What is the undistributed middle?

• A. The middle term is distributed in at least one premise.
• B. The middle term is distributed in both premises.
• C. The middle term is not distributed in either premise.
• D. The middle term must be distributed in the conclusion.

Answer: (C)

In categorical syllogisms, a term is distributed when the statement asserts something about all members of that class. The middle term is the term that appears in both premises and serves to connect the major and minor terms. For a syllogism to be potentially valid, the middle term must be distributed in at least one premise to tie the two end terms together. When the middle term is not distributed in either premise—i.e., it is used only as the predicate in both premises—it’s called an undistributed middle. This means the premises do not establish a definite link between the major and minor terms, allowing an invalid conclusion.

So the undistributed middle is precisely that the middle term is not distributed in either premise. For example, “All poets are humans” and “All scientists are humans” use the middle term as the predicate in both premises, so the middle term is undistributed, and you cannot validly conclude that poets are scientists.