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What is a logical fallacy?

What is a logical fallacy? Here are some definitions.

Noun
  1. A fallacy; a clearly defined error in reasoning used to support or refute an argument, excluding simple unintended mistakes.
  2. A formal fallacy.
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Examples
If anything, it's a pointing indictment of the logical fallacy in our society's way of thinking.
The little logical fallacy that bugged me the most was the scene where the earthquake followed the Amtrak train.
It seems to me to be a logical fallacy to think that by staying out of a conflict one is maintaining some kind of purity or neutrality.
It turns out to be a technical term in the study of logic and describes a specific type of logical fallacy, a form of circular reasoning.
The belief that the connection between two events causes an outcome is a logical fallacy.
Your argument is still emotional, and still rooted purely in logical fallacy.

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