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Quantifier-Shift Fallacy Summary

(also known as: illicit quantifier shift)

Description: A fallacy of reversing the order of two quantifiers.

Logical Form:

Every X has a related Y.

Therefore, there is some Y related to every X.

Example #1:

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.

Example #2:

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.

References:

Cook, R. T. (2009). A Dictionary of Philosophical Logic. Edinburgh University Press.