Bill James was asked about the Holmes saying "When you have eliminated the impossible, whatever remains, however improbable, must be the truth". He responded:

That Sherlock Holmes line is very, very interesting. It's false, and extremely arrogant, and very dangerous. That's not a real way to think about the world. This concept of eliminating the impossible -- we could never do that. The whole idea of Sherlock Holmes is dangerous because it encourages people to think that -- if they're intelligent enough -- they could put all the pieces together in absolute terms. But the human mind is not sophisticated enough to do that. People are not that smart. It's not that Sherlock Holmes would need to be twice as smart as the average person; he'd have to be a billion times as smart as the average person.