Fallacy of (the) Undistributed Middle
A categorical syllogism commits the undistributed-middle fallacy when its middle term is not distributed in either premise. Sharing a category does not establish the relationship asserted in the conclusion.
THE IDEA
Description
A formal fallacy in a categorical syllogism where the middle term—the term absent from the conclusion—is not distributed in either premise. Neither premise makes a claim about every member of the middle term’s category.
Logical Form
- All A are B.
- All C are B.
- Therefore, all A are C.
Example #1
All dogs are mammals. All cats are mammals. Therefore, all dogs are cats.
Explanation
Both dogs and cats belong to the broader category of mammals. That shared membership does not show that dogs are cats. The same invalid form appears in the next example.
Example #2
All ghosts are imaginary. All unicorns are imaginary. Therefore, all ghosts are unicorns.
Explanation
While there may be ghosts that are unicorns, it does not follow from the premises: the only thing the premises tell us about ghosts and unicorns is that they are both imaginary – we have no information how they are related to each other.
Exception
None.
When to use it
In debates, people often assume that because two things share a common property, they must be identical. For example, arguing that since both Einstein and left-handed people are creative, Einstein must have been left-handed.
In marketing, claiming that because a product is popular and a competitor is also popular, the products must be the same in quality or features.
In political discourse, asserting that two policies must be the same because both are supported by the same demographic group.
FROM THEORY TO EVERYDAY LIFE
In practice
Example #1
All dogs are mammals. All cats are mammals. Therefore, all dogs are cats.
Example #2
All ghosts are imaginary. All unicorns are imaginary. Therefore, all ghosts are unicorns.
A MOMENT TO REFLECT
Put it to work.
Why is it important to ensure the middle term is distributed in a categorical syllogism?
Can you think of an argument you've encountered that commits the fallacy of the undistributed middle?
How would you explain this fallacy to someone unfamiliar with formal logic?
CONTINUE THE CONVERSATION
Source texts
- Logically Fallacious - The Ultimate Collection of Over 300 Logical Fallacies