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Fallacy of Division

(also known as: false division, faulty deduction, division fallacy)

Description: Inferring that something is true of one or more of the parts from the fact that it is true of the whole.  This is the opposite of the fallacy of composition.

Logical Form:

A is part of B.

B has property X.

Therefore, A has property X.

Example #1:

His house is about half the size of most houses in the neighborhood. Therefore, his doors must all be about 3 1/2 feet high.

Explanation: The size of one’s house almost certainly does not mean that the doors will be smaller, especially by the same proportions.  The size of the whole (the house) is not directly related to the size of every part of the house.

Example #2:

I heard that the Catholic Church was involved in a sex scandal cover-up.  Therefore, my 102-year-old Catholic neighbor, who frequently attends Church, is guilty as well!

Explanation: While it is possible that the 102-year-old granny is guilty for some things, like being way too liberal with her perfume, she would not be guilty in any sex scandals just by her association with the Church alone.

Exception: When a part of the whole has a property that, by definition, causes the part to take on that property.

My 102-year-old neighbor is a card-carrying member of an organization of thugs that requires its members to kick babies.  Therefore, my neighbor is a thug... and she wears way too much perfume.

References:

Goodman, M. F. (1993). First Logic. University Press of America.



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