for interacting with the world, otherwise one would be petrified by the infinity of possible yet improbable ways in which they might die, for example; however, in sensemaking it is essential not to. One must rescue the improbable from one’s implicit bias to ignore or disregard it.
One illustration of the implicit difficulty in regarding the improbable as the truth is another magic trick. [it is worth spending the nine minutes watching this clip, it will make my point more salient]. In this trick, the explanation for how the trick is done is so unbelievable, so improbable as to sound absurd, and yet it is true. Most people would likely fail to reach the correct inference; they would falsely classify the truth as impossible, and seek elsewhere for the explanation. This trick is an important illustration of the resistance of the human mind to consider the unbelievable and the improbable as potential truth.
There is perhaps little harm done by those who commit the fallacy in Part 1 of invoking the supernatural to explain the inexplicable, but there is potential harm done by those who commit the Part 2 fallacy of failing to include the improbable in the set of possibilities by not accounting for their potential consequences. I would recommend the Nassim Taleb book The Black Swan for a more comprehensive exposition of this idea, which he terms “tail risk”. One prescient example of this fallacy can perhaps be illustrated with the Cumbre Vieja volcano irrupting on La Palma in the Canary Islands (as of today, October 18 2021 it is irrupting with no end in sight). The volcanic ridge could cause a portion of the island to sheer off into the Atlantic Ocean and cause a tsunami capable of devastating the Atlantic seaboard. Such a scenario sounds so improbable as to be not worth worrying about, but because it is not impossible, and given the magnitude of the catastrophe it could cause, it is worth worrying about. If this story is new to you, it is worth meditating on your innate response to it, and noticing if there is a tendency in you to fall for this fallacy of disregarding the improbable.
As much as the Holmesian Principle is about resisting the temptation to invoke the supernatural for the inexplicable, it is equally about resisting this temptation to exclude the improbable for being too extraordinary to be true. Perhaps one reason the extraordinary is often fallaciously eliminated from the set of possibility is the heuristic established when Carl Sagan famously said, “extraordinary claims requires extraordinary evidence”. Often people misinterpret this heuristic as meaning that anything that seems unlikely is not worth worrying about until there is substantial evidence that it is likely (and thus, not unlikely at all). In fact, this heuristic only applies when the extraordinariness of a claim is determined by its conflict with other established models of reality, not by its subjective adjudication by human intuition and perception. Therefore, extraordinary claims such as the Cumbre Vieja volcanic tsunami scenario do not require extraordinary evidence, for they are not in conflict with established models of reality.
The skeptic community is one which misapplies the extraordinary claims heuristic too broadly, and frequently eliminates possibilities speciously. Take for example the evidence required to prove the existence of Bigfoot. Establishing the existence of Bigfoot as a living species need not exceed the burden of evidence to establish the existence of any other species — a process which happens regularly. The existence of Bigfoot, were it to be true, is not in conflict with any models of reality (unless the creature itself is supernatural). The burden of evidence simply has not been reached to establish Bigfoot as an extant species; however, that Bigfoot exists is of course not impossible, and must be included in the set of possible explanations for the thousands of sightings that have accrued. The skeptical position might be that it should not be considered possible that Bigfoot exists without hard evidence, like DNA or a body. Such a position forces the skeptic to ignore or disregard evidence to the contrary, like the handful of reliable witnesses and physical evidence. What is more, such a position fails to acknowledge any existing data as legitimate, for it presupposes that such data cannot possibly exist. And any model that is predicated on the rejection of data is a fragile and biased model.
There is a stigma against contemplation of the improbable that is often conflated with how well it explains reality. It can be difficult to resist this stigma, or to resist the avoidance of it, but it is essential to make proper sense of the world. History is riddled with examples of absurd, improbable, stigmatized claims being true. A better tool for establishing which explanations to exclude and which to consider is the one Sherlock Holmes uses: the ability of an explanation to account for the available data points. The plausibility of a claim should be measured by how many data points it explains versus conflicts with, not in how probable it seems.
It is important to recognize this balance between eliminating the impossible and rescuing the improbable when making sense of the world. There is no escaping the subjectivity that exists in the grey areas of this distinction, but one must resist the temptation to disregard that which seems impossible, but by no laws of nature actually is. As our scientific exploration of the fundamental properties of the Universe continue to expand, it is becoming increasingly clear how peculiar and bizarre it is, and how unreliable our intuitions are at making sense of it.
To err on the side of including the improbable in one’s set of possible explanations is to acknowledge with humility the wondrous peculiarity of our Universe.
To err on the side of excluding the improbable is to disregard with hubris that there are explanations beyond human imagination for realities in our Universe.
To wield the Holmesian Principle is to resist the temptation to invoke the supernatural, and to resist the stigma to ignore the improbable.
Epilogue
It occurs to me that there is a fundamental philosophical presupposition built into the Holmesian Principle that not everyone will agree with. This presupposition at its core is that human logic is fallible, and that evidence should be prioritized over logic in building one’s models of reality. To an empiricist, evidence is the most fundamental unit of sensemaking, but to a rationalist, logic is primary and can be used to justify the elimination of evidence which does not fit a logical model. A rationalist may still reject the premise of the Holmesian Principle on the basis of its fundamental axioms. The Holmesian Principle is predicated on the central belief that logical models of reality should be made to fit the data rather than data should be made to fit the logical models of reality. And while I do not believe in the supernatural or the paranormal, I do believe that if there are truths to the universe that we do not understand and cannot comprehend, those truths will be discovered through evidence rather than logic. And, as someone who is primarily motivated and captivated by the possibility of discovering the unknown, it is, I believe, through data that those discoveries will be made, not logic.
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Great posts. May I ask why there is no comments section for your most recently published post ? I wanted to report a typo: "go out of there way to intentionally contract Covid,"