(also known as: illicit quantifier shift)
Description: A fallacy of reversing the order of two quantifiers.
Every X has a related Y.
Therefore, there is some Y related to every X.
Everybody has a mother.
Therefore, there is some woman out there who is the mother of us all.
Explanation: While it is true that everyone has (or had) a mother, the term “mother” is not a singular term that is shared — it is implied that it is a category in which many mothers reside. The conclusion is asserting the opposite of the meaning — that there is actually just one mother shared by everyone. This form of reasoning is invalid; therefore, fallacious.
Everybody has a brain.
Therefore, there is a single brain we all share.
Explanation: Everybody has his or her own brain, not one we all share. Although I have met many people who seem not to have their own brain. This form of reasoning is invalid; therefore, fallacious.
What Now: Remember that a quantifier is an expression (e.g. all, some) that indicates the scope of a term to which it is attached.
Cook, R. T. (2009). A Dictionary of Philosophical Logic. Edinburgh University Press.