Quantifier-Shift Fallacy
A quantifier-shift fallacy changes the order of quantifiers without justification: a different object may satisfy a condition for each person, while no single object satisfies it for everyone.
THE IDEA
Quantifier-Shift Fallacy
(also known as: illicit quantifier shift)
Description: A fallacy of reversing the order of two quantifiers.
Logical Form: The symbolic form is missing; the examples below show the shift in words.
Example #1: Everyone has (or had) a mother. Therefore, there exists a mother that everyone has (or had).
Explanation: The premise allows a different person to satisfy the relation “mother” for each individual. It does not establish a single mother shared by everyone. The conclusion therefore does not follow, even though the premise alone is not a proof of its negation.
Example #2: Everybody has their own brain. Therefore, there is one brain that everybody has.
Explanation: Everybody has their 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.
Exception: None.
When to use it
Evaluating arguments in logic puzzles or proofs that involve multiple quantifiers, such as in mathematics or computer science.
Debating generalizations in everyday discussions, e.g., 'Everyone likes pizza, so there is one pizza that everyone likes.'
Recognizing flawed reasoning in political or social arguments that confuse 'for all' with 'there exists' in statements about groups.
Teaching critical thinking by contrasting the fallacy with valid forms of reasoning like universal instantiation or existential generalization.
FROM THEORY TO EVERYDAY LIFE
In practice
The Mother Fallacy
Everyone has (or had) a mother. Therefore, there exists a mother that everyone has (or had). The relation “mother” can be satisfied by a different person for each individual; the premise supplies no single person shared by everyone.
The Brain Fallacy
Everybody has their own brain. Therefore, there is one brain that everybody has. Explanation: Everybody has their 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.
A MOMENT TO REFLECT
Put it to work.
Can you identify a situation where someone argued that because every person has a certain characteristic, there must be a single universal instance of that characteristic? How would you point out the quantifier shift?
Think of a mathematical statement with multiple quantifiers (e.g., 'for every x, there exists y such that...'). How could reversing the order lead to an incorrect conclusion?
Consider the statement 'Every student in this class owns a textbook.' Does it follow that 'There is a textbook that every student in this class owns'? Why or why not?
CONTINUE THE CONVERSATION
Source texts
- Logically Fallacious - The Ultimate Collection of Over 300 Logical Fallacies