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Undistributed Middle

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Undistributed Middle:

This fallacy occurs when the middle term of a standard three-step syllogism is not distributed in either premise. This picture is a case of undistributed middle. Using that image, "black and white" is the middle term, the term that appears in both premises; it is undistributed because neither premise refers to all things that are "black and white". Newspapers are black and white as well, and they are neither penguins nor old TV shows. "Things that are black and white" is the superset, and it contains many subsets that do not overlap at all. In casual use, undistributed middle can be hard to spot.

Liberals always want to raise taxes.
Alice says that she's a Conservative, but she also says that the sales tax needs to be raised.
She's lying about being a Conservative; she's really a Liberal.

The point is not how "Liberal" and "Conservative" are defined; it's that at no point is it established that "only Liberals want to raise taxes". Put another way, saying "All Liberals are people who want to raise taxes" is not the same as saying "All people who want to raise taxes are Liberals."

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