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Logic and rhetoric
A Holmesian fallacy (also Sherlock Holmes fallacy or process of elimination fallacy) is a logical fallacy that occurs 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.
- far-fetched hypothesis
- arcane explanation
This fallacy usually occurs when someone uses the Holmes Method without being a superhuman genius. The Holmes Method is illustrated by the quote from "The Adventure of the Blanched Soldier"[note 1], a 1926 Sherlock Holmes short story:
"When you have eliminated all which is impossible, then whatever remains, however improbable, must be the truth." —Sherlock Holmes
To apply this method, one must find explanations and eliminate them one by one. However, to draw a logical conclusion from this is fallacious, because both steps require omniscience:
- Find every possible explanation.
- Correctly disprove every possible explanation, except the true and undisprovable one.
As should be obvious, this is incredibly difficult, requires all knowledge of the situation, and may lead one to ridiculously improbable explanations.
In essence, a major flaw in this line of reasoning is that there may be explanations that you simply have not thought of.
Despite it being a quotation from a fictional character (Holmes) starring in a series of detective novels where the narrative contrives to have the mystery inevitably solved thanks to the hero's superior powers of observation, the saying is often mistakenly attributed to Arthur Conan Doyle himself. It is typically offered by ghost enthusiasts as an example of why one must not discount belief in the spirit world. Star Trek's Spock even uttered a version of it in Star Trek VI - The Undiscovered Country. It's no surprise that paranormal claims of all kinds have adopted this fallacy. For example, crop circles:
Look at that mutilated cow in the field, and see that flattened grass. Since the farmer is away and couldn't have done the deed, aliens must have landed in a flying saucer and savaged the cow to learn more about the beings on our planet.
Naturally, these are not the only explanations. Angry neighbors, rival farmers, pranksters, predators (not the Schwarzenegger movie kind), undetonated ordnances from a past war (if applicable), and many other perfectly mundane probabilities exist that must be eliminated. Even assuming they are, there are myriads of other supernatural phenomena that could potentially explain the death of the cow and the flattening of the grass that would similarly need to be falsified before the conclusion of "UFOs" or "Aliens" can be accepted under this logic (for example, perhaps it was attacked by an avian cryptid. Perhaps it was struck down by [Insert Deity Here]. Perhaps it was possessed by ghosts or demons, causing the cow to burst as they departed its body. Perhaps it is evidence of an airborne biological weapons test by Monsanto, designed to kill all cattle and force America to eat GMO-fed meat. And so on. Ad
According to Aristotle in De Anima, the philosopher Thales of Miletus once said (paraphrased):
The lodestone has a soul because it moves iron. This proves that all things are full of gods.
Thales failed to falsify all alternate explanations because he didn't know that magnetism existed. Similarly, we may be disproven by future discoveries.
Lord Kelvin is almost infamous for these. Because he had no knowledge of nuclear fusion, isotopic decay, or nuclear fission, there was in his mind no way to reconcile the evidence that had been found by biologists and geologists that the Earth is at least hundreds of millions of years old with the seeming impossibility of the sun shining almost as bright as it does today for that period. As such, he believed the sun was at most a few millions of years old and that either the biologists and geologists were wrong or the Earth far predated the sun.
Most often, the Holmes method leads people to explanations that are easy to find but difficult or impossible to falsify, such as a god of the gaps or other supernatural entities with unknown properties. Often, people ignore the flaws in their preferred explanations.
It is possible to grant provisional (scientific, not logical) assent to an explanation if it explains something better (or more simply) than all known alternatives. This isn't an absolute truth, merely the most probable one.
An alternate formulation, that is closer to what Holmes actually practiced, rather than preached, is that "when you have eliminated the common possibilities, one of what remains must be truth, no matter how improbable what remains may be".
- Beware The Logic of Sherlock Holmes, Skeptical Science
- A Sherlock Holmes Logical Fallacy, Steven Novella
- The Holmesian Fallacy, Bob Frankston
- A Fallacy of Sherlock Holmes, Philosophy 12
- Arcane Explanation, Bruce Thompson
- Far-Fetched Hypothesis, Internet Encyclopedia of Philosophy
- Skeptical Fallacies: The Holmes Retroduction, Topher Cooper
- Similar quotes appear in Chapter 6 of the 1890 Sherlock Holmes novel The Sign of the Four ("How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable. must be the truth?") and in the 1892 Sherlock Holmes short story "The Adventure of the Beryl Coronet" ("It is an old maxim of mine that when you have eliminated the impossible, whatever remains, however improbable, must be the truth.")