Sherlock Holmes said, “How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?" Although the statement may be valid, many have pointed out that “eliminating the impossible” is an arduous task and is practically impossible.

However, what about the inverse, or a reformation of it? “All explanations that we currently think are impossible should be eliminated in favor of explanations known to be possible”

For example, suppose I win the state lottery three times in a row. If I go to Sherlock and then tell him that I believe an angel helped me win, would he be correct in stating that me winning by luck is a favorable explanation over the angel helping me, and hence should be eliminated as an explanation?

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    – Geoffrey Thomas
    Commented Sep 14, 2023 at 16:47
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    Does this answer your question? Can a coincidence be evidence of a god? Commented Sep 15, 2023 at 6:38
  • I could be wrong, but your 'reformulation' reads like a mere rephrasing (it is certainly not inverse). Holmes is asserting roughly the same as you, ie. that "All explanations that we currently think are impossible should be eliminated in favour of explanations known to be possible" (because, as Holmes states, whatever remains is possible and must be the truth). This might explain all the downvotes. Commented Sep 15, 2023 at 13:10

3 Answers 3


That statement is a fallacy It's called the Holmesian fallacy.

See the post: Fallacy by Sherlock Holmes: "Eliminate the impossible, and what remains must be the truth".

A simple one minute search found this so why didn't you? I suggest Googling "due dillegence" and applying it to your future questions.

The answer is yes, you can rewrite the Holmes quote and make it a non fallacy. You could change all the words. But then it would no longer be a Holmes quote. It would be a non fallacious statement that no one but you would care about.

When can I expect to see your attempt? Talk is cheap. If you can rewrite the statement then do it and post it for review. Please show all your work including any probability calculations.

Here's my failed attempt:

After dismissing n-1 possible explanations, the nth explanation ( no matter how stupid, moronic, and implausible) must be true.

Unfortunately, it's still a falacy.

This is better:

After dismissing n-1 possible explanations, the nth explanation ( no matter how stupid, moronic, and implausible) must be true. Unless it isn't true. Then you are screwed.

Also: Equations are reformulated. Chemical compounds are reformulated. Recipes for cookies are reformulated.

Literary quotes from fictional characters are NOT reformulated. They are rewritten.

Does this really pass for philosophy?

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    Did you read the question? The post in the question you linked is the original formulation of it. This is a reformulation. Perhaps you should actually read things before telling others to “do a search.”
    – user62907
    Commented Sep 14, 2023 at 14:45
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    I don’t think it is. The reformulation doesn’t say require one knowing if a certain explanation is impossible. It just requires one knowing if a certain explanation has evidence or not.
    – user62907
    Commented Sep 14, 2023 at 15:03
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    If it isn't usefully different then why is the new question worthwhile given the one that already exists. "It just requires one knowing if a certain explanation has evidence or not." no that is your personal definition of "impossible", things can be possible without having evidence for it. Commented Sep 14, 2023 at 15:04
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    Reformulation? This is simply yet another Rube Goldberg hypothetical probability question formulated to try to pass off your useless unsubstantiated opinions as legitimate. Commented Sep 14, 2023 at 15:09
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    @IdiosyncraticSoul How is "I suggest Googling 'due dillegence'" not hugely condescending? Implying that they don't even know what the words "due diligence" means due to their presumed failure in applying the concept is at best facetious, and at worst fallacious, which certainly doesn't seem like a valid critique. If you honestly think what you wrote is likely to evoke future change, as opposed to merely offending, I'd be curious to see your evidence for that (but you did say "valid" and not "constructive", so maybe you don't care whether your critique actually result in any improvement).
    – NotThatGuy
    Commented Sep 15, 2023 at 13:27

If you have a set of causes that are known to be impossible and a set that are not known to be impossible, then clearly you should be looking in the second set for your explanation, regardless of which way you frame Sherlock's advice. If you can further subdivide that second set into causes that are definitely possible and then into causes that are highly likely, you might want to focus your researches in that much smaller subset first. Of course, that all assumes you have sufficient data to go on, otherwise you should bear in mind Sherlock's other dictum about the foolishness of speculating upon inadequate information. Or, to quote that big SH fan, Marco Ocram...

“I’m sorry Marco, truly I am, but you have written what you have written, and now you must make the most of it. I’m sure that all will become clear in good time. Remember what Sherlock Holmes always said about the futility of hypothesising in the absence of conclusive data.”

“You’re right, Herbert. I must stop agonising pointlessly about the Professor’s role until I find some conclusive data to agonise pointlessly about.”

Excerpt From The Awful Truth About the Sushing Prize


I wouldn't really go with that reformulation, because "impossible" is still a problematic term. I don't know that I'd say I think much is strictly "impossible".

You could potentially use "plausible" / "implausible" instead (implausible explanations should be eliminated in favor of plausible explanations). "Inconceivable" could also be a useful formulation. This may be roughly what you'd get with a generous interpretation of the original quote.

If you want, you could potentially also use "impossible" in the context of a specific model of reality, e.g. if angels don't exist, then it would be impossible for angels to do something. But this treats your foundational knowledge of reality as inviolable for the purposes of evaluating a specific claim, which may be a bit problematic if that claim undermines your foundational beliefs about reality (but it might also be useful if the "impossibility" of an explanation is supported by other evidence).

In any case, plausible/implausible could be considered some variant of Occam's razor / IBE. It's also related to coherentism, in that you can consider how well some explanation coheres with everything else you know about reality, favouring explanations that coheres more closely above ones that require additional claims, especially claims that seem like they should have far-reaching effects, and especially when we don't observe said effects.*

* Note that for, say, rejections of one scientific theory in favour of another, this commonly requires additional claims in any case, if there is some data that is contradicted by the current theory. We also accept that scientific theories aren't necessarily objective truths, but rather merely models reality as best we understand it, which carries a lower burden to warrant change. So, while favouring explanations that fit with what you already believe is extremely problematic if taken to extremes (as this might mean building an entire worldview around a false belief), there's also a question of how contrived your explanations need to be for this to work, and it's also reasonable to not keep adding claims and throw your entire worldview into disarray in response to every piece of data that can be explained perfectly well without any changes to a worldview.

The existence of angels may not be strictly impossible, but it's unfalsifiable, it has little to no coherence value (because they typically aren't posited to actually do much), and the existence of angels (of a particular religion) would arguably imply a lot more effects than a few lottery wins, and that might lead one to, say, the problem of evil / suffering, if that religion contains an all-powerful all-loving deity. An improbable event carries much less epistemic weight. Improbable things happen all the time.

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