I think there's a story about an inquisition that's often used to illustrate this mistake. It has to do with witches and gossip.
There's a lady on trial for some crime that has outraged the public. It doesn't matter what the crime is, but the public's had time to gossip about it and everybody has had a chance to add their own two bits to the story. Pretty much everybody implies that the girl must be evil because the crime was such an evil act. However, the more ideologically motivated of the gossipers quickly imply that the girl did the crime because she is evil and, obviously because she's a women, this makes her a witch.
Then the trial begins, but now instead of her being on trial because she possibly committed the crime, she's on trial for being evil.
The only witness says he did not see the crime, but he did see the girl standing there the moment after the crime occurred. The Judge calls for anymore witnesses. When no one stands up, he asks if anyone can attest to the girls character or motives. The Accusator gestures for volunteers and everybody in the town lines up to recount their memories of the girl. Each story begins innocently enough but, with everyone listening, the story has to accommodate the new presumption that the girl is a witch...the milk man drops off a bottle of milk, but the rest of his bottles go sour; the shopkeeper gets an itchy neck every time she come's in his store; and the local priest has moments of temptation every time he thinks about her.... They all conclude that she must have committed the crime because she is a witch and witches are evil.
When the judge says the girl is free to go, the crowd raises a commotion for the lack of justice. They chant, "she was there" and "she is a witch". The Accusator speaks up, "The simplest conclusion is that the girl was there because she committed the crime and we have proven by testimony that the girl is obviously a witch. Witches are evil, and only an evil person could have committed the crime. Occam's razor attests that the simplest explanation is often the right one. Therefore, she must be the culprit".
The judge says, "Being there does not make her guilty and she need not be a witch to have committed the crime. If she committed the crime, it was not proven here."
Hmmm. Did Occam's razor fail? Nope, just its proper usage.
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