### 3.4 Fallacies in Logic

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• Math Help

Like all fallacies, the fallacy of the undistributed middle carries with it a terrible sense of injustice. This fallacy is summed up in the phrase "guilty by association."

 • Premise: All A are B. • Premise: Jeffrey is a B. • Conclusion: Therefore, Jeffrey is an A.

One shudders to think of how many innocent people have been judged guilty in situations involving "guilty by association."

This type of incident has occurred throughout history. One famous example is described in a 1940 western novel by Walter Van Tilburg Clark. It is called The Ox-Bow Incident. In the story two drifters join a lynch mob to find and hang three men presumed to be rustlers and the killers of a local man.

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• Checkpoint Solution

Here is a description of the situation in Salem, Massachusetts.

In 1692, as part of the Salem witch trials, several people were arrested and accused of witchcraft. Their accusers claimed that young girls were having fits whenever the accused were present.

As the Salem witch trials continued, the residents of Salem gradually came to see that the young girls were not having fits because of a supernatural power, but because they were relishing in the power and attention that circumstance had given them.

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```  ______   __   __   _    _      ___     ______
/_____//  \ \\/ // | \  / ||   / _ \\  |      \\
`____ `    \ ` //  |  \/  ||  / //\ \\ |  --  //
/___//      | ||   | .  . || |  ___  |||  --  \\
`__ `       |_||   |_|\/|_|| |_||  |_|||______//
/_//        `-`'   `-`  `-`  `-`   `-` `------`
`-`
```