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The Most Fundamental Fallacy

There are dozens of different types of fallacies: formal fallacies, informal fallacies, faulty generalizations, red herring fallacies, and so on...

But is there one simple, singular condition that all of these meet that makes them eligible for such a classification?

Such as If x is y, then x is a logical fallacy.

Where x is the proposition and y is the condition that it meets.