Fallacies

Categorical syllogism with undistributed middle term

Invalid syllogism when the middle term is not distributed.

The undistributed middle fallacy occurs when the middle term is not distributed at least once, so it fails to connect the other terms.

Example

“All A are C.
All B are C.
Therefore, all A are B.”
(C does not connect A with B.)

Applied example (political)

“All patriots respect the flag.
All voters of party X respect the flag.
Therefore, all patriots vote for party X.”
(Sharing a symbol does not imply identity.)

Why it is fallacious

  • The middle term fails to link the categories.
  • The conclusion does not follow from the premises.
  • Shared membership is mistaken for identity.

How to spot it

  • The middle term appears only as an undistributed predicate.
  • A and B are linked only by sharing C.
  • The conclusion is stronger than justified.

How to respond

  • Ask for a premise that distributes the middle term.
  • Show that sharing a property does not imply identity.
  • Offer a simple counterexample.